Markov chain cycles reveal hidden patterns in Bayesian statistics
Thermodynamic Cyclic Processes with Markov Samplers in Bayesian Inference
Artificial Intelligence
Summary
Bayesian inference is a way to learn from data, but some problems are harder to understand than others. The authors compare a method called Markov chain Monte Carlo (MCMC) to how engines go through cycles, and they create a way to adjust this method while running it. They discover that if the data follows a simple, bell-shaped pattern (Gaussian), these cycles don’t produce extra 'work,' but if the data is more complicated (non-Gaussian), the cycles do produce work. This means their method can tell how complex or unusual the data is, which they tested using information about exploding stars called supernovae.
Bayesian inferenceMarkov chain Monte Carlothermodynamic cyclesGaussian distributionnon-Gaussianityensemble methodsadaptive algorithmsstatistical modelssupernova cosmologywork output
Authors
Heinrich von Campe, Bjoern Malte Schaefer
Abstract
The concept of Markov chain Monte Carlo (MCMC) cycles, an analogy to cyclic processes in heat engines, is presented in order to examine Bayesian inference problems. In this effort, we develop adaptive ensemble schedulers that allow the tuning of external parameters of a Bayesian canonical ensemble during an MCMC run, realising the MCMC cycles in practice. We run these cycles on different statistical models. As a fundamental insight, we find (both theoretically and in practice) that such systems can produce a non-zero net work output if and only if the considered model is non-Gaussian. As such, they may serve as a measure of non-Gaussianity in Bayesian inference, which we test on an example from supernova cosmology.