Hisayuki Hara

On connectivity of fibers with positive marginals in multiple logistic regression

In this paper we consider exact tests of a multiple logistic regression with categorical covariates via Markov bases. In many applications of multiple logistic regression, the sample size is positive for each combination of levels of the covariates. In this case we do not need a whole Markov basis, which guarantees connectivity of all fibers. We first give an explicit Markov basis for multiple Poisson regression. By the Lawrence lifting of this basis, in the case of bivariate logistic regression, we show a simple subset of the Markov basis which connects all fibers with a positive sample size for each combination of levels of covariates.

Markov bases for two-way subtable sum problems

Abstract It is well known that for two-way contingency tables with fixed row sums and column sums the set of square-free moves of degree two forms a Markov basis. However when we impose an additional constraint that the sum of cell counts in a subtable is also fixed, then these moves do not necessarily form a Markov basis. Thus, in this paper, we show a necessary and sufficient condition on a subtable so that the set of square-free moves of degree two forms a Markov basis.

A Localization Approach to Improve Iterative Proportional Scaling in Gaussian Graphical Models

We discuss an efficient implementation of the iterative proportional scaling procedure in the multivariate Gaussian graphical models. We show that the computational cost can be reduced by localization of the update procedure in each iterative step by using the structure of a decomposable model obtained by triangulation of the graph associated with the model. Some numerical experiments demonstrate the competitive performance of the proposed algorithm.

Minimal and minimal invariant Markov bases of decomposable models for contingency tables

We study Markov bases of decomposable graphical models consisting of primitive moves (i.e., square-free moves of degree two) by determining the structure of fibers of sample size two. We show that the number of elements of fibers of sample size two are powers of two and we characterize primitive moves in Markov bases in terms of connected components of induced subgraphs of the independence graph of a hierarchical model. This allows us to derive a complete description of minimal Markov bases and minimal invariant Markov bases for decomposable models.

A Markov basis for conditional test of common diagonal effect in quasi-independence model for square contingency tables

In two-way contingency tables we sometimes find that frequencies along the diagonal cells are relatively larger (or smaller) compared to off-diagonal cells, particularly in square tables with the common categories for the rows and the columns. In this case the quasi-independence model with an additional parameter for each of the diagonal cells is usually fitted to the data. A simpler model than the quasi-independence model is to assume a common additional parameter for all the diagonal cells. We consider testing the goodness of fit of the common diagonal effect by the Markov chain Monte Carlo (MCMC) method. We derive an explicit form of a Markov basis for performing the conditional test of the common diagonal effect. Once a Markov basis is given, MCMC procedure can be easily implemented by techniques of algebraic statistics. We illustrate the procedure with some real data sets.

Hierarchical subspace models for contingency tables

For the statistical analysis of multiway contingency tables, we propose modeling interaction terms in each maximal compact component of a hierarchical model. By this approach we can search for parsimonious models with smaller degrees of freedom than the usual hierarchical model, while preserving the localization property of the inference in the hierarchical model. This approach also enables us to evaluate the localization property of a given log-affine model. We discuss estimation and exact tests of the proposed model and illustrate the advantage of the proposed modeling with some data sets.

Running Markov Chain Without Markov Bases

In this chapter we provide an algorithm for performing exact tests with a lattice basis, even in the case where Markov bases are not known. As mentioned in Sect. 15, computation of lattice bases is much easier than that of Markov bases. With many examples we show that the approach with lattice bases is practical. We also check that its performance is comparable to Markov bases for the problems where Markov bases are known. This chapter is based on Hara et al. (Proceedings of the Second CREST-SBM International Conference, “Harmony of Grobner Bases and the Modern Industrial Society”. World Scientfic, Singapore, 2012. To appear).

IDENTIFIABILITY OF DIRECTED GAUSSIAN GRAPHICAL MODELS WITH ONE LATENT SOURCE

We study parameter identifiability of directed Gaussian graphical models with one latent variable. In the scenario we consider, the latent variable is a confounder that forms a source node of the graph and is a parent to all other nodes, which correspond to the observed variables. We give a graphical condition that is sufficient for the Jacobian matrix of the parametrization map to be full rank, which entails that the parametrization is generically finite-to-one, a fact that is sometimes also referred to as local identifiability. We also derive a graphical condition that is necessary for such identifiability. Finally, we give a condition under which generic parameter identifiability can be determined from identifiability of a model associated with a subgraph. The power of these criteria is assessed via an exhaustive algebraic computational study on models with 4, 5, and 6 observable variables.

ESTIMATING A COVARIANCE MATRIX IN MANOVA MODEL

On the estimation of the covariance matrix in the framework of multivariate analysis of variance(MANOVA) model, Sinha and Ghosh[5] proposed a Stein type truncated estimator improving on the uniformly m i n i m n m variance unbiased(UMVU) estimator under the entropy loss. However the estimator is discontinuous. This article obtains some other continuous estimators which dominate the UMVU estimator and, furthermore, one of which is shown analytically to improve on Sinha-Ghoehs estimator.

Contract Workers in Japan’s Nuclear Utility Industry: Can We Maintain Safety and Health Standards at Nuclear Power Plants?

Many small contracting firms are used to maintain nuclear power plants in Japan. The accident at the Fukushima nuclear plant raised the serious question as to whether safety standards can be upheld with this system. A review of regulations governing Japans nuclear utility industry derived two imperfect information models that implied opposing incentives for utility companies to use contract workers rather than hire employees. We then analyzed the dataset of nuclear plant workers exposure to radiation in the power generation industry. The results suggest that using contract workers enables the utility companies to implement lower standards than those imposed by regulations and to reduce costs by circumventing responsibilities legally imposed on employers. caused one of worlds worst nuclear accidents at the Fukushima Daiichi nuclear power station of the Tokyo Electric Power Company (TEPCO). It had been believed that Japans nuclear utility industry could safely withstand such natural disasters. After the accident, the question of whether nuclear plants were prepared for future disasters became a critical and controversial issue. Therefore, this study examines the relationship between occupational risks and types of employment at Japans nuclear power plants. The practice of replacing permanent employees with temporary workers has been spreading throughout all major industries in developed countries. Thus, employees of contracting firms who are doing their jobs on sites specified by the host plant (hereafter, contract workers) are becoming more important. These workers are similar to temporary agency workers, but with the important difference that contract workers include many permanent employees. With the demand for contract workers increasing, differences in the working conditions of these workers and the host companys employees have become important subjects of study, because these differences might compromise the safety conditions on industrial sites. In the United States, safety and health education and training (hereafter, safety training) of contract workers attracted attention following the 1989 Phillips Petroleum