20
21
// logBeta returns log(Beta(a, b)) = lgamma(a) + lgamma(b) - lgamma(a+b).
23
>
la, _ := math.Lgamma(a)
24
>
lb, _ := math.Lgamma(b)
25
>
lab, _ := math.Lgamma(a + b)
26
>
return la + lb - lab
27
>
}
28
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// logBetaBinomial returns the log marginal likelihood of observing k failures
30
// in n trials with a Beta(alpha, beta) prior on the failure probability.
31
// With Beta(1,1) prior this is the log Beta-Binomial marginal likelihood.
33
>
return logBeta(float64(k)+alpha, float64(n-k)+beta) - logBeta(alpha, beta)
34
>
}
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36
// logSumExpNormalize converts log-weights to probabilities using the log-sum-exp trick