How do you interpret a Bayes factor?

hard

Answer

$\mathrm{BF}_{12}\; = \;p(D\; \mid \;M_{1})\; / \;p(D\; \mid \;M_{2})$
$M_{1}$
$H_{0}$
$Weakness: hypersensitive to prior choice for nuisance parameters (Lindley's paradox).$
$Alternative in practice: LOO-CV, WAIC, PSIS-LOO for predictive model comparison.$

Check yourself — multiple choice

Random
Ratio of marginal likelihoods; Jeffreys scale > 10 strong, > 100 decisive; symmetric $(\mathrm{supports}\;H_{0})$ ; prior-sensitive → also use LOO-CV / WAIC
Same as p-value
Not useful

Bayes factor: $p(D \mid \mathrm{M1}) / p(D \mid \mathrm{M2})$ ; symmetric; prior-sensitive.

#bayesian

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