論文

Random effects meta-analyses have been widely applied in evidence synthesis for various types of medical studies. However, standard inference methods (e.g. restricted maximum likelihood estimation) usually underestimate statistical errors and possibly provide highly overconfident results under realistