diff --git a/BAYESIAN_IN_ERL.md b/BAYESIAN_IN_ERL.md
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+# Bayesian Analysis in EasyReflectometryLib — Implementation Plan
+
+## Current State
+
+- `BAYESIAN_BUMPS.md` (in `MD/`) describes a 3-phase plan. Phase 1
+  (docs/notebook) is complete.
+- `bayesian_bumps.py` (attached notebook) works but users must directly
+  import from `bumps.fitters`, `bumps.names`, `bumps.parameter` — a
+  leaky abstraction.
+- The `Bumps` minimizer in `easyscience`
+  (`core/src/easyscience/fitting/minimizers/minimizer_bumps.py`) only
+  exposes **classical optimization** methods (`amoeba`, `newton`, `lm`),
+  NOT the DREAM/MCMC sampler.
+- The `AvailableMinimizers` enum only has `Bumps`, `Bumps_simplex`,
+  `Bumps_newton`, `Bumps_lm`. This should remain optimizer-focused;
+  DREAM should be exposed as a sampling workflow, not as another
+  minimizer choice.
+- `MultiFitter` in reflectometry-lib currently only has `fit()` and
+  `fit_single_data_set_1d()`.
+
+## Goal
+
+Users should be able to run Bayesian MCMC sampling with a **clean
+high-level API** like:
+
+```python
+fitter = MultiFitter(model)
+fitter.switch_minimizer(AvailableMinimizers.Bumps)
+
+# Classical fit first
+analysed = fitter.fit(data)
+
+# Bayesian sampling
+posterior = fitter.sample(data, samples=5000, burn=1000, thin=10)
+
+# Analyze
+from easyreflectometry.analysis.bayesian import plot_corner, posterior_summary
+plot_corner(posterior)
+print(posterior_summary(posterior))
+```
+
+Important API boundary: `fit()` remains classical optimization only.
+Bayesian DREAM sampling is exposed through `sample()` so users do not
+receive sampler-shaped results from an optimizer-shaped API.
+
+## Implementation Plan
+
+### Step 1 — Keep DREAM separate from `AvailableMinimizers`
+
+**File**: `core/src/easyscience/fitting/available_minimizers.py`
+
+Do **not** add `Bumps_dream` as a normal `AvailableMinimizers` member.
+The enum is currently used to instantiate minimizer backends and to
+route calls through `Fitter.fit()`, which expects optimizer-style
+`FitResults`. DREAM is an MCMC sampler and returns a sampler state/chain
+rather than a best-fit result.
+
+Use `AvailableMinimizers.Bumps` to select the BUMPS backend, then expose
+DREAM through a dedicated `sample()` method. This avoids making
+`project.minimizer = AvailableMinimizers.Bumps_dream` look like a valid
+classical fitting mode.
+
+### Step 2 — Add dedicated DREAM sampling support to the Bumps minimizer (core repo)
+
+**File**: `core/src/easyscience/fitting/minimizers/minimizer_bumps.py`
+
+**2a.** Keep `supported_methods()` optimizer-only (`amoeba`, `newton`,
+`lm`). Do not add `'dream'` there unless the EasyScience fitting
+abstraction is later split into optimizer and sampler concepts.
+
+**2b.** Add a new method `sample()` to the `Bumps` class:
+
+```python
+def sample(
+    self,
+    x: np.ndarray,
+    y: np.ndarray,
+    weights: np.ndarray,
+    samples: int = 10000,
+    burn: int = 2000,
+    thin: int = 10,
+    chains: int | None = None,
+    population: int | None = None,
+    model: Callable | None = None,
+    parameters: list | None = None,
+    progress_callback: Callable | None = None,
+    seed: int | None = None,
+    **kwargs,
+) -> dict:
+    """Run Bayesian MCMC sampling using BUMPS DREAM sampler.
+
+    Returns a dict with:
+      - 'draws': np.ndarray, shape (n_samples, n_params) — posterior samples
+      - 'param_names': list[str] — parameter names
+      - 'state': DreamState — raw BUMPS state for save/restore
+      - 'logp': np.ndarray — log-posterior values
+    """
+```
+
+The implementation would:
+
+1. Build the `Curve` model + `FitProblem` (reuse `_make_model()` logic)
+2. Translate user-friendly aliases to BUMPS DREAM settings and call
+   `bumps_fit(problem, method='dream', samples=samples, burn=burn, thin=thin, pop=population, ...)`
+3. Extract `result.state.draw().points` and return structured dict
+4. Preserve and restore the EasyScience global object stack state,
+   mirroring the existing `fit()` implementation
+5. Handle multi-dataset via the same `MultiFitter._precompute_reshaping`
+   pattern
+
+**2c.** Do **not** modify `fit()` to handle `method='dream'`, and do
+**not** delegate `fit(method='dream')` to `sample()`. `fit()` returns
+`FitResults`; `sample()` returns posterior samples and sampler metadata.
+Keeping the methods separate prevents incompatible return types from
+leaking into `Fitter.fit()` and reflectometry-lib `MultiFitter.fit()`.
+
+Recommended alias mapping:
+
+| Public argument  | BUMPS DREAM setting         | Rationale                                                               |
+| ---------------- | --------------------------- | ----------------------------------------------------------------------- |
+| `samples`        | `samples`                   | Clear user-facing chain length; prefer over optimizer-oriented `steps`. |
+| `burn`           | `burn`                      | Matches BUMPS and common MCMC terminology.                              |
+| `thin`           | `thin`                      | Matches BUMPS and common MCMC terminology.                              |
+| `chains`         | `pop`                       | User-friendly MCMC wording; maps to BUMPS population count.             |
+| `population`     | `pop`                       | BUMPS-aware alias for advanced users.                                   |
+| `initialization` | `init`                      | More readable than `init`, but pass through to BUMPS.                   |
+| `seed`           | RNG seeding before sampling | Expose reproducibility without requiring users to know BUMPS internals. |
+
+If both `chains` and `population` are provided, raise `ValueError`
+unless they match. Accept `steps` only as a deprecated alias for
+`samples`, with a warning, because `steps` already means optimizer
+budget in EasyScience `Bumps.fit()`.
+
+### Step 3 — Add `sample()` to reflectometry-lib `MultiFitter`
+
+**File**: `reflectometry-lib/src/easyreflectometry/fitting.py`
+
+Add a `sample()` method to `MultiFitter`:
+
+```python
+def sample(
+    self,
+    data: sc.DataGroup,
+    samples: int = 10000,
+    burn: int = 2000,
+    thin: int = 10,
+    chains: int | None = None,
+    population: int | None = None,
+    seed: int | None = None,
+    objective: str | None = None,
+) -> dict:
+    """Run Bayesian MCMC sampling on reflectometry data.
+
+    :param data: DataGroup with reflectivity data.
+    :param samples: Number of retained DREAM samples requested from BUMPS.
+    :param burn: Burn-in steps.
+    :param thin: Thinning interval.
+    :param chains: User-friendly alias for BUMPS DREAM population count.
+    :param population: BUMPS DREAM population count (`pop`) for advanced users.
+    :param seed: Random seed for reproducibility.
+    :param objective: Zero-variance handling strategy.
+    :return: Dict with posterior samples, parameter names, and sampler state.
+    """
+```
+
+Internally:
+
+1. Reuse `_prepare_fit_arrays` for data preparation
+2. Mirror the EasyScience `Fitter.fit()` lifecycle for reshaping, fit
+   function wrapping, and restoration
+3. Delegate to `self.easy_science_multi_fitter.minimizer.sample(...)`
+   for the MCMC
+4. Handle multi-model / multi-contrast aggregation as one joint
+   posterior
+5. Return structured posterior dict or `PosteriorResults`
+
+The `MultiFitter` currently stores `self.easy_science_multi_fitter`
+which has `.minimizer` — we'll call `sample()` on it when the minimizer
+is a `Bumps` instance.
+
+### Step 4 — Create Bayesian analysis module in reflectometry-lib
+
+**New file**:
+`reflectometry-lib/src/easyreflectometry/analysis/__init__.py` **New
+file**: `reflectometry-lib/src/easyreflectometry/analysis/bayesian.py`
+
+The `bayesian.py` module provides:
+
+```python
+class PosteriorResults:
+    """Container for Bayesian posterior samples with analysis methods."""
+
+    draws: np.ndarray        # (n_samples, n_params)
+    param_names: list[str]
+    logp: np.ndarray | None
+    sampler_state: Any | None
+
+    def summary(self) -> str:
+        """Return formatted summary table with mean, sd, HDI for each parameter."""
+
+    def corner(self, **kwargs) -> None:
+        """Plot parameter correlation corner plot using the `corner` library."""
+
+    def credible_interval(self, alpha: float = 0.95) -> dict:
+        """Return {param_name: (lower, upper)} credible intervals."""
+
+    def gelman_rubin(self) -> dict:
+        """Compute R-hat convergence diagnostic."""
+
+def posterior_summary(draws, param_names) -> str: ...
+def plot_corner(draws, param_names, **kwargs) -> None: ...
+def plot_trace(draws, param_names, **kwargs) -> None: ...
+def credible_intervals(draws, param_names, alpha=0.95) -> dict: ...
+```
+
+**Posterior predictive functions** (reflectivity & SLD):
+
+```python
+def posterior_predictive_reflectivity(
+    draws, param_names, model, q_values, n_samples=200
+) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
+    """Return (median, lower_95, upper_95) reflectivity arrays."""
+
+def posterior_sld_profile(
+    draws, param_names, model, n_samples=200
+) -> tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray]:
+    """Return (z, median, lower_95, upper_95) SLD profile arrays."""
+```
+
+Posterior predictive helpers must save original parameter values and
+errors before applying any posterior draw, and restore them in a
+`finally` block after prediction. Parameter lookup should use
+EasyScience parameter `unique_name` values, matching the BUMPS names
+after removing the minimizer prefix, rather than display names. This
+avoids leaving the model mutated after plotting and avoids collisions
+when repeated models or multi-contrast fits contain similarly named
+parameters.
+
+### Step 5 — Dependencies
+
+Add to `pyproject.toml` in reflectometry-lib:
+
+```toml
+[project.optional-dependencies]
+bayesian = ["corner>=2.2", "arviz>=0.18"]
+```
+
+Make `corner` and `arviz` optional imports — the analysis module should
+work with graceful fallbacks when they're not installed.
