Robust Bayesian inference via coarsening
Speaker
Jeff Miller
Harvard
Host
Tamara Broderick
Robust Bayesian inference via coarsening
The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a Bayesian procedure, particularly when the data set is large. We introduce a simple, coherent approach to Bayesian inference that improves robustness to small departures from the model: rather than conditioning on the observed data exactly, one conditions on the event that the model generates data close to the observed data, with respect to a given statistical distance. When closeness is defined in terms of relative entropy, the resulting "coarsened posterior" can be approximated by simply raising the likelihood to a certain fractional power, making the method computationally efficient and easy to implement in practice. We illustrate with real and simulated data, and provide theoretical results.
The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a Bayesian procedure, particularly when the data set is large. We introduce a simple, coherent approach to Bayesian inference that improves robustness to small departures from the model: rather than conditioning on the observed data exactly, one conditions on the event that the model generates data close to the observed data, with respect to a given statistical distance. When closeness is defined in terms of relative entropy, the resulting "coarsened posterior" can be approximated by simply raising the likelihood to a certain fractional power, making the method computationally efficient and easy to implement in practice. We illustrate with real and simulated data, and provide theoretical results.