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L1-inferencebasics

# See ref 4 we can interpret p d h as being the

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Unformatted text preview: said about the interpretation of the Marginal likelihood, or Integrated likelihood or Evidence (note, however, [3]). See Ref. [4] We can interpret p (D |H) as being the probability of our data if we accept our hypothesized model structure H (namely π (θ, D |H)) and integrate out our parameters p (D |H) = p (D |θ, H)π (θ|H)d θ. I’ll draw an example of p (D |H1 ) and p (D |H2 ) and discuss Occam’s razor [2]. Nick Jones Inference, Control and Driving of Natural Systems Model Comparison and Bayes Factors Given two models which are equivalent to two diﬀerent hypotheses about the data, H1 and H2 with respective prior probabilities p (H1 ) and p (H2 ), we can ask about the relative probabilities of the data under these hypotheses. This is given by the Bayes Factor. Bayes Factor B= p (D |H1 ) p (D |H2 ) This is a ratio of the marginal likelihoods or model evidence. A rule of thumb is that if B > 3 then there is substantial evidence against hypothesis 2 relative to 1. Nick Jones Inference, Control and Driving of Natural Systems Bayesian Protocol for Humans 1 Understand your problem and its context. 2 Formulate an appropriate probabilistic model which allows you to write down p (D |θ, H) a likelihood for your data D ....
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