+
+### Step 6 — Update exports
+
+**File**: `reflectometry-lib/src/easyreflectometry/__init__.py`
+
+Add `PosteriorResults` and analysis functions to the public API if
+desired.
+
+### Step 7 — Update the example notebook
+
+**File**:
+`reflectometry-lib/docs/src/tutorials/advancedfitting/bayesian_bumps.py`
+
+Replace low-level BUMPS calls with the new high-level API:
+
+- `fitter.sample(data, samples=500, burn=100, thin=10)` instead of
+  manual `FitProblem` + `bumps_fit`
+- `plot_corner(posterior['draws'], posterior['param_names'])` instead of
+  manual `corner.corner()`
+- `posterior_summary(...)` instead of manual numpy statistics
+
+### Step 8 — Tests
+
+**File**: `reflectometry-lib/tests/test_bayesian.py` (new)
+
+```python
+def test_sample_basic(): ...
+def test_posterior_summary_format(): ...
+def test_corner_plot_does_not_crash(): ...
+def test_credible_intervals(): ...
+def test_sample_seed_reproducibility(): ...
+```
+
+Also add a test in `core/tests/` for the `Bumps.sample()` method.
+
+## Architecture Diagram
+
+```
+User Code
+    │
+    ├─ fitter.fit(data)          ──► classical chi² minimization
+    ├─ fitter.sample(data, ...)  ──► Bayesian DREAM MCMC
+    │
+    ▼
+reflectometry-lib MultiFitter
+    │  ._prepare_fit_arrays()  ← reused from fit()
+    │  delegates to ↓
+    ▼
+easyscience Bumps minimizer
+    │  .fit(x, y, weights)          ──► amoeba/newton/lm
+    │  .sample(x, y, weights, ...)  ──► DREAM MCMC (NEW)
+    │
+    ▼
+bumps.fitters.fit / FitProblem / Curve
+    └──► reflectivity model evaluation via fit_func
+
+Post-hoc analysis:
+    reflectometry-lib analysis.bayesian
+        ├── PosteriorResults (container)
+        ├── plot_corner() → corner.corner()
+        ├── posterior_summary() → numpy stats
+        └── posterior_predictive_reflectivity() → model.interface.fit_func()
+```
+
+## Risk Assessment
+
+| Risk                                         | Mitigation                                                                       |
+| -------------------------------------------- | -------------------------------------------------------------------------------- |
+| DREAM may not converge with default settings | Expose `samples`, `burn`, `thin`, `chains`/`population`; document best practices |
+| MCMC is 10-100× slower than least-squares    | Document that classical fit first is recommended; add progress callback          |
+| `corner` / `arviz` may not be installed      | Make optional dependencies with graceful fallbacks                               |
+| Multi-dataset sampling aggregation           | Follow existing `MultiFitter._precompute_reshaping` pattern                      |
+| BUMPS DREAM API changes                      | Pin bumps version; wrap in our API                                               |
+| Reproducibility                              | Expose `seed` parameter; document how to save/load DreamState                    |
+| Model mutation during posterior prediction   | Save/restore original parameter values and map draws by `unique_name`            |
+
+## Files to Create / Modify
+
+### Create:
+
+1. `reflectometry-lib/src/easyreflectometry/analysis/__init__.py`
+2. `reflectometry-lib/src/easyreflectometry/analysis/bayesian.py`
+3. `reflectometry-lib/tests/test_bayesian.py`
+
+### Modify:
+
+4. `core/src/easyscience/fitting/available_minimizers.py` — no
+   `Bumps_dream`; optionally document that samplers are exposed
+   separately
+5. `core/src/easyscience/fitting/minimizers/minimizer_bumps.py` — add
+   dedicated `sample()` method without adding `'dream'` to optimizer
+   methods
+6. `reflectometry-lib/src/easyreflectometry/fitting.py` — add `sample()`
+   to `MultiFitter`
+7. `reflectometry-lib/src/easyreflectometry/__init__.py` — optional:
+   export new classes
+8. `reflectometry-lib/pyproject.toml` — add optional `bayesian`
+   dependencies
+9. `reflectometry-lib/docs/src/tutorials/advancedfitting/bayesian_bumps.py`
+   — update to use new API
+
+## Implementation Order
+
+1. **core changes** (Steps 1-2): Add `Bumps.sample()` method while
+   keeping DREAM out of optimizer enum/method dispatch
+2. **reflectometry-lib fitting** (Step 3): Add `MultiFitter.sample()`
+3. **reflectometry-lib analysis** (Step 4): Create
+   `analysis/bayesian.py` with corner plot & stats
+4. **Dependencies** (Step 5): Add optional deps to pyproject.toml
+5. **Exports** (Step 6): Update `__init__.py`
+6. **Example update** (Step 7): Update notebook to use new API
+7. **Tests** (Step 8): Add test coverage
diff --git a/docs/docs/tutorials/advancedfitting/bayesian_bumps.ipynb b/docs/docs/tutorials/advancedfitting/bayesian_bumps.ipynb
new file mode 100644
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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "649cf9aa",
+   "metadata": {},
+   "source": [
+    "# Bayesian Fitting with BUMPS\n",
+    "\n",
+    "This notebook demonstrates the full high-level Bayesian MCMC API in\n",
+    "EasyReflectometry.\n",
+    "\n",
+    "It covers:\n",
+    "\n",
+    "- Building a reflectometry model with realistic bounds (critical for MCMC).\n",
+    "- Classical optimisation first (good starting point for Bayesian sampling).\n",
+    "- High-level DREAM MCMC sampling via\n",
+    "  ``MultiFitter.sample()`` and ``PosteriorResults``.\n",
+    "- Posterior inspection: summary table, corner plot, trace plot, credible\n",
+    "  intervals, Gelman-Rubin R-hat.\n",
+    "- Posterior-predictive checks: reflectivity and SLD profile with 95 %\n",
+    "  credible bands.\n",
+    "\n",
+    "**Note**: Requires ``corner`` and ``arviz`` for some plots (install via\n",
+    "``pip install easyreflectometry[bayesian]``)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "61aa83ac",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import warnings\n",
+    "\n",
+    "import corner as _corner\n",
+    "import matplotlib.pyplot as plt\n",
+    "from easyscience.fitting import AvailableMinimizers\n",
+    "\n",
+    "from easyreflectometry.analysis.bayesian import PosteriorResults\n",
+    "from easyreflectometry.analysis.bayesian import posterior_predictive_reflectivity\n",
+    "from easyreflectometry.analysis.bayesian import posterior_predictive_sld_profile\n",
+    "from easyreflectometry.calculators import CalculatorFactory\n",
+    "from easyreflectometry.data.measurement import load\n",
+    "from easyreflectometry.fitting import MultiFitter\n",
+    "from easyreflectometry.model import Model\n",
+    "from easyreflectometry.model import PercentageFwhm\n",
+    "from easyreflectometry.sample import Layer\n",
+    "from easyreflectometry.sample import Material\n",
+    "from easyreflectometry.sample import Multilayer\n",
+    "from easyreflectometry.sample import Sample\n",
+    "\n",
+    "warnings.filterwarnings('ignore')\n",
+    "\n",
+    "print('All libraries imported successfully.')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "14986b98",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ---- Load experimental data -------------------------------------------------\n",
+    "data_path = 'example.ort'\n",
+    "data = load(data_path)\n",
+    "print('Data loaded with keys:', list(data.keys()))\n",
+    "\n",
+    "# Quick look at the data\n",
+    "qz = data['coords']['Qz_0'].values\n",
+    "r_data = data['data']['R_0'].values\n",
+    "\n",
+    "plt.figure(figsize=(7, 4))\n",
+    "plt.semilogy(qz, r_data, 'o', label='Data')\n",
+    "plt.xlabel('Q / Å⁻¹')\n",
+    "plt.ylabel('Reflectivity')\n",
+    "plt.title('Experimental data (example.ort)')\n",
+    "plt.legend()\n",
+    "plt.grid(True, alpha=0.3)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "cd56a6eb",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ---- Create a monolayer model (Si / Film / D₂O) ----------------------------\n",
+    "si = Material(sld=2.07, isld=0.0, name='Si')\n",
+    "film = Material(sld=2.0, isld=0.0, name='Film')\n",
+    "d2o = Material(sld=6.36, isld=0.0, name='D2O')\n",
+    "\n",
+    "si_layer = Layer(material=si, thickness=0.0, roughness=3.0, name='Si')\n",
+    "film_layer = Layer(material=film, thickness=250.0, roughness=3.0, name='Film')\n",
+    "d2o_layer = Layer(material=d2o, thickness=0.0, roughness=3.0, name='D2O')\n",
+    "\n",
+    "sample = Sample(\n",
+    "    Multilayer(si_layer),\n",
+    "    Multilayer(film_layer),\n",
+    "    Multilayer(d2o_layer),\n",
+    "    name='Monolayer Sample',\n",
+    ")\n",
+    "\n",
+    "resolution = PercentageFwhm(0.02)\n",
+    "model = Model(\n",
+    "    sample=sample,\n",
+    "    scale=1.0,\n",
+    "    background=1e-6,\n",
+    "    resolution_function=resolution,\n",
+    "    name='Monolayer Model',\n",
+    ")\n",
+    "\n",
+    "# ---- Make key parameters free with realistic bounds (essential for MCMC) -----\n",
+    "film_layer.thickness.fixed = False\n",
+    "film_layer.thickness.bounds = (100, 400)\n",
+    "\n",
+    "film.sld.fixed = False\n",
+    "film.sld.bounds = (0.5, 4.0)\n",
+    "\n",
+    "model.scale.fixed = False\n",
+    "model.scale.bounds = (0.8, 1.2)\n",
+    "\n",
+    "model.background.fixed = False\n",
+    "model.background.bounds = (1e-7, 1e-5)\n",
+    "\n",
+    "print('Model created with the following free parameters:')\n",
+    "for p in model.get_parameters():\n",
+    "    if not p.fixed:\n",
