Priors in bayesians

Noninformative priors: 1-tailed p value equals post prob for normal dist

• Uniform (flat): exploratory data analysis, no prior knowledge, simple models with few parameters, improper posteriors that do not integrate to 1, no regularization

• Jeffreys: some regularization to prevent overfitting with many parameters

Weakly informative priors:

• Normal Priors with Large Variance: L2 regularization (ridge), sensitive to the choice of variance, improper posteriors if the variance is too large, Bayesian neural network

• Cauchy: default neutral(0, 0.707), pessimistic cauchy(0, 1), optimistic cauchy(0, 0.5); heavy-tailed, outliers and extreme values, somw regularization to prevent overfitting

• t dist: heavy-tailed

• Unit information: mean 0 sd 2, may lead to improper posteriors

• Laplace: double exponential, L1 regularization (lasso), heavy-tailed

• Lognormal: positive numbers, heavy-tailed

• Pareto: positive numbers, heavy-tailed

• Half cauchy: default for var, positive numbers, residual var, variance components in random effects, sensitive to the choice of scale parameter

• Gamma: positive numbers, heavy-tailed, variance components in random effects, some regularization

• Inverse gamma: positive numbers, heavy-tailed, variance components in linear regression model with heteroscedastic errors, some regularization to prevent overfitting

• Beta: for [0, 1] binomial parameters

• Dirichlet: multinomial