The aim of this study is to propose a method to analyze objects in meta-analysis in symbolic data analysis, and represent an application for real data. Meta-analysis aims to obtain a higher level of evidence by integrating multiple studies. Then, it is important to take heterogeneity among the studies into consideration. When we regard the studies as concepts in symbolic data analysis, we can find out factors which may bring heterogeneity. The study proposes a method of hierarchical symbolic clustering when concepts are described as two-way contingency tables. The target data from multiple randomized trials on acupuncture clinical trials contain two-way contingency tables of outcomes and interventions, and individual patient data. The results reveal interpretable clusters and detect some variables for heterogeneity.

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　Identifying the most relevant or interesting units is a common task in large-scale statistical inference. Recently, Henderson & Newton (2016; Journal of the Royal Statistical Society, Series B, 78, 781-804) proposed a new ranking measure named r-value to achieve optimal ranking in Bayesian inference. The r-value depends on the assumed Bayes model and its ranking accuracy can be violated by model misspecification. In medical and biological studies, large-scale candidate variables often consist of a mixture of null (the effect sizes are zero; non-interesting units) and nonnull (the effect sizes are non-zero; interesting units) components, e.g., for genome-wide association studies. In this article, to provide accurate ranking outputs, we propose to apply the Bayesian hierarchical mixture modeling for the ranking and selection inferences. We also propose to use a semiparametric approach using Laird's nonparametric maximum likelihood estimation in empirical Bayes inference. Using the mixture modeling, we can estimate false discovery rate (FDR) for the selected highly ranked units. We assess the effectiveness of the proposed method via an application to a breast cancer clinical study.

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　Using the 16S rRNA sequence analysis, which analyzes the 16S rRNA region of the whole microbial genome, compositional data of microbial species can be obtained nowadays. As an analysis method for these data, the latent Dirichlet allocation (LDA) model has been proposed as a dimension reduction method.
　Microbiome data from the 16S rRNA sequence analysis are often measured in time series to observe the changes in the microbial environment of a subject over time. As an LDA model for time-series data, the dynamic topic model (DTM) is often used. Although the number of topics need to be pre-specified when using the DTM, the number of topics from the data may be automatically deduced by extending the DTM model to a Bayesian nonparametric model. Therefore, a Bayesian nonparametric topic model for microbiome data measured in time series was proposed and compared to the DTM using real microbiome data. As a result, using the proposed model, the topic proportions of only a few topics became averagely large regardless of the pre-specified number of topics. In addition, the number of topics whose proportion became the largest for any subject did not change depending on the pre-specified number of topics. Therefore, it was suggested that the number of topics from microbiome data could be automatically decided using this proposed model.

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　Exploratory factor analysis is a statistical method for analyzing quantitative data; however, qualitative data are often observed in psychological and/or social sciences. Several exploratory factor analysis methods have been developed in previous studies to analyze qualitative data. In this paper, we focus on nonmetric factor analysis and discuss the similarities and differences between the models and estimation methods presented in literature. Then, we show that studies on the interpretability of solutions via matrix decomposition factor analysis can be extended to nonmetric factor analysis. Finally, future issues associated with nonmetric factor analysis are discussed.

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