When is a Bayesian analysis genuinely worth the extra effort?

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Answer

$When you have real prior information, when the sample is small, or when you need the probability statement itself.$
$With little data, a weakly informative prior stabilizes estimates that maximum likelihood pushes to absurd values, which is why hierarchical models are standard for many small groups such as per-store or per-user effects: partial pooling shrinks noisy groups toward the overall mean by exactly as much as the data warrants.$
$It is also the right frame when a decision needs the probability that an effect exceeds a threshold, since that is a statement about the parameter and only a posterior supports it.$
$Where it is not worth it is a large-sample, well-identified problem with a single parameter, because the posterior will match the likelihood and you will have added computational and communication cost for no inferential gain.$

Check yourself — multiple choice

Always, it is strictly better
With genuine prior information, small samples where hierarchical partial pooling stabilizes estimates, or when a decision needs the probability that an effect exceeds a threshold
Never in industry
Only when you lack data entirely

Priors and hierarchical shrinkage pay off with sparse data; with large samples the posterior tracks the likelihood.

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