A reversible jump MCMC algorithm for Bayesian curve fitting by using smooth transition regression models

This paper proposes a Bayesian algorithm to estimate the parameters of a smooth transition regression model. With in this model, time series are divided into segments and a linear regression analysis is performed on each segment. Unlike a piecewise regression model, smooth transition functions are introduced to model smooth transitions between the sub-models. Appropriate prior distributions are associated with each parameter to penalize a data-driven criterion, leading to a fully Bayesian model. Then, a reversible jump Markov Chain Monte Carlo algorithm is derived to sample the parameter posterior distributions. It allows one to compute standard Bayesian estimators, providing a sparse representation of the data. Results are obtained for real-world electrical transients with a view to non-intrusive load monitoring applications.