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6 changes: 3 additions & 3 deletions lectures/Probability Theory Review.jl
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Expand Up @@ -72,7 +72,7 @@ md"""
- [Edwin Jaynes, Probability Theory–The Logic of Science (2003)](https://bayes.wustl.edu/etj/science.pdf.html)
- Brilliant book on the Bayesian view of probability theory. Just for fun, scan the annotated bibliography and references.

- [Aubrey Clayton, Bernoulli's Fallacy–Statistical Illogic and the Crisis of Modern Science (2021)](https://aubreyclayton.com/bernoulli)
- [Aubrey Clayton, Bernoulli's Fallacy–Statistical Illogic and the Crisis of Modern Science (2021)](https://aubreyclayton.com/bernoulli.html)
- A very readable account of the history of statistics and probability theory. Discusses why most popular statistics recipes are very poor scientific analysis tools. Use probability theory instead!

- [Ariel Caticha, Entropic Inference and the Foundations of Physics (2012)](https://github.com/bmlip/course/blob/main/assets/files/Caticha-2012-Entropic-Inference-and-the-Foundations-of-Physics.pdf), pp.7-56 (ch.2: probability)
Expand Down Expand Up @@ -325,7 +325,7 @@ The Bayesian viewpoint is clearly favored in the machine learning community. (In

# ╔═╡ 3e198336-d294-11ef-26fd-03cd15876486
md"""
Aubrey Clayton, in his wonderful book [Bernoulli's fallacy](https://aubreyclayton.com/bernoulli) (2021), writes about this issue:
Aubrey Clayton, in his wonderful book [Bernoulli's fallacy](https://aubreyclayton.com/bernoulli.html) (2021), writes about this issue:

> “Compared with Bayesian methods, standard [frequentist] statistical techniques use only a small fraction of the available information about a research hypothesis (how well it predicts some observation), so naturally they will struggle when that limited information proves inadequate. Using standard statistical methods is like driving a car at night on a poorly lit highway: to keep from going in a ditch, we could build an elaborate system of bumpers and guardrails and equip the car with lane departure warnings and sophisticated navigation systems, and even then we could at best only drive to a few destinations. Or we could turn on the headlights.”

Expand Down Expand Up @@ -1489,7 +1489,7 @@ p( D=1 &| T=1) \\\\

Note that ``p(\\text{sick}|\\text{positive test}) = $(n(result))`` while ``p(\\text{positive test} | \\text{sick}) = $(n(sensitivity))``. This is a huge difference that is sometimes called the "medical test paradox" or the [base rate fallacy](https://en.wikipedia.org/wiki/Base_rate_fallacy).

Many people have trouble distinguishing ``p(A|B)`` from ``p(B|A)`` in their heads. This has led to major negative consequences. For instance, unfounded convictions in the legal arena and numerous unfounded conclusions in the pursuit of scientific results. See [Ioannidis (2005)](https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.0020124) and [Clayton (2021)](https://aubreyclayton.com/bernoulli).
Many people have trouble distinguishing ``p(A|B)`` from ``p(B|A)`` in their heads. This has led to major negative consequences. For instance, unfounded convictions in the legal arena and numerous unfounded conclusions in the pursuit of scientific results. See [Ioannidis (2005)](https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.0020124) and [Clayton (2021)](https://aubreyclayton.com/bernoulli.html).

""")
end
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6 changes: 3 additions & 3 deletions mlss/Probability Theory Review.jl
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Expand Up @@ -705,7 +705,7 @@ md"""
- **Edwin Jaynes, Probability Theory–The Logic of Science (2003)**
- Brilliant book on the Bayesian view of probability theory. Just for fun, scan the annotated bibliography and references.

- [Aubrey Clayton, Bernoulli's Fallacy–Statistical Illogic and the Crisis of Modern Science (2021)](https://aubreyclayton.com/bernoulli)
- [Aubrey Clayton, Bernoulli's Fallacy–Statistical Illogic and the Crisis of Modern Science (2021)](https://aubreyclayton.com/bernoulli.html)
- A very readable account of the history of statistics and probability theory. Discusses why most popular statistics recipes are very poor scientific analysis tools. Use probability theory instead!

- [Ariel Caticha, Entropic Inference and the Foundations of Physics (2012)](https://github.com/bmlip/course/blob/main/assets/files/Caticha-2012-Entropic-Inference-and-the-Foundations-of-Physics.pdf), pp.7-56 (ch.2: probability)
Expand Down Expand Up @@ -806,7 +806,7 @@ The Bayesian viewpoint is clearly favored in the machine learning community. (In

# ╔═╡ 3e198336-d294-11ef-26fd-03cd15876486
md"""
Aubrey Clayton, in his wonderful book [Bernoulli's fallacy](https://aubreyclayton.com/bernoulli) (2021), writes about this issue:
Aubrey Clayton, in his wonderful book [Bernoulli's fallacy](https://aubreyclayton.com/bernoulli.html) (2021), writes about this issue:

> “Compared with Bayesian methods, standard [frequentist] statistical techniques use only a small fraction of the available information about a research hypothesis (how well it predicts some observation), so naturally they will struggle when that limited information proves inadequate. Using standard statistical methods is like driving a car at night on a poorly lit highway: to keep from going in a ditch, we could build an elaborate system of bumpers and guardrails and equip the car with lane departure warnings and sophisticated navigation systems, and even then we could at best only drive to a few destinations. Or we could turn on the headlights.”

Expand Down Expand Up @@ -1446,7 +1446,7 @@ p( D=1 &| T=1) \\\\

Note that ``p(\\text{sick}|\\text{positive test}) = $(n(result))`` while ``p(\\text{positive test} | \\text{sick}) = $(n(sensitivity))``. This is a huge difference that is sometimes called the "medical test paradox" or the [base rate fallacy](https://en.wikipedia.org/wiki/Base_rate_fallacy).

Many people have trouble distinguishing ``p(A|B)`` from ``p(B|A)`` in their heads. This has led to major negative consequences. For instance, unfounded convictions in the legal arena and numerous unfounded conclusions in the pursuit of scientific results. See [Ioannidis (2005)](https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.0020124) and [Clayton (2021)](https://aubreyclayton.com/bernoulli).
Many people have trouble distinguishing ``p(A|B)`` from ``p(B|A)`` in their heads. This has led to major negative consequences. For instance, unfounded convictions in the legal arena and numerous unfounded conclusions in the pursuit of scientific results. See [Ioannidis (2005)](https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.0020124) and [Clayton (2021)](https://aubreyclayton.com/bernoulli.html).

""")
end
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