Parameter inference in a probabilistic model from data: Regulation of transition rate in the Monte Carlo method

We consider the inference of parameters in a probabilistic model from a data set, which is generated by an unknown probabilistic model. The Monte Carlo method is a tool for obtaining a data set obeying a given probability distribution. A set of transition rates is required to satisfy three conditions (irreducible, aperiodic, and stationary) for a sampled data set to represent a probability distribution. We utilize the stationary condition of a probability distribution with respect to transition rates to infer parameters. A frequency distribution by a data set substitutes for an unknown probability distribution in the condition. Our method includes minimum probability flow as a special case and becomes superior to it as the number of samples increases.