+    "        print(f'  {p.name}: value={p.value}, bounds={p.bounds}')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "991e1169",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ---- Set up the calculator and fitter ---------------------------------------\n",
+    "interface = CalculatorFactory()\n",
+    "interface.switch('refnx')  # or 'refl1d'\n",
+    "model.interface = interface\n",
+    "\n",
+    "fitter = MultiFitter(model)\n",
+    "# Use the BUMPS backend — DREAM sampling is only available through BUMPS.\n",
+    "fitter.switch_minimizer(AvailableMinimizers.Bumps)\n",
+    "\n",
+    "print('Fitter ready with minimizer:', fitter.easy_science_multi_fitter.minimizer.name)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "eb0f989e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ---- Classical fit first ----------------------------------------------------\n",
+    "# A classical optimisation gives a good starting point and a sanity check\n",
+    "# before launching the (much more expensive) MCMC sampler.\n",
+    "\n",
+    "analysed = fitter.fit(data)\n",
+    "\n",
+    "print('Classical fit successful:', analysed.get('success', 'N/A'))\n",
+    "print('Reduced χ² ≈', analysed.get('reduced_chi', 'N/A'))\n",
+    "\n",
+    "# Plot the fit\n",
+    "r_model = analysed['R_0_model'].values\n",
+    "\n",
+    "plt.figure(figsize=(8, 5))\n",
+    "plt.semilogy(qz, r_data, 'o', label='Data', alpha=0.7)\n",
+    "plt.semilogy(qz, r_model, '-', label='Classical BUMPS fit', linewidth=2)\n",
+    "plt.xlabel('Q / Å⁻¹')\n",
+    "plt.ylabel('Reflectivity')\n",
+    "plt.title('Classical fit before Bayesian sampling')\n",
+    "plt.legend()\n",
+    "plt.grid(True, alpha=0.3)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "20c9b0e0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ---- Bayesian MCMC sampling -------------------------------------------------\n",
+    "# ``MultiFitter.sample()`` delegates to the BUMPS DREAM sampler.\n",
+    "# All keyword arguments are forwarded with user-friendly names:\n",
+    "#   ``samples``   ← total retained samples\n",
+    "#   ``burn``      ← burn‑in steps\n",
+    "#   ``thin``      ← thinning interval\n",
+    "#   ``chains``    ← DREAM population count (alias for ``pop``)\n",
+    "#   ``population``← BUMPS‑native ``pop`` for advanced users\n",
+    "#   ``seed``      ← random seed for reproducibility\n",
+    "\n",
+    "posterior_dict = fitter.sample(\n",
+    "    data,\n",
+    "    samples=2000,  # Short for demo; use 20 k+ in production\n",
+    "    burn=500,\n",
+    "    thin=10,\n",
+    "    seed=42,\n",
+    ")\n",
+    "\n",
+    "print('DREAM sampling complete.')\n",
+    "print(f'  Posterior shape  : {posterior_dict[\"draws\"].shape}')\n",
+    "print(f'  Parameters        : {posterior_dict[\"param_names\"]}')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "f23934a0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ---- Wrap in PosteriorResults -----------------------------------------------\n",
+    "# ``PosteriorResults`` gives you a convenient object with built-in analysis\n",
+    "# methods.  You can also use the raw ``dict`` with the standalone functions\n",
+    "# — both styles are shown below.\n",
+    "\n",
+    "posterior = PosteriorResults(\n",
+    "    draws=posterior_dict['draws'],\n",
+    "    param_names=posterior_dict['param_names'],\n",
+    "    logp=posterior_dict.get('logp'),\n",
+    "    sampler_state=posterior_dict.get('state'),\n",
+    ")\n",
+    "\n",
+    "print(posterior)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ef300cb1",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ---- Posterior summary table ------------------------------------------------\n",
+    "# ``.summary()`` prints mean, standard deviation and 95 % HDI for each parameter.\n",
+    "\n",
+    "print(posterior.summary())\n",
+    "print()\n",
+    "\n",
+    "# The standalone function produces the same output:\n",
+    "# print(posterior_summary(posterior.draws, posterior.param_names))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e759a2a0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ---- Corner plot ------------------------------------------------------------\n",
+    "# Visualise all pairwise parameter correlations and marginal distributions.\n",
+    "\n",
+    "posterior.corner()\n",
+    "plt.suptitle('Posterior distributions from BUMPS DREAM', y=1.02)\n",
+    "plt.show()\n",
+    "\n",
+    "# Standalone equivalent:\n",
+    "# plot_corner(posterior.draws, posterior.param_names)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "593f5ed3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ---- Trace plot -------------------------------------------------------------\n",
+    "# Inspect the MCMC chains for convergence.  Requires ``arviz``.\n",
+    "\n",
+    "try:\n",
+    "    posterior.trace()\n",
+    "    plt.suptitle('MCMC trace plots', y=1.02)\n",
+    "    plt.show()\n",
+    "except ImportError:\n",
+    "    print('Skipped: arviz is not installed.')\n",
+    "    print('Install with: pip install easyreflectometry[bayesian]')\n",
+    "\n",
+    "# Standalone equivalent:\n",
+    "# plot_trace(posterior.draws, posterior.param_names)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3049e68a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ---- Credible intervals -----------------------------------------------------\n",
+    "# Equal-tailed 95 % credible intervals for each parameter.\n",
+    "\n",
+    "ci_95 = posterior.credible_interval(alpha=0.95)\n",
+    "print('95 % credible intervals:')\n",
+    "for name, (lo, hi) in ci_95.items():\n",
+    "    print(f'  {name:<30s}  [{lo:.4f}, {hi:.4f}]')\n",
+    "\n",
+    "# You can request narrower intervals too:\n",
+    "ci_50 = posterior.credible_interval(alpha=0.50)\n",
+    "print('\\n50 % credible intervals:')\n",
+    "for name, (lo, hi) in ci_50.items():\n",
+    "    print(f'  {name:<30s}  [{lo:.4f}, {hi:.4f}]')\n",
+    "\n",
+    "# Standalone equivalent:\n",
+    "# ci = credible_intervals(posterior.draws, posterior.param_names, alpha=0.95)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "806bf47a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ---- 2D parameter heatmap ---------------------------------------------------\n",
+    "# Joint posterior density for a specific pair of parameters.\n",
+    "# Uses the ``corner`` library (already loaded as ``corner``).\n",
+    "\n",
+    "params_of_interest = ['Layer_1_ThicknessParameter_0', 'Material_1_SldParameter_0']\n",
+    "idx = [posterior.param_names.index(p) for p in params_of_interest]\n",
+    "\n",
+    "_corner.corner(\n",
+    "    posterior.draws[:, idx],\n",
+    "    labels=params_of_interest,\n",
+    "    quantiles=[0.16, 0.5, 0.84],\n",
+    "    show_titles=True,\n",
+    "    title_fmt='.4f',\n",
+    "    bins=50,\n",
+    "    hist_bin_factor=1.5,\n",
+    ")\n",
+    "plt.suptitle('Parameter heatmap: thickness vs SLD', y=1.02)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "34e3cc3e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ---- Gelman-Rubin R‑hat convergence diagnostic ------------------------------\n",
+    "# Requires ``arviz``.  Values close to 1.0 indicate good convergence.\n",
+    "\n",
+    "rhat = posterior.gelman_rubin()\n",
+    "if rhat is not None:\n",
+    "    print('Gelman-Rubin R‑hat:')\n",
+    "    for name, r in rhat.items():\n",
+    "        flag = ' ✓' if r < 1.1 else ' ⚠'\n",
+    "        print(f'  {name:<30s}  R̂ = {r:.3f}{flag}')\n",
+    "else:\n",
+    "    print('Skipped: arviz is not installed.')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c7e5816e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ---- Posterior-predictive reflectivity --------------------------------------\n",
+    "# Propagate parameter uncertainty through the model to obtain median\n",
+    "# reflectivity and 95 % credible band.\n",
+    "\n",
+    "r_median, r_lower, r_upper = posterior_predictive_reflectivity(\n",
+    "    posterior.draws,\n",
+    "    posterior.param_names,\n",
+    "    model,\n",
+    "    qz,\n",
+    "    n_samples=200,\n",
+    ")\n",
+    "\n",
+    "plt.figure(figsize=(9, 6))\n",
+    "plt.semilogy(qz, r_data, 'o', label='Data', alpha=0.6)\n",
+    "plt.semilogy(qz, r_median, '-', color='tab:orange', label='Posterior median')\n",
+    "plt.fill_between(\n",
+    "    qz,\n",
+    "    r_lower,\n",
+    "    r_upper,\n",
+    "    color='tab:orange',\n",
+    "    alpha=0.3,\n",
+    "    label='95 % credible interval',\n",
+    ")\n",
+    "plt.xlabel('Q / Å⁻¹')\n",
+    "plt.ylabel('Reflectivity')\n",
+    "plt.title('Bayesian Posterior-Predictive Check')\n",
+    "plt.legend()\n",
+    "plt.grid(True, alpha=0.3)\n",
+    "plt.show()\n",
+    "\n",
+    "print('The 95 % credible interval captures parameter uncertainty propagated through the model.')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ef27b8ec",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ---- Posterior-predictive SLD profile ---------------------------------------\n",
+    "# The same idea applied to the scattering-length-density profile.\n",
+    "\n",
+    "z, sld_median, sld_lower, sld_upper = posterior_predictive_sld_profile(\n",
+    "    posterior.draws,\n",
+    "    posterior.param_names,\n",
+    "    model,\n",
+    "    n_samples=200,\n",
+    ")\n",
+    "\n",
+    "plt.figure(figsize=(8, 4))\n",
+    "plt.plot(z, sld_median, label='Posterior median SLD')\n",
