Frequentists treat parameters as fixed and probability as a long-run frequency, so they reason about how the data would vary over repeated samples. Bayesians treat parameters as uncertain, start from a prior distribution and update it with the data into a posterior.
Card 1 of 244. Answer: Frequentists treat parameters as fixed and probability as a long-run frequency, so they reason about how the data would vary over repeated samples. Bayesians treat parameters as uncertain, start from a prior distribution and update it with the data into a posterior.
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The two schools answer different questions. Frequentist methods, such as p-values and confidence intervals, describe how a procedure behaves over hypothetical repeated samples. Bayesian methods use Bayes' theorem to combine a prior with the likelihood of the data and give a posterior distribution, so they can state the probability that a parameter lies in a range.
Example: a new campaign gets 3 conversions in 10 visits. The frequentist estimate is 0.3, with an exact 95% confidence interval of about 0.07 to 0.65. A Bayesian who encodes past campaigns as a Beta(2, 18) prior, centred on 10%, gets a Beta(5, 25) posterior: mean 5/30 ≈ 0.17, and a 95% probability that the rate is between about 0.06 and 0.32. The prior pulls a small sample towards what was known before.
In practice the two usually agree when data are plentiful, because the likelihood swamps the prior. Bayesian methods shine with small samples, hierarchical models and decisions that need a probability; their costs are choosing and defending a prior, and computation, often by MCMC sampling. The classic follow-up asks you to contrast a 95% confidence interval with a 95% credible interval.
