Informative Prior

TL;DR

• Uses past data or domain knowledge to shape the prior distribution in a Bayesian model.
• Can improve the accuracy of predictions and inferences by adding relevant information.
• Requires careful assessment of the relevance and reliability of the information; overreliance can introduce confirmation bias.

Definition

Informative priors are a type of prior probability distribution used in Bayesian statistics that are based on existing data or knowledge about the subject under study, in contrast to non-informative priors which provide little to no information about the likelihood of certain events or outcomes.

Explanation

An informative prior encodes relevant, previously known information into the prior distribution of a Bayesian model. Because it leverages historical data or domain knowledge, an informative prior can guide inference and prediction more strongly than a non-informative prior. This additional information can improve the accuracy of Bayesian analysis when the prior information is relevant and reliable.

Examples

Sales forecasting

Using past sales data to predict future sales of a product. The prior probability distribution would be based on historical sales data and reflect observed patterns (for example, stronger sales during the holiday season and weaker sales in the summer), yielding more accurate predictions of future sales.

Medical risk prediction

Using medical records to predict the likelihood of a patient developing a certain disease. The prior probability distribution would be based on the patient’s medical history, including any previous diagnoses and risk factors, providing insight into the likelihood of developing the disease and informing predictions and treatment recommendations.

Use cases

• Improving the accuracy of predictions and inferences in Bayesian analysis by providing additional information and context.

Notes or pitfalls

• The relevance and reliability of the data used to construct an informative prior must be carefully considered, as these affect result accuracy.
• Overreliance on an informative prior can lead to confirmation bias and hinder the ability to adapt to new information or changing circumstances.

Related terms

• Non-informative prior
• Prior probability distribution
• Bayesian statistics
• Bayesian analysis