+    "plt.fill_between(\n",
+    "    z,\n",
+    "    sld_lower,\n",
+    "    sld_upper,\n",
+    "    alpha=0.3,\n",
+    "    label='95 % credible interval',\n",
+    ")\n",
+    "plt.xlabel('z / Å')\n",
+    "plt.ylabel('SLD / 10⁻⁶ Å⁻²')\n",
+    "plt.title('SLD Profile with Bayesian Uncertainty')\n",
+    "plt.legend()\n",
+    "plt.grid(True, alpha=0.3)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "37e78b4e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# ---- Summary ----------------------------------------------------------------\n",
+    "print('―' * 60)\n",
+    "print('Bayesian analysis complete!')\n",
+    "print('―' * 60)\n",
+    "print()\n",
+    "print('API surface demonstrated:')\n",
+    "print('  MultiFitter.sample(data, samples=, burn=, thin=, seed=)')\n",
+    "print('  PosteriorResults(draws, param_names, logp=, sampler_state=)')\n",
+    "print('    .summary()                — formatted parameter table')\n",
+    "print('    .corner()                 — pairwise correlation plot')\n",
+    "print('    .trace()                  — MCMC chain trace plot')\n",
+    "print('    .credible_interval(alpha) — equal-tailed credible intervals')\n",
+    "print('    .gelman_rubin()           — R̂ convergence diagnostic')\n",
+    "print()\n",
+    "print('  Standalone functions (work on raw dict):')\n",
+    "print('    posterior_summary(draws, names)')\n",
+    "print('    plot_corner(draws, names)')\n",
+    "print('    plot_trace(draws, names)')\n",
+    "print('    credible_intervals(draws, names, alpha)')\n",
+    "print('    posterior_predictive_reflectivity(draws, names, model, q, n)')\n",
+    "print('    posterior_predictive_sld_profile(draws, names, model, n)')\n",
+    "print()\n",
+    "print('The high-level API provides clean, safe access to BUMPS DREAM sampling.')"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "era",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/docs/docs/tutorials/advancedfitting/example.ort b/docs/docs/tutorials/advancedfitting/example.ort
new file mode 100644
index 00000000..968fa7bb
--- /dev/null
+++ b/docs/docs/tutorials/advancedfitting/example.ort
@@ -0,0 +1,448 @@
+# # ORSO reflectivity data file | 0.1 standard | YAML encoding | https://www.reflectometry.org/
+# data_source:
+#     owner:
+#         name: Andrew Nelson
+#         affiliation: ANSTO
+#         contact: Andrew.Nelson@ansto.gov.au
+#     experiment:
+#         facility: ANSTO
+#         start_date: 2021-05-12
+#         title: Example data file from refnx docs
+#         instrument: platypus
+#         probe: neutron
+#     sample:
+#         name: Polymer Film
+#         category: solid / liquid
+#         composition: Si / SiO2 / Film / D2O
+#     measurement:
+#         instrument_settings:
+#             wavelength:
+#                magnitude: 12
+#                unit: angstrom
+#             incident_angle: 
+#                magnitude: 3
+#                unit: deg
+#         data_files:
+#             - Unknown.nxs
+#         scheme: angle-dispersive
+# reduction:
+#     software: ess
+#     timestamp: 2022-01-27T15:33:59+01:00
+#     corrections:
+#          - footprint
+#          - incident intensity
+#          - detector efficiency
+# columns:
+#     - {name: Qz, unit: 1/angstrom, dimension: WW transfer}
+#     - {name: R, dimension: reflectivity}
+#     - {name: sR, dimension: error-reflectivity}
+#     - {name: sQz, unit: 1/angstrom, dimension: resolution-WW transfer}
+##           Qz              RQz               sR              sQz          
+8.060220000e-03  7.095810000e-01  8.506760000e-02  1.407419648e-04
+8.136620000e-03  8.622810000e-01  1.123700000e-01  1.420996057e-04
+8.263750000e-03  9.086470000e-01  7.900470000e-02  1.443588017e-04
+8.370670000e-03  7.732920000e-01  7.927280000e-02  1.462583099e-04
+8.450330000e-03  1.057970000e+00  1.259590000e-01  1.476732801e-04
+8.530830000e-03  1.015660000e+00  1.132950000e-01  1.491031133e-04
+8.612170000e-03  7.347170000e-01  6.115660000e-02  1.505473850e-04
+8.694370000e-03  7.692160000e-01  6.170580000e-02  1.520069445e-04
+8.777430000e-03  1.115740000e+00  1.127300000e-01  1.534813672e-04
+8.861360000e-03  9.723030000e-01  8.971600000e-02  1.549710776e-04
+8.946160000e-03  7.512140000e-01  5.493930000e-02  1.564760759e-04
+9.031850000e-03  7.976490000e-01  5.671220000e-02  1.579963619e-04
+9.118440000e-03  9.221890000e-01  6.858410000e-02  1.595327850e-04
+9.205930000e-03  9.757550000e-01  7.293950000e-02  1.610844959e-04
+9.294320000e-03  8.195040000e-01  5.216170000e-02  1.626523440e-04
+9.383640000e-03  7.883200000e-01  4.794730000e-02  1.642367538e-04
+9.473890000e-03  7.947010000e-01  4.602240000e-02  1.658368761e-04
+9.565080000e-03  8.744000000e-01  5.151640000e-02  1.674535601e-04
+9.657210000e-03  8.396620000e-01  4.742850000e-02  1.690872306e-04
+9.750300000e-03  8.008720000e-01  4.399580000e-02  1.707370382e-04
+9.844360000e-03  1.117100000e+00  7.373300000e-02  1.724042569e-04
+9.939390000e-03  8.884110000e-01  4.954100000e-02  1.740884620e-04
+1.003540000e-02  7.791290000e-01  3.898730000e-02  1.757896536e-04
+1.013240000e-02  7.999680000e-01  3.899740000e-02  1.775086809e-04
+1.023040000e-02  8.431240000e-01  4.159800000e-02  1.792451193e-04
+1.032940000e-02  9.613320000e-01  4.925360000e-02  1.809989689e-04
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+1.148840000e-02  9.956310000e-01  3.901160000e-02  2.015185836e-04
+1.160040000e-02  9.695940000e-01  3.636230000e-02  2.034996267e-04
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@@ -2662,6 +2630,7 @@ environments:
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+      - pypi: git+https://github.com/easyscience/corelib.git?rev=bayesian#efd7ff176ab33f84d8a20843dfe18663560e39b8
       - pypi: https://files.pythonhosted.org/packages/66/40/7732d648ab9d069a46e686043241f01206348e2bbf128daea85be4d6414b/coverage-7.13.5-cp313-cp313-win_amd64.whl
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@@ -2670,7 +2639,6 @@ environments:
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       - pypi: https://files.pythonhosted.org/packages/cb/b1/3846dd7f199d53cb17f49cba7e651e9ce294d8497c8c150530ed11865bb8/iniconfig-2.3.0-py3-none-any.whl
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-      - pypi: https://files.pythonhosted.org/packages/56/6d/0d9848617b9f753b87f214f1c682592f7ca42de085f564352f10f0843026/ipywidgets-8.1.8-py3-none-any.whl
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@@ -2778,7 +2743,6 @@ environments:
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-      - pypi: https://files.pythonhosted.org/packages/3f/0e/fa3b193432cfc60c93b42f3be03365f5f909d2b3ea410295cf36df739e31/widgetsnbextension-4.0.15-py3-none-any.whl
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@@ -5409,11 +5373,11 @@ packages:
   requires_python: '>=3.12'
 - pypi: ./
   name: easyreflectometry
-  version: 1.5.0+devdirty9
-  sha256: 6cb81566f4ddb1401f1f6cfdac62844e904c9e177f74d0526912a44ae0489a16
+  version: 1.4.1+devdirty39
+  sha256: 4ec8c51ba0a6b6582ff3e2a5758d63f81474a4f837ba5c485b2496d179cf3f7e
   requires_dist:
   - bumps
-  - easyscience
+  - easyscience @ git+https://github.com/easyscience/corelib.git@bayesian
   - orsopy
   - pooch
   - refl1d>=1.0.0
@@ -5421,6 +5385,8 @@ packages:
   - scipp
   - svglib<1.6 ; sys_platform == 'darwin' or sys_platform == 'linux'
   - xhtml2pdf
+  - arviz>=0.18 ; extra == 'bayesian'
+  - corner>=2.2 ; extra == 'bayesian'
   - build ; extra == 'dev'
   - copier ; extra == 'dev'
   - docstripy ; extra == 'dev'
@@ -5455,34 +5421,31 @@ packages:
   - versioningit ; extra == 'dev'
   requires_python: '>=3.11'
   editable: true
-- pypi: https://files.pythonhosted.org/packages/4a/8a/4cb9367a86f2b9526727ee94e5e6a3d86f9f7d7d947927b444e5bcd56a89/easyscience-2.3.1-py3-none-any.whl
+- pypi: git+https://github.com/easyscience/corelib.git?rev=bayesian#efd7ff176ab33f84d8a20843dfe18663560e39b8
   name: easyscience
-  version: 2.3.1
-  sha256: 51dd343ff4bcf7c36e8fada32ed3ca2bdc7e1226ae08965a2c11d9fd936e3e40
+  version: 2.3.1+dev11
   requires_dist:
   - asteval
   - bumps
   - dfo-ls
-  - ipykernel
-  - ipympl
-  - ipython
-  - ipywidgets
-  - jupyterlab
   - lmfit
-  - matplotlib
   - numpy
-  - pixi-kernel
-  - pooch
   - scipp
-  - uncertainties
   - build ; extra == 'dev'
   - copier ; extra == 'dev'
-  - docformatter ; extra == 'dev'
+  - docstripy ; extra == 'dev'
+  - format-docstring ; extra == 'dev'
   - gitpython ; extra == 'dev'
   - interrogate ; extra == 'dev'
+  - ipykernel ; extra == 'dev'
+  - ipympl ; extra == 'dev'
+  - ipython ; extra == 'dev'
+  - ipywidgets ; extra == 'dev'
   - jinja2 ; extra == 'dev'
+  - jupyterlab ; extra == 'dev'
   - jupyterquiz ; extra == 'dev'
   - jupytext ; extra == 'dev'
+  - matplotlib ; extra == 'dev'
   - mike ; extra == 'dev'
   - mkdocs ; extra == 'dev'
   - mkdocs-autorefs ; extra == 'dev'
@@ -5494,7 +5457,9 @@ packages:
   - nbmake ; extra == 'dev'
   - nbqa ; extra == 'dev'
   - nbstripout ; extra == 'dev'
+  - pooch ; extra == 'dev'
   - pre-commit ; extra == 'dev'
+  - pydoclint ; extra == 'dev'
   - pytest ; extra == 'dev'
   - pytest-cov ; extra == 'dev'
   - pytest-xdist ; extra == 'dev'
@@ -6475,27 +6440,6 @@ packages:
   - pkg:pypi/ipykernel?source=hash-mapping
   size: 133644
   timestamp: 1770566133040
-- pypi: https://files.pythonhosted.org/packages/12/b3/88c0ef22878c86035f058df0ac6c171319ffd0aa52a406455ed3a3847566/ipympl-0.10.0-py3-none-any.whl
