A Bayes factor framework for unified parameter estimation and hypothesis testing

Area of Science:

• Statistical inference
• Bayesian statistics
• Quantitative analysis

Background:

• Bayes factors naturally measure statistical evidence for hypotheses.
• Current methods for parameter estimation have limitations.
• A unified framework for statistical inference is needed.

Purpose of the Study:

• To demonstrate the utility of Bayes factors for parameter estimation.
• To introduce a unified inference framework using Bayes factors.
• To provide practical tools for quantitative inferences in data analysis.

Main Methods:

• Utilizing Bayes factors as a function of the null hypothesis parameter value ('support curve').
• Inverting the support curve to obtain maximum evidence estimates (point estimates).
• Inverting the support curve to obtain support intervals (interval estimates).

Main Results:

• A unified framework for statistical inference is established.
• Bayes factors, point estimates, and interval estimates can be derived from a single plot.
• The method effectively handles nuisance parameters and is applicable to meta-analysis, replication studies, and logistic regression.

Conclusions:

• The proposed method offers a unified approach to statistical inference.
• Maximum evidence estimates and support intervals provide valuable alternatives to conventional methods.
• This framework enhances the practical value of quantitative inferences in various research applications.