
Contents
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What is step 1?
What is step 1?
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What is step 2?
What is step 2?
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What is step 3?
What is step 3?
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What is step 4?
What is step 4?
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How exactly do we compute the likelihood?
How exactly do we compute the likelihood?
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Which of the two hypotheses more closely matches the observed rate?
Which of the two hypotheses more closely matches the observed rate?
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If likelihood is a probability, how do we quantify this “consistency” in terms of probability?
If likelihood is a probability, how do we quantify this “consistency” in terms of probability?
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What is step 5?
What is step 5?
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Where are the priors in this equation?
Where are the priors in this equation?
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Where is the posterior probability of the Hamilton hypothesis in this equation?
Where is the posterior probability of the Hamilton hypothesis in this equation?
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Where are the likelihoods of the observed data under each hypothesis in this equation?
Where are the likelihoods of the observed data under each hypothesis in this equation?
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So, what is the posterior probability of the Hamilton hypothesis?
So, what is the posterior probability of the Hamilton hypothesis?
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How do we set the prior probabilities?
How do we set the prior probabilities?
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What if we found more papers known to be authored by Hamilton and Madison?
What if we found more papers known to be authored by Hamilton and Madison?
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Do the likelihoods of the data have to add to 1.0?
Do the likelihoods of the data have to add to 1.0?
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Did Mosteller and Wallace really use this approach?
Did Mosteller and Wallace really use this approach?
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Can we summarize this problem?
Can we summarize this problem?
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How does this problem differ from the Breast Cancer Problem in the last chapter?
How does this problem differ from the Breast Cancer Problem in the last chapter?
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5 The Author Problem: Bayesian Inference with Two Hypotheses
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Published:May 2019
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Abstract
The “Author Problem” provides a concrete example of Bayesian inference. This chapter draws on work by Frederick Mosteller and David Wallace, who used Bayesian inference to assign authorship for unsigned Federalist Papers. The Federalist Papers were a collection of papers known to be written during the American Revolution. However, some papers were unsigned by the author, resulting in disputed authorship. The chapter provides a very basic Bayesian analysis of the unsigned “Paper 54,” which was written by Alexander Hamilton or James Madison. The example illustrates the principles of Bayesian inference for two competing hypotheses, including the concepts of alternative hypothesis, prior probability distribution, posterior probability distribution, prior probability of a hypothesis, likelihood of the observed data, and posterior probability of a hypothesis.
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