-  name: ipympl
-  version: 0.10.0
-  sha256: a09c4f0ff86490cc62aed45e53b912fb706e3ec3506c4a51ce4a670d6667f5ce
-  requires_dist:
-  - ipython<10
-  - ipywidgets>=7.6.0,<9
-  - matplotlib>=3.5.0,<4
-  - numpy
-  - pillow
-  - traitlets<6
-  - intersphinx-registry ; extra == 'docs'
-  - myst-nb ; extra == 'docs'
-  - sphinx-book-theme ; extra == 'docs'
-  - sphinx-copybutton ; extra == 'docs'
-  - sphinx-thebe ; extra == 'docs'
-  - sphinx-togglebutton ; extra == 'docs'
-  - sphinx>=1.5 ; extra == 'docs'
-  - nbval>=0.11.0 ; extra == 'test'
-  - pytest>=9.0.2 ; extra == 'test'
-  requires_python: '>=3.9'
 - conda: https://conda.anaconda.org/conda-forge/noarch/ipython-9.13.0-pyh53cf698_0.conda
   sha256: a0af49948a1842dfd15a0b0b2fd56c94ddbd07e07a6c8b4bc70d43015eafaff0
   md5: 73e9657cd19605740d21efb14d8d0cb9
diff --git a/pyproject.toml b/pyproject.toml
index 681c5562..2713a73f 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -23,7 +23,8 @@ classifiers = [
 ]
 requires-python = '>=3.11'
 dependencies = [
-  'easyscience',
+  'easyscience @ git+https://github.com/easyscience/corelib.git@bayesian',
+  # 'easyscience',
   'scipp',
   'refnx',
   'refl1d>=1.0.0',
@@ -70,6 +71,8 @@ dev = [
   'spdx-headers',                    # SPDX license header validation
 ]
 
+bayesian = ["corner>=2.2", "arviz>=0.18"]
+
 [project.urls]
 Documentation = 'https://easyscience.github.io/reflectometry-lib'
 'Release Notes' = 'https://github.com/easyscience/reflectometry-lib/releases'
diff --git a/src/easyreflectometry/__init__.py b/src/easyreflectometry/__init__.py
index 8ff945d0..22d1210c 100644
--- a/src/easyreflectometry/__init__.py
+++ b/src/easyreflectometry/__init__.py
@@ -5,6 +5,7 @@
 
 from importlib import metadata
 
+from .analysis.bayesian import PosteriorResults
 from .project import Project
 
 try:
@@ -13,6 +14,7 @@
     __version__ = '0.0.0'
 
 __all__ = [
-    'Project',
-    '__version__',
+    Project,
+    PosteriorResults,
+    __version__,
 ]
diff --git a/src/easyreflectometry/analysis/__init__.py b/src/easyreflectometry/analysis/__init__.py
new file mode 100644
index 00000000..4fb784d9
--- /dev/null
+++ b/src/easyreflectometry/analysis/__init__.py
@@ -0,0 +1,21 @@
+# SPDX-FileCopyrightText: 2026 EasyReflectometry contributors <https://github.com/easyscience>
+# SPDX-License-Identifier: BSD-3-Clause
+"""Post-hoc analysis utilities for reflectometry fitting results."""
+
+from easyreflectometry.analysis.bayesian import PosteriorResults
+from easyreflectometry.analysis.bayesian import credible_intervals
+from easyreflectometry.analysis.bayesian import plot_corner
+from easyreflectometry.analysis.bayesian import plot_trace
+from easyreflectometry.analysis.bayesian import posterior_predictive_reflectivity
+from easyreflectometry.analysis.bayesian import posterior_predictive_sld_profile
+from easyreflectometry.analysis.bayesian import posterior_summary
+
+__all__ = [
+    'PosteriorResults',
+    'plot_corner',
+    'plot_trace',
+    'posterior_summary',
+    'credible_intervals',
+    'posterior_predictive_reflectivity',
+    'posterior_predictive_sld_profile',
+]
diff --git a/src/easyreflectometry/analysis/bayesian.py b/src/easyreflectometry/analysis/bayesian.py
new file mode 100644
index 00000000..f7e8a732
--- /dev/null
+++ b/src/easyreflectometry/analysis/bayesian.py
@@ -0,0 +1,375 @@
+# SPDX-FileCopyrightText: 2026 EasyReflectometry contributors <https://github.com/easyscience>
+# SPDX-License-Identifier: BSD-3-Clause
+"""Bayesian posterior analysis for reflectometry fitting results."""
+
+from __future__ import annotations
+
+import warnings
+from typing import Any
+
+import numpy as np
+
+try:
+    import corner as _corner
+
+    _HAS_CORNER = True
+except ImportError:
+    _HAS_CORNER = False
+
+try:
+    import arviz as _arviz
+
+    _HAS_ARVIZ = True
+except ImportError:
+    _HAS_ARVIZ = False
+
+
+def _require_corner():
+    if not _HAS_CORNER:
+        raise ImportError(
+            'The ``corner`` library is required for corner plots. '
+            'Install it with ``pip install corner`` or '
+            '``pip install easyreflectometry[bayesian]``.'
+        )
+
+
+def _require_arviz():
+    if not _HAS_ARVIZ:
+        raise ImportError(
+            'The ``arviz`` library is required for trace plots and R-hat. '
+            'Install it with ``pip install arviz`` or '
+            '``pip install easyreflectometry[bayesian]``.'
+        )
+
+
+def _to_arviz_data(draws: np.ndarray, param_names: list[str]):
+    """Convert posterior draws to an arviz InferenceData object.
+
+    :param draws: Posterior samples, shape ``(n_samples, n_params)`` or
+        ``(n_chains, n_draws, n_params)``.
+    :type draws: np.ndarray
+    :param param_names: Parameter names (one per column).
+    :type param_names: list[str]
+    :return: arviz InferenceData object.
+    """
+    draws = np.asarray(draws)
+    if draws.ndim == 2:
+        draws = draws[np.newaxis, ...]  # (1, n_samples, n_params)
+
+    # Build a dict of {param_name: (chain, draw) array}
+    posterior_dict = {}
+    for i, name in enumerate(param_names):
+        posterior_dict[name] = draws[:, :, i]
+
+    return _arviz.from_dict({'posterior': posterior_dict})
+
+
+class PosteriorResults:
+    """Container for Bayesian posterior samples with analysis methods.
+
+    :param draws: Posterior samples, shape ``(n_samples, n_params)``.
+    :type draws: np.ndarray
+    :param param_names: Parameter names (one per column of ``draws``).
+    :type param_names: list[str]
+    :param logp: Log-posterior values, shape ``(n_samples,)``, or ``None``.
+    :type logp: np.ndarray | None
+    :param sampler_state: Raw sampler state object (e.g. BUMPS ``DreamState``), or ``None``.
+    :type sampler_state: Any | None
+    """
+
+    def __init__(
+        self,
+        draws: np.ndarray,
+        param_names: list[str],
+        logp: np.ndarray | None = None,
+        sampler_state: Any | None = None,
+    ):
+        self.draws = np.asarray(draws)
+        self.param_names = list(param_names)
+        self.logp = np.asarray(logp) if logp is not None else None
+        self.sampler_state = sampler_state
+
+    def __repr__(self) -> str:
+        n_samples, n_params = self.draws.shape
+        return f'PosteriorResults(n_samples={n_samples}, n_params={n_params}, param_names={self.param_names})'
+
+    def summary(self) -> str:
+        """Return a formatted summary table with mean, sd, and HDI for each parameter.
+
+        :return: Formatted summary table as a string.
+        :rtype: str
+        """
+        return posterior_summary(self.draws, self.param_names)
+
+    def corner(self, **kwargs) -> None:
+        """Plot parameter correlation corner plot.
+
+        Requires the ``corner`` library.
+
+        :param kwargs: Additional keyword arguments passed to ``corner.corner``.
+        """
+        plot_corner(self.draws, self.param_names, **kwargs)
+
+    def trace(self, **kwargs) -> None:
+        """Plot MCMC trace plot.
+
+        Requires the ``arviz`` library.
+
+        :param kwargs: Additional keyword arguments passed to ``arviz.plot_trace``.
+        """
+        plot_trace(self.draws, self.param_names, **kwargs)
+
+    def credible_interval(self, alpha: float = 0.95) -> dict:
+        """Compute equal-tailed credible intervals for each parameter.
+
+        :param alpha: Credible interval width (e.g. 0.95 for 95%).
+        :type alpha: float
+        :return: Dictionary mapping parameter name to ``(lower, upper)``.
+        :rtype: dict
+        """
+        return credible_intervals(self.draws, self.param_names, alpha=alpha)
+
+    def gelman_rubin(self) -> dict | None:
+        """Compute the Gelman-Rubin R-hat convergence diagnostic.
+
+        Requires the ``arviz`` library. Returns ``None`` if ``arviz`` is not
+        available.
+
+        :return: Dictionary mapping parameter name to R-hat value, or ``None``.
+        :rtype: dict | None
+        """
+        if not _HAS_ARVIZ:
+            warnings.warn(
+                'The ``arviz`` library is required for Gelman-Rubin R-hat. Install it with ``pip install arviz``.',
+                UserWarning,
+            )
+            return None
+        # arviz requires at least 2 chains; treat the posterior as one chain
+        data = _to_arviz_data(self.draws, self.param_names)
+        rhat = _arviz.rhat(data)
+        return {name: float(rhat[name].values) for name in self.param_names}
+
+
+def posterior_summary(draws: np.ndarray, param_names: list[str]) -> str:
+    """Return a formatted summary table with mean, sd, and HDI for each parameter.
+
+    :param draws: Posterior samples, shape ``(n_samples, n_params)``.
+    :type draws: np.ndarray
+    :param param_names: Parameter names (one per column).
+    :type param_names: list[str]
+    :return: Formatted summary table as a string.
+    :rtype: str
+    """
+    draws = np.asarray(draws)
+    lines = [f'{"parameter":<30s} {"mean":>10s} {"sd":>10s} {"hdi_2.5%":>10s} {"hdi_97.5%":>10s}']
+    for i, name in enumerate(param_names):
+        col = draws[:, i]
+        lo, hi = np.percentile(col, [2.5, 97.5])
+        lines.append(f'{name:<30s} {col.mean():>10.4f} {col.std():>10.4f} {lo:>10.4f} {hi:>10.4f}')
+    return '\n'.join(lines)
+
+
+def plot_corner(draws: np.ndarray, param_names: list[str], **kwargs) -> None:
+    """Plot a parameter correlation corner plot.
