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Correcting Bayesian inference footnotes (#521)

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Corrected a few typos and removed the incorrect statement about Dutch Book arguments. The original phrasing suggested that Dutch Book arguments expose contradictions in Bayesian reasoning, when in fact the reverse is true. Dutch Book arguments demonstrate that only probability assignments consistent with Bayesian reasoning avoid self-contradiction. Any other system of belief or betting odds leads to guaranteed loss.
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Wesley DeMontigny
2025-10-28 13:03:16 -04:00
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parent b3fb36db30
commit 9d3b98948b
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user-guide/modules/ROOT/pages/task-machine-learning.adoc
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@@ -566,7 +566,7 @@ The _kernel trick_ is a method used in machine learning to apply a linear classi
[#footnote3]
link:#footnote3-location[(3)]
_Bayesion inference_ is used to calculate a probability for a hypothesis (using Bayes theorum), based on existing evidence, and then update it as more data becomes available. This approach has proved to be robust as it does not require the sample size to be known in advance, and has a wide range of applications. There are downsides to this popular inference method, including a kind of self-contradiction called a _Dutch Book_. A _Markov chain_ describes a sequence of possible events, where the probability of an event occurring in the chain is _solely_ dependent on the previous event. Markov chains are popular in statistical modeling, partly because of the simplification it provides in that only the current state of affairs is important - not any previous history. Markov chain _Monte Carlo_ methods are often used to study probability distributions too complex for analytical methods alone.
_Bayesian inference_ is used to calculate a probability for a hypothesis (using Bayes theorem), based on existing evidence, and then update it as more data becomes available. This approach has proved to be robust as it does not require the sample size to be known in advance, and has a wide range of applications. A _Markov chain_ describes a sequence of possible events, where the probability of an event occurring in the chain is _solely_ dependent on the previous event. Markov chains are popular in statistical modeling, partly because of the simplification it provides in that only the current state of affairs is important - not any previous history. Markov chain _Monte Carlo_ methods are often used to study probability distributions too complex for analytical methods alone.
[#footnote4]
link:#footnote4-location[(4)]