Brief comparison of Bayesian and frequentist inference paradigms
| Bayesian | Frequentist | |
|---|---|---|
| Philosophy of probability | Quantification of uncertainty | Frequency of events |
| Data inference | P(hypothesis|data) “data driven” | P(data|hypothesis) |
| Decision rules | HDI, credible interval, ROPE, distribution of observed data distributions, Bayes’ factors | P-value, confidence interval, Type I/II error control |
| Model parameters | Distributions formed around uncertainty in observed data | Fixed but unknown values inferred from estimators (maximum likelihood/least squares) |
| Data distributions | Any distribution | Parametric models require data to follow normal distributions. Nonparametric methods are limited |
| Requires explicit declaration of prior distribution | Yes | No |
| Computational complexity | Higher | Lower |
| Advantages | Inference backed by evidence from observed data, a complete probabilistic description of experimental data, inference less dependent on sample size. Error control through prior and posterior predictive checks | Robust error control (with proper experimental design), quick and easy to implement |