Genya Kobayashi

Gibbs sampling methods for Bayesian quantile regression

This paper considers quantile regression models using an asymmetric Laplace distribution from a Bayesian point of view. We develop a simple and efficient Gibbs sampling algorithm for fitting the quantile regression model based on a location-scale mixture representation of the asymmetric Laplace distribution. It is shown that the resulting Gibbs sampler can be accomplished by sampling from either normal or generalized inverse Gaussian distribution. We also discuss some possible extensions of our approach, including the incorporation of a scale parameter, the use of double exponential prior, and a Bayesian analysis of Tobit quantile regression. The proposed methods are illustrated by both simulated and real data.

Generalized multiple-point Metropolis algorithms for approximate Bayesian computation

It is well known that the approximate Bayesian computation algorithm based on Markov chain Monte Carlo methods suffers from the sensitivity to the choice of starting values, inefficiency and a low acceptance rate. To overcome these problems, this study proposes a generalization of the multiple-point Metropolis algorithm, which proceeds by generating multiple-dependent proposals and then by selecting a candidate among the set of proposals on the basis of weights that can be chosen arbitrarily. The performance of the proposed algorithm is illustrated by using both simulated and real data.

A transdimensional approximate Bayesian computation using the pseudo-marginal approach for model choice

When the likelihood functions are either unavailable analytically or are computationally cumbersome to evaluate, it is impossible to implement conventional Bayesian model choice methods. Instead, approximate Bayesian computation (ABC) or the likelihood-free method can be used in order to avoid direct evaluation of the intractable likelihoods. This paper proposes a new Markov chain Monte Carlo (MCMC) method for model choice. This method is based on the pseudo-marginal approach and is appropriate for situations where the likelihood functions for the competing models are intractable. This method proposes jumps between the models with different dimensionalities without matching the dimensionalities. Therefore, it enables the construction of a flexible proposal distribution. The proposal distribution used in this paper is convenient to implement and works well in the context of ABC. Because the posterior model probabilities can be estimated simultaneously, it is expected that the proposed method will be useful, especially when the number of competing models is large. In the simulation study, a comparison between the proposed and existing methods is presented. The method is then applied to the model choice problem for an exchange return model.

Latent mixture modeling for clustered data

This article proposes a mixture modeling approach to estimating cluster-wise conditional distributions in clustered (grouped) data. We adapt the mixture-of-experts model to the latent distributions, and propose a model in which each cluster-wise density is represented as a mixture of latent experts with cluster-wise mixing proportions distributed as Dirichlet distribution. The model parameters are estimated by maximizing the marginal likelihood function using a newly developed Monte Carlo Expectation–Maximization algorithm. We also extend the model such that the distribution of cluster-wise mixing proportions depends on some cluster-level covariates. The finite sample performance of the proposed model is compared with some existing mixture modeling approaches as well as mixed effects models through the simulation studies. The proposed model is also illustrated with the posted land price data in Japan.

Approximate Bayesian computation for Lorenz curves from grouped data

This paper proposes a new Bayesian approach to estimate the Gini coefficient from the grouped data on the Lorenz curve. The proposed approach assumes a hypothetical income distribution and estimates the parameter by directly working on the likelihood function implied by the Lorenz curve of the income distribution from the grouped data. It inherits the advantages of two existing approaches through which the Gini coefficient can be estimated more accurately and a straightforward interpretation about the underlying income distribution is provided. Since the likelihood function is implicitly defined, the approximate Bayesian computational approach based on the sequential Monte Carlo method is adopted. The usefulness of the proposed approach is illustrated through the simulation study and the Japanese income data.