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Prior and Posterior Distributions

What Is a Prior?

In Bayesian analysis, a prior distribution represents your beliefs about a parameter before seeing data. If you're estimating a coin's bias (probability of heads), your prior might be: Uniform(0,1)—'I have no idea, any bias is equally likely' (uninformative prior). Or Beta(50,50)—'I strongly believe the coin is fair, centered at 0.5 with little spread' (informative prior). The choice of prior is often criticized as subjective, but all statistical analyses involve subjective choices (what model to use, what significance level, which variables to include). The advantage of Bayesian priors is that the subjectivity is explicit and transparent, rather than hidden in analytical choices.

Prior and Posterior Distributions

What Is a Prior?

In Bayesian analysis, a prior distribution represents your beliefs about a parameter before seeing data. If you're estimating a coin's bias (probability of heads), your prior might be: Uniform(0,1)—'I have no idea, any bias is equally likely' (uninformative prior). Or Beta(50,50)—'I strongly believe the coin is fair, centered at 0.5 with little spread' (informative prior). The choice of prior is often criticized as subjective, but all statistical analyses involve subjective choices (what model to use, what significance level, which variables to include). The advantage of Bayesian priors is that the subjectivity is explicit and transparent, rather than hidden in analytical choices.