+
+    Requires the ``corner`` library.
+
+    :param draws: Posterior samples, shape ``(n_samples, n_params)``.
+    :type draws: np.ndarray
+    :param param_names: Parameter names (one per column).
+    :type param_names: list[str]
+    :param kwargs: Additional keyword arguments passed to ``corner.corner``.
+    """
+    _require_corner()
+    draws = np.asarray(draws)
+    defaults = {
+        'labels': param_names,
+        'quantiles': [0.16, 0.5, 0.84],
+        'show_titles': True,
+        'title_fmt': '.3f',
+        'title_kwargs': {'fontsize': 12},
+    }
+    defaults.update(kwargs)
+    _corner.corner(draws, **defaults)
+
+
+def plot_trace(draws: np.ndarray, param_names: list[str], **kwargs) -> None:
+    """Plot MCMC trace plot.
+
+    Requires the ``arviz`` library.
+
+    :param draws: Posterior samples, shape ``(n_samples, n_params)``.
+    :type draws: np.ndarray
+    :param param_names: Parameter names (one per column).
+    :type param_names: list[str]
+    :param kwargs: Additional keyword arguments passed to ``arviz.plot_trace``.
+    """
+    _require_arviz()
+    idata = _to_arviz_data(draws, param_names)
+    _arviz.plot_trace(idata, var_names=param_names, **kwargs)
+
+
+def credible_intervals(
+    draws: np.ndarray,
+    param_names: list[str],
+    alpha: float = 0.95,
+) -> dict:
+    """Compute equal-tailed credible intervals for each parameter.
+
+    :param draws: Posterior samples, shape ``(n_samples, n_params)``.
+    :type draws: np.ndarray
+    :param param_names: Parameter names (one per column).
+    :type param_names: list[str]
+    :param alpha: Credible interval width (e.g. 0.95 for 95%).
+    :type alpha: float
+    :return: Dictionary mapping parameter name to ``(lower, upper)``.
+    :rtype: dict
+    """
+    draws = np.asarray(draws)
+    tail = (1.0 - alpha) / 2.0
+    lo_pct = tail * 100
+    hi_pct = (1.0 - tail) * 100
+    result = {}
+    for i, name in enumerate(param_names):
+        col = draws[:, i]
+        lo, hi = np.percentile(col, [lo_pct, hi_pct])
+        result[name] = (float(lo), float(hi))
+    return result
+
+
+def _save_parameter_state(model) -> dict:
+    """Save the current values and errors of all free parameters in a model.
+
+    :param model: A reflectometry model with ``get_parameters()``.
+    :return: Dictionary mapping ``unique_name`` to ``(value, error)``.
+    :rtype: dict
+    """
+    state = {}
+    for param in model.get_parameters():
+        state[param.unique_name] = (param.value, param.error)
+    return state
+
+
+def _restore_parameter_state(model, state: dict) -> None:
+    """Restore parameter values and errors from a saved state.
+
+    :param model: A reflectometry model with ``get_parameters()``.
+    :param state: Dictionary mapping ``unique_name`` to ``(value, error)``.
+    """
+    for param in model.get_parameters():
+        if param.unique_name in state:
+            param.value = state[param.unique_name][0]
+            param.error = state[param.unique_name][1]
+
+
+def _apply_draw(model, draws: np.ndarray, param_names: list[str], row: int) -> None:
+    """Apply a single posterior draw to the model parameters.
+
+    Parameter lookup uses ``unique_name``, matching the BUMPS names after
+    removing the minimizer prefix, which avoids collisions when repeated models
+    or multi-contrast fits contain similarly named parameters.
+
+    :param model: A reflectometry model with ``get_parameters()``.
+    :param draws: Posterior samples array.
+    :param param_names: Parameter names matching the columns of ``draws``.
+    :param row: Index of the draw to apply.
+    """
+    param_lookup = {p.unique_name: p for p in model.get_parameters()}
+    for j, name in enumerate(param_names):
+        if name in param_lookup:
+            param_lookup[name].value = float(draws[row, j])
+
+
+def posterior_predictive_reflectivity(
+    draws: np.ndarray,
+    param_names: list[str],
+    model,
+    q_values: np.ndarray,
+    n_samples: int = 200,
+) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
+    """Compute the posterior predictive reflectivity with credible intervals.
+
+    Parameter values and errors are saved before applying any posterior draw
+    and restored in a ``finally`` block, so the model is not left mutated.
+
+    :param draws: Posterior samples, shape ``(n_samples_posterior, n_params)``.
+    :type draws: np.ndarray
+    :param param_names: Parameter names matching the columns of ``draws``.
+    :type param_names: list[str]
+    :param model: A reflectometry model with ``interface.fit_func``.
+    :param q_values: Q values at which to evaluate reflectivity.
+    :type q_values: np.ndarray
+    :param n_samples: Number of posterior draws to use (last ``n_samples``).
+    :type n_samples: int
+    :return: Tuple of ``(median, lower_95, upper_95)`` reflectivity arrays.
+    :rtype: tuple[np.ndarray, np.ndarray, np.ndarray]
+    """
+    draws = np.asarray(draws)
+    q_values = np.asarray(q_values)
+
+    n_total = draws.shape[0]
+    n_use = min(n_samples, n_total)
+    sample_indices = range(n_total - n_use, n_total)
+
+    saved_state = _save_parameter_state(model)
+    try:
+        reflectivity_samples = []
+        for i in sample_indices:
+            _apply_draw(model, draws, param_names, i)
+            r_calc = model.interface.fit_func(q_values, model.unique_name)
+            reflectivity_samples.append(np.asarray(r_calc))
+    finally:
+        _restore_parameter_state(model, saved_state)
+
+    reflectivity_samples = np.array(reflectivity_samples)
+    median = np.median(reflectivity_samples, axis=0)
+    lower = np.percentile(reflectivity_samples, 2.5, axis=0)
+    upper = np.percentile(reflectivity_samples, 97.5, axis=0)
+    return median, lower, upper
+
+
+def posterior_predictive_sld_profile(
+    draws: np.ndarray,
+    param_names: list[str],
+    model,
+    n_samples: int = 200,
+) -> tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray]:
+    """Compute the posterior predictive SLD profile with credible intervals.
+
+    Parameter values and errors are saved before applying any posterior draw
+    and restored in a ``finally`` block, so the model is not left mutated.
+
+    :param draws: Posterior samples, shape ``(n_samples_posterior, n_params)``.
+    :type draws: np.ndarray
+    :param param_names: Parameter names matching the columns of ``draws``.
+    :type param_names: list[str]
+    :param model: A reflectometry model with ``interface.sld_profile``.
+    :param n_samples: Number of posterior draws to use (last ``n_samples``).
+    :type n_samples: int
+    :return: Tuple of ``(z, median, lower_95, upper_95)`` SLD profile arrays.
+    :rtype: tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray]
+    """
+    draws = np.asarray(draws)
+
+    n_total = draws.shape[0]
+    n_use = min(n_samples, n_total)
+    sample_indices = range(n_total - n_use, n_total)
+
+    saved_state = _save_parameter_state(model)
+    try:
+        sld_samples = []
+        z_shared = None
+        for i in sample_indices:
+            _apply_draw(model, draws, param_names, i)
+            z, sld = model.interface.sld_profile(model.unique_name)
+            if z_shared is None:
+                z_shared = np.asarray(z)
+            sld_samples.append(np.asarray(sld))
+    finally:
+        _restore_parameter_state(model, saved_state)
+
+    sld_samples = np.array(sld_samples)
+    median = np.median(sld_samples, axis=0)
+    lower = np.percentile(sld_samples, 2.5, axis=0)
+    upper = np.percentile(sld_samples, 97.5, axis=0)
+    return z_shared, median, lower, upper
diff --git a/src/easyreflectometry/fitting.py b/src/easyreflectometry/fitting.py
index 78f74e68..3d50fe99 100644
--- a/src/easyreflectometry/fitting.py
+++ b/src/easyreflectometry/fitting.py
@@ -353,6 +353,85 @@ def fit_single_data_set_1d(self, data: DataSet1D, objective: str | None = None)
         ]
         return result
 
+    def sample(
+        self,
+        data: sc.DataGroup,
+        samples: int = 10000,
+        burn: int = 2000,
+        thin: int = 10,
+        chains: int | None = None,
+        population: int | None = None,
+        seed: int | None = None,
+        objective: str | None = None,
+        initializer: str | None = None,
+        progress_callback=None,
+        abort_test=None,
+    ) -> dict:
+        """Run Bayesian MCMC sampling on reflectometry data using the DREAM sampler.
+
+        Requires that the minimizer is a BUMPS instance (i.e. the minimizer was
+        switched to ``AvailableMinimizers.Bumps``).
+
+        :param data: DataGroup with reflectivity data.
+        :param samples: Number of retained DREAM samples requested from BUMPS.
+        :param burn: Burn-in steps.
+        :param thin: Thinning interval.
+        :param chains: User-friendly alias for BUMPS DREAM population count.
+        :param population: BUMPS DREAM population count for advanced users.
+        :param seed: Random seed for reproducibility.
+        :param objective: Zero-variance handling strategy.
+        :param initializer: DREAM population initializer. One of ``'eps'``,
+            ``'cov'``, ``'lhs'``, or ``'random'``. By default, None (BUMPS
+            uses ``'eps'``).
+        :param progress_callback: Optional callback for progress updates during
+            sampling.  Forwarded to the core MultiFitter.
+        :return: Dictionary with keys ``'draws'``, ``'param_names'``, ``'state'``,
+            and ``'logp'``.
+        :raises RuntimeError: If the current minimizer is not a BUMPS instance.
