A Bayesian Comparison of Different Classes of Dynamic Models Using Empirical Data.

摘要

This paper deals with the Bayesian methods of comparing different types of dynamical structures for representing the given set of observations. Specifically, given that a given process y obeys one of r distinct stochastic difference equations each involves a vector of unknown parameters, we compute the posterior probability that a set of observations y(1),...,y(N) obey the i-th equation, after making suitable assumptions about the prior probability distribution of the parameters in each class. The difference equations can be nonlinear in the variable y but should be linear in the parameter vector to the data (i.e., zero residual variance) etc. The method can be used not only to compare different types of structures but also to determine a reliable estimate of spectral density of process. We compare the method in detail with the hypothesis testing method, maximum entropy spectral analysis method and other methods and give a number of illustrative examples.