Classification of Priors

In Bayesian statistics, priors are classified based on the amount of information content in it. Below discussed are some of the types of priors:

• Informative Priors
• Weakly Informative Priors
• Non-informative Priors
• Improper Priors

Informative Priors

These kind of priors have detailed knowledge or are decided from the expert opinions. These priors are chosen based on the past or historical data, or under expert guidance. These priors have a significant impact on the posterior distribution. These kind of priors are useful only when we have strong information that can drive the analysis.

Weakly Informative Priors

These kind of priors are in-between informative and non-informative priors. They have some prior knowledge but cannot eventually influence the posterior distribution. These priors provide some regularization and also prevents from noise fitting but it still allows the data to influence the posterior distribution. Normal prior with the high variance can be considered as weakly informative priors.

Non-informative Priors

Non informative priors are also known as uninformative priors. These kind of priors have very little or practically no prior knowledge about the parameter. They have a minimum influence to posterior distribution, allowing the data to primarily drive the inference. Uniform prior is an example of non-informative prior that assigns equal probabilities to all the possible outcomes, reflecting the lack of prior knowledge.

Improper Priors

These are non-informative priors but it does not integrate over one parameter space, i.e. they do not have a valid probability distribution. These kind of priors are still used in Bayesian statistics as long as the resulting posterior distribution remains proper which integrates over one parameter space. These priors are generally used for parameters with unbounded ranges such as it uses 1/θ over a parameter θ.

Understanding Prior probability and its study is important as it helps us to combine the new information with the past data to make better decisions and improve accuracy. Prior probability forms as a foundation of Bayesian Theorem which allows us to integrate the new data with the old data to improve the estimation accuracy.

In this article, we will take a deeper look into prior probability, its applications in various fields and some examples for understanding it better.