Bayesian Estimations with Isotropic and Anisotropic Matrices for a Multinomial Logit Model

AbstractThis paper studies a Metropolis-Hastings (MH) algorithm of unknown parameters for a multinomial logit model. The MH algorithm which is one of the Bayesian estimation requires prior and proposal distributions. A selection of the prior and proposal distributions is an important issue of the Bayesian estimation. However, there is no a decisive approach for the determination of prior and proposal distributions. A posterior distribution is obtained from two distributions. The MH algorithm generates samples from the posterior distribution of the unknown parameters. Unless we give appropriate distributions, it leads to an inappropriate posterior distribution. In this paper, we discuss differences in the behaviors of autocorrelation functions in a selection of the proposal distributions