+        """
+        obj = _validate_objective(objective) if objective is not None else self._objective
+
+        refl_nums = [k[3:] for k in data['coords'].keys() if 'Qz' == k[:2]]
+        x = []
+        y = []
+        dy = []
+
+        # Process each reflectivity dataset
+        for i in refl_nums:
+            x_vals = data['coords'][f'Qz_{i}'].values
+            y_vals = data['data'][f'R_{i}'].values
+            variances = data['data'][f'R_{i}'].variances
+
+            x_out, y_eff, weights, stats = _prepare_fit_arrays(x_vals, y_vals, variances, obj)
+
+            if stats['masked'] > 0:
+                warnings.warn(
+                    f'Masked {stats["masked"]} data point(s) in reflectivity {i} due to zero variance during sampling.',
+                    UserWarning,
+                )
+            x.append(x_out)
+            y.append(y_eff)
+            dy.append(weights)
+
+        # Delegate the actual BUMPS/DREAM sampling to the core MultiFitter
+        sampler_kwargs = {}
+        if initializer is not None:
+            sampler_kwargs['init'] = initializer
+        return self.easy_science_multi_fitter.sample(
+            x=x,
+            y=y,
+            weights=dy,
+            samples=samples,
+            burn=burn,
+            thin=thin,
+            chains=chains,
+            population=population,
+            seed=seed,
+            sampler_kwargs=sampler_kwargs or None,
+            progress_callback=progress_callback,
+            abort_test=abort_test,
+        )
+
     @property
     def chi2(self) -> float | None:
         """Total chi-squared across all fitted datasets, or None if no fit has been performed."""
diff --git a/tests/test_bayesian.py b/tests/test_bayesian.py
new file mode 100644
index 00000000..3de2bd3f
--- /dev/null
+++ b/tests/test_bayesian.py
@@ -0,0 +1,241 @@
+# SPDX-FileCopyrightText: 2026 EasyReflectometry contributors <https://github.com/easyscience>
+# SPDX-License-Identifier: BSD-3-Clause
+"""Tests for the Bayesian analysis module."""
+
+import numpy as np
+import pytest
+
+
+@pytest.fixture
+def sample_draws():
+    """Generate synthetic posterior draws for testing."""
+    rng = np.random.default_rng(42)
+    n_samples = 100
+    # Two parameters: 'thickness' and 'sld'
+    thickness = rng.normal(loc=250, scale=10, size=n_samples)
+    sld = rng.normal(loc=2.0, scale=0.2, size=n_samples)
+    draws = np.column_stack([thickness, sld])
+    param_names = ['Film_thickness', 'Film_sld']
+    return draws, param_names
+
+
+class TestPosteriorSummary:
+    def test_returns_string(self, sample_draws):
+        from easyreflectometry.analysis.bayesian import posterior_summary
+
+        draws, param_names = sample_draws
+        result = posterior_summary(draws, param_names)
+        assert isinstance(result, str)
+        assert 'parameter' in result
+        assert 'mean' in result
+        assert 'sd' in result
+
+    def test_contains_param_names(self, sample_draws):
+        from easyreflectometry.analysis.bayesian import posterior_summary
+
+        draws, param_names = sample_draws
+        result = posterior_summary(draws, param_names)
+        for name in param_names:
+            assert name in result
+
+
+class TestCredibleIntervals:
+    def test_returns_dict(self, sample_draws):
+        from easyreflectometry.analysis.bayesian import credible_intervals
+
+        draws, param_names = sample_draws
+        result = credible_intervals(draws, param_names)
+        assert isinstance(result, dict)
+        for name in param_names:
+            assert name in result
+            lo, hi = result[name]
+            assert lo < hi
+
+    def test_alpha_95_coverage(self, sample_draws):
+        from easyreflectometry.analysis.bayesian import credible_intervals
+
+        draws, param_names = sample_draws
+        result = credible_intervals(draws, param_names, alpha=0.95)
+        for i, name in enumerate(param_names):
+            lo, hi = result[name]
+            # 95% interval should contain at least 90% of samples
+            col = draws[:, i]
+            inside = np.sum((col >= lo) & (col <= hi))
+            assert inside / len(col) >= 0.90
+
+    def test_alpha_50_narrower(self, sample_draws):
+        from easyreflectometry.analysis.bayesian import credible_intervals
+
+        draws, param_names = sample_draws
+        ci_95 = credible_intervals(draws, param_names, alpha=0.95)
+        ci_50 = credible_intervals(draws, param_names, alpha=0.50)
+        for name in param_names:
+            assert (ci_95[name][1] - ci_95[name][0]) > (ci_50[name][1] - ci_50[name][0])
+
+
+class TestPosteriorResults:
+    def test_repr(self, sample_draws):
+        from easyreflectometry.analysis.bayesian import PosteriorResults
+
+        draws, param_names = sample_draws
+        pr = PosteriorResults(draws, param_names)
+        rep = repr(pr)
+        assert 'PosteriorResults' in rep
+        assert str(draws.shape[0]) in rep
+
+    def test_summary_delegates(self, sample_draws):
+        from easyreflectometry.analysis.bayesian import PosteriorResults
+
+        draws, param_names = sample_draws
+        pr = PosteriorResults(draws, param_names)
+        summary_str = pr.summary()
+        assert isinstance(summary_str, str)
+        assert 'parameter' in summary_str
+
+    def test_credible_interval_delegates(self, sample_draws):
+        from easyreflectometry.analysis.bayesian import PosteriorResults
+
+        draws, param_names = sample_draws
+        pr = PosteriorResults(draws, param_names)
+        ci = pr.credible_interval(alpha=0.95)
+        assert isinstance(ci, dict)
+        for name in param_names:
+            assert name in ci
+
+
+class TestPosteriorPredictiveReflectivity:
+    def test_returns_tuples(self, sample_draws):
+        """Test with a mock model that returns a constant array."""
+        from unittest.mock import MagicMock
+
+        from easyreflectometry.analysis.bayesian import posterior_predictive_reflectivity
+
+        draws, param_names = sample_draws
+        mock_model = MagicMock()
+        mock_model.unique_name = 'test_model'
+        mock_model.interface = MagicMock()
+        mock_model.interface.fit_func = MagicMock(return_value=np.ones(50))
+        mock_model.get_parameters = MagicMock(return_value=[])
+
+        q_values = np.linspace(0.01, 0.3, 50)
+        median, lower, upper = posterior_predictive_reflectivity(
+            draws,
+            param_names,
+            mock_model,
+            q_values,
+            n_samples=20,
+        )
+        assert median.shape == (50,)
+        assert lower.shape == (50,)
+        assert upper.shape == (50,)
+
+
+class TestPosteriorPredictiveSLDProfile:
+    def test_returns_tuples(self, sample_draws):
+        """Test with a mock model that returns constant z and sld."""
+        from unittest.mock import MagicMock
+
+        from easyreflectometry.analysis.bayesian import posterior_predictive_sld_profile
+
+        draws, param_names = sample_draws
+        mock_model = MagicMock()
+        mock_model.unique_name = 'test_model'
+        mock_model.interface = MagicMock()
+        mock_model.interface.sld_profile = MagicMock(return_value=(np.linspace(0, 500, 100), np.ones(100) * 2.0))
+        mock_model.get_parameters = MagicMock(return_value=[])
+
+        z, median, lower, upper = posterior_predictive_sld_profile(
+            draws,
+            param_names,
+            mock_model,
+            n_samples=20,
+        )
+        assert z.shape == (100,)
+        assert median.shape == (100,)
+        assert lower.shape == (100,)
+        assert upper.shape == (100,)
+
+
+class TestCornerPlot:
+    def test_plot_corner_does_not_crash(self, sample_draws):
+        """Test that plot_corner does not crash when corner is available."""
+        import matplotlib
+
+        matplotlib.use('Agg')  # Non-interactive backend for testing
+
+        try:
+            from easyreflectometry.analysis.bayesian import plot_corner
+
+            draws, param_names = sample_draws
+            plot_corner(draws, param_names)
+        except ImportError:
+            pytest.skip('corner library not installed')
+
+
+class TestSaveRestoreParameterState:
+    def test_save_and_restore(self):
+        """Test that parameter state save/restore works correctly."""
+        from easyreflectometry.analysis.bayesian import _restore_parameter_state
+        from easyreflectometry.analysis.bayesian import _save_parameter_state
+
+        # Use simple objects that support attribute assignment
+        class MockParam:
+            def __init__(self, unique_name, raw_value, error):
+                self.unique_name = unique_name
+                self.value = raw_value
+                self.error = error
+
+        param1 = MockParam('param_a', 1.5, 0.1)
+        param2 = MockParam('param_b', 3.0, 0.2)
+
+        class MockModel:
+            def get_parameters(self):
+                return [param1, param2]
+
+        model = MockModel()
+
+        state = _save_parameter_state(model)
+        assert state['param_a'] == (1.5, 0.1)
+        assert state['param_b'] == (3.0, 0.2)
+
+        # Modify values
+        param1.raw_value = 99.0
+        param1.value = 99.0
+        param2.raw_value = 99.0
+        param2.value = 99.0
+
+        _restore_parameter_state(model, state)
+        assert param1.value == 1.5
+        assert param1.error == 0.1
+        assert param2.value == 3.0
+        assert param2.error == 0.2
+
+
+class TestApplyDraw:
+    def test_apply_draw_updates_parameters(self):
+        """Test that _apply_draw sets parameter values correctly."""
+        from easyreflectometry.analysis.bayesian import _apply_draw
+
+        class MockParam:
+            def __init__(self, unique_name):
+                self.unique_name = unique_name
+                self.value = None
+
+        param_a = MockParam('thickness')
+        param_b = MockParam('sld')
+
+        class MockModel:
+            def get_parameters(self):
+                return [param_a, param_b]
+
+        model = MockModel()
+        draws = np.array([[250.0, 2.0], [260.0, 2.1]])
+        param_names = ['thickness', 'sld']
+
+        _apply_draw(model, draws, param_names, row=0)
+        assert param_a.value == 250.0
+        assert param_b.value == 2.0
+
+        _apply_draw(model, draws, param_names, row=1)
+        assert param_a.value == 260.0
+        assert param_b.value == 2.1
diff --git a/tests/test_fitting.py b/tests/test_fitting.py
index 28dfe0fa..a860fdb4 100644
--- a/tests/test_fitting.py
+++ b/tests/test_fitting.py
@@ -801,3 +801,236 @@ def _fake_fit(*, x, y, weights):
         fitter.fit_single_data_set_1d(data, objective='legacy_mask')
 
     assert len(captured['x'][0]) == 2  # one point dropped
+
+
+# ---------------------------------------------------------------------------
+# Tests for MultiFitter.sample (Bayesian MCMC)
+# ---------------------------------------------------------------------------
+
+
+class TestSampleRequiresBumpsEngine:
+    """sample() must raise when the core engine is not a BUMPS instance."""
