Robust Bayesian inference via coarsening.

Area of Science:

• Statistics
• Computational Statistics

Background:

• Standard Bayesian inference assumes data perfectly fits the model, but minor deviations can significantly skew results.
• Robustness in statistical modeling is crucial for reliable inference when model assumptions are imperfectly met.

Purpose of the Study:

• To develop a novel Bayesian inference approach enhancing robustness against small model departures.
• To provide a method that maintains reliable outcomes even when data distributions slightly deviate from the chosen model.

Main Methods:

• Introduced a new Bayesian inference technique by conditioning on model-generated data being 'close' to observed data, using relative entropy for closeness.
• Approximated the resulting 'coarsened' posterior by tempering the likelihood function (raising to a fractional power).
• Applied standard inference algorithms and derived analytical solutions for conjugate priors.

Main Results:

• The proposed method demonstrates improved robustness to minor violations of the model assumption.
• Tempering the likelihood provides a practical approximation for the robust Bayesian inference.
• The approach yielded accurate results when tested on mixture and autoregressive models with real and simulated data.

Conclusions:

• The novel Bayesian inference method offers enhanced reliability by addressing model misspecification.
• Likelihood tempering is an effective technique for achieving robustness in Bayesian analysis.
• This approach is broadly applicable across various statistical models and data types.