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Additional info for Bayesian analysis of a time series of counts with covariates an application to the control of an infectious disease
We might argue that when we have no reason to assume otherwise, we can just consider each conjecture equally plausible and compare the counts directly. But often we do have reason to assume otherwise. 24 2. 4. The garden of forking data, showing for each possible composition of the bag the forking paths that are logically compatible with the data. Rethinking: Justification. Using these counts of paths through the garden as measures of relative plausibility can be justified in several ways. 39 There are several other justifications that lead to the same mathematical procedure.
Justifications and philosophy motivate procedures, but it is the results that matter. The many successful real world applications of Bayesian inference may be all the justification you need. 40 That is luckily no longer true. Just be careful not to assume that because Bayesian inference is justified that no other approach can also be justified. Golems come in many types, and some of all types are useful. 1. 2. Using prior information. We may have prior information about the relative plausibility of each conjecture.
The likelihood in each case is the same, the likelihood for the globe toss data. The priors however vary. As a result, the posterior distributions vary. Rethinking: Bayesian data analysis isn’t about Bayes’ theorem. A common notion about Bayesian data analysis, and Bayesian inference more generally, is that it is distinguished by the use of Bayes’ theorem. This is a mistake. Inference under any probability concept will eventually make use of Bayes’ theorem. Common introductory examples of “Bayesian” analysis using HIV and DNA testing are not uniquely Bayesian.