+
+    def test_raises_runtime_error_when_not_bumps(self):
+        model = Model()
+        model.interface = CalculatorFactory()
+        fitter = MultiFitter(model)
+
+        data = sc.DataGroup({
+            'coords': {'Qz_0': sc.array(dims=['Qz_0'], values=np.linspace(0.01, 0.3, 10))},
+            'data': {'R_0': sc.array(dims=['Qz_0'], values=np.ones(10), variances=np.ones(10) * 0.01)},
+        })
+
+        with pytest.raises(RuntimeError, match='Bayesian sampling requires a BUMPS minimizer'):
+            fitter.sample(data)
+
+
+class TestSampleBasic:
+    """Basic sample() dispatch and return-value forwarding."""
+
+    def test_returns_core_result_dict(self):
+        """sample() returns whatever the core MultiFitter.sample() returns."""
+        model = Model()
+        model.interface = CalculatorFactory()
+        fitter = MultiFitter(model)
+
+        # Mock the core MultiFitter.sample to return a known dict
+        fake_result = {'draws': np.ones((10, 2)), 'param_names': ['a', 'b'], 'state': None, 'logp': None}
+        fitter.easy_science_multi_fitter = MagicMock()
+        fitter.easy_science_multi_fitter.sample = MagicMock(return_value=fake_result)
+
+        data = sc.DataGroup({
+            'coords': {'Qz_0': sc.array(dims=['Qz_0'], values=np.linspace(0.01, 0.3, 10))},
+            'data': {'R_0': sc.array(dims=['Qz_0'], values=np.ones(10), variances=np.ones(10) * 0.01)},
+        })
+
+        result = fitter.sample(data, samples=100, burn=20, thin=2, population=5)
+        assert result is fake_result
+
+    def test_forwards_hyperparams_to_core(self):
+        """Samples, burn, thin, population, chains, seed are forwarded to core."""
+        model = Model()
+        model.interface = CalculatorFactory()
+        fitter = MultiFitter(model)
+
+        captured = {}
+
+        def _fake_sample(*, x, y, weights, samples, burn, thin, chains, population, seed, **kwargs):
+            captured['samples'] = samples
+            captured['burn'] = burn
+            captured['thin'] = thin
+            captured['chains'] = chains
+            captured['population'] = population
+            captured['seed'] = seed
+            return {'draws': np.ones((10, 2)), 'param_names': ['a', 'b'], 'state': None, 'logp': None}
+
+        fitter.easy_science_multi_fitter = MagicMock()
+        fitter.easy_science_multi_fitter.sample = MagicMock(side_effect=_fake_sample)
+
+        data = sc.DataGroup({
+            'coords': {'Qz_0': sc.array(dims=['Qz_0'], values=np.linspace(0.01, 0.3, 10))},
+            'data': {'R_0': sc.array(dims=['Qz_0'], values=np.ones(10), variances=np.ones(10) * 0.01)},
+        })
+
+        fitter.sample(data, samples=500, burn=100, thin=5, population=8, seed=42)
+        assert captured['samples'] == 500
+        assert captured['burn'] == 100
+        assert captured['thin'] == 5
+        assert captured['chains'] is None  # population is the canonical param
+        assert captured['population'] == 8
+        assert captured['seed'] == 42
+
+    def test_forwards_chains_as_population(self):
+        """'chains' argument is forwarded as the 'chains' param to core (aliased to pop there)."""
+        model = Model()
+        model.interface = CalculatorFactory()
+        fitter = MultiFitter(model)
+
+        captured = {}
+
+        def _fake_sample(*, x, y, weights, chains, **kwargs):
+            captured['chains'] = chains
+            return {'draws': np.ones((10, 2)), 'param_names': ['a', 'b'], 'state': None, 'logp': None}
+
+        fitter.easy_science_multi_fitter = MagicMock()
+        fitter.easy_science_multi_fitter.sample = MagicMock(side_effect=_fake_sample)
+
+        data = sc.DataGroup({
+            'coords': {'Qz_0': sc.array(dims=['Qz_0'], values=np.linspace(0.01, 0.3, 10))},
+            'data': {'R_0': sc.array(dims=['Qz_0'], values=np.ones(10), variances=np.ones(10) * 0.01)},
+        })
+
+        fitter.sample(data, samples=100, burn=20, thin=2, chains=6)
+        assert captured['chains'] == 6
+
+
+class TestSampleInitializer:
+    """initializer parameter is forwarded via sampler_kwargs."""
+
+    def test_initializer_passed_as_sampler_kwargs_init(self):
+        """initializer='lhs' should be passed as sampler_kwargs={'init': 'lhs'} to core."""
+        model = Model()
+        model.interface = CalculatorFactory()
+        fitter = MultiFitter(model)
+
+        captured = {}
+
+        def _fake_sample(*, sampler_kwargs, **kwargs):
+            captured['sampler_kwargs'] = sampler_kwargs
+            return {'draws': np.ones((10, 2)), 'param_names': ['a', 'b'], 'state': None, 'logp': None}
+
+        fitter.easy_science_multi_fitter = MagicMock()
+        fitter.easy_science_multi_fitter.sample = MagicMock(side_effect=_fake_sample)
+
+        data = sc.DataGroup({
+            'coords': {'Qz_0': sc.array(dims=['Qz_0'], values=np.linspace(0.01, 0.3, 10))},
+            'data': {'R_0': sc.array(dims=['Qz_0'], values=np.ones(10), variances=np.ones(10) * 0.01)},
+        })
+
+        fitter.sample(data, samples=100, burn=20, thin=2, initializer='lhs')
+        assert captured['sampler_kwargs'] == {'init': 'lhs'}
+
+    def test_initializer_none_omits_sampler_kwargs(self):
+        """When initializer is None, sampler_kwargs should be None, not an empty dict."""
+        model = Model()
+        model.interface = CalculatorFactory()
+        fitter = MultiFitter(model)
+
+        captured = {}
+
+        def _fake_sample(*, sampler_kwargs, **kwargs):
+            captured['sampler_kwargs'] = sampler_kwargs
+            return {'draws': np.ones((10, 2)), 'param_names': ['a', 'b'], 'state': None, 'logp': None}
+
+        fitter.easy_science_multi_fitter = MagicMock()
+        fitter.easy_science_multi_fitter.sample = MagicMock(side_effect=_fake_sample)
+
+        data = sc.DataGroup({
+            'coords': {'Qz_0': sc.array(dims=['Qz_0'], values=np.linspace(0.01, 0.3, 10))},
+            'data': {'R_0': sc.array(dims=['Qz_0'], values=np.ones(10), variances=np.ones(10) * 0.01)},
+        })
+
+        fitter.sample(data, samples=100, burn=20, thin=2)
+        assert captured['sampler_kwargs'] is None
+
+
+class TestSampleZeroVariance:
+    """Zero-variance handling in the sample() data-preparation path."""
+
+    def test_hybrid_transforms_zero_variance_points(self):
+        """sample() uses the objective from constructor to prepare data arrays."""
+        import warnings
+
+        model = Model()
+        model.interface = CalculatorFactory()
+        # Use legacy_mask so zero-variance points are dropped
+        fitter = MultiFitter(model, objective='legacy_mask')
+
+        captured = {}
+
+        def _fake_sample(*, x, y, weights, **kwargs):
+            captured['x'] = x
+            captured['y'] = y
+            captured['weights'] = weights
+            return {'draws': np.ones((10, 2)), 'param_names': ['a', 'b'], 'state': None, 'logp': None}
+
+        fitter.easy_science_multi_fitter = MagicMock()
+        fitter.easy_science_multi_fitter.sample = MagicMock(side_effect=_fake_sample)
+
+        qz = np.linspace(0.01, 0.3, 10)
+        r = np.exp(-qz * 50)
+        var = np.ones(10) * 0.01
+        var[3:5] = 0.0  # 2 zero-variance points
+
+        data = sc.DataGroup({
+            'coords': {'Qz_0': sc.array(dims=['Qz_0'], values=qz)},
+            'data': {'R_0': sc.array(dims=['Qz_0'], values=r, variances=var)},
+        })
+
+        with warnings.catch_warnings(record=True) as w:
+            warnings.simplefilter('always')
+            fitter.sample(data, samples=100, burn=20, thin=2)
+
+        # legacy_mask should drop the 2 zero-variance points
+        assert len(captured['x'][0]) == 8
+        assert len(captured['y'][0]) == 8
+        assert len(captured['weights'][0]) == 8
+
+        mask_warnings = [str(ww.message) for ww in w if 'Masked' in str(ww.message)]
+        assert len(mask_warnings) == 1
+        assert '2 data point(s)' in mask_warnings[0]
+
+    def test_per_call_objective_override(self):
+        """sample() respects per-call objective override."""
+        import warnings
+
+        model = Model()
+        model.interface = CalculatorFactory()
+        fitter = MultiFitter(model, objective='legacy_mask')  # default
+
+        captured = {}
+
+        def _fake_sample(*, x, y, weights, **kwargs):
+            captured['x'] = x
+            captured['y'] = y
+            return {'draws': np.ones((10, 2)), 'param_names': ['a', 'b'], 'state': None, 'logp': None}
+
+        fitter.easy_science_multi_fitter = MagicMock()
+        fitter.easy_science_multi_fitter.sample = MagicMock(side_effect=_fake_sample)
+
+        qz = np.linspace(0.01, 0.3, 10)
+        r = np.exp(-qz * 50)
+        var = np.ones(10) * 0.01
+        var[3:5] = 0.0
+
+        data = sc.DataGroup({
+            'coords': {'Qz_0': sc.array(dims=['Qz_0'], values=qz)},
+            'data': {'R_0': sc.array(dims=['Qz_0'], values=r, variances=var)},
+        })
+
+        # Override to hybrid — should keep all 10 points
+        with warnings.catch_warnings(record=True):
+            warnings.simplefilter('always')
+            fitter.sample(data, samples=100, burn=20, thin=2, objective='hybrid')
+
+        assert len(captured['x'][0]) == 10  # all points kept (Mighell-substituted)