Bayesian statistics: principles and benefits

http://library.wur.nl/frontis/bayes/03_o_hagan.pdf

This article is meant to summarize the basics of Bayesian statistics for beginners.

In Bayesian statistics:

• a statistical model is created to link data to parameters
• prior information about parameters is formulated
• inferences about parameters are derived from the resulting posterior distribution

Graphically, the narrower the curve, the tighter the parameters. The difference between frequentist methods and Bayesian analysis is the use of past information, which is principally subjective. It is important for the prior information to be defensible and reasonable. The author believes subjectivity is a strength of the system because it allows for the examination of posterior distributions from different informed observers.

Until the 1990s, computational tools for conducting Bayesian analysis were nascent or non-existent. While there are tools for the specialist available today, the general practitioner of Bayesian analysis will find there are few user friendly tools available.

The author enumerates a number of benefits for using Bayesian analysis. They are:

• It provides meaningful and intuitive inferences.
• It can answer complex questions cleanly and exactly.
• It makes use of all available information.
• It is well suited for decision-making.