Researchers are shifting towards Bayesian statistical methods, given the increasing resources and computational support for Bayesian modeling. The classical, or frequentist, approach to statistical inference has commonly been used to answer research questions using techniques such as least squares regression and analysis of variance. Bayesian methods provide an alternative modeling approach to these techniques that combines prior knowledge via a statistical distribution with data to draw conclusions.

In Bayesian statistics, unknown parameters are regarded as random, contrary to the frequentist approach, which assumes unknown fixed parameters. Frequentist parameter estimation is commonly determined by the likelihood function and leads to interpretations of probability based on the frequency of findings in the data. However, Bayesian parameter estimation combines prior beliefs with data in the form of a distribution. Beliefs about the unknown parameter before observing data are used to assign a subjective prior distribution. The likelihood is then formed conditioned on observed data, and the beliefs are updated by applying Bayes’ rule to produce a posterior distribution. Parameter estimates can then be determined from the posterior distribution using relevant information leading to the Bayesian interpretation of probability that describes the certainty of the finding.

Bayesian inference incorporates prior knowledge with observed data, whereas frequentist inference relies solely on observed data.

If you are interested in learning more about the Bayesian approach or would like to schedule an appointment for help with research, please contact OIT HelpDesk at 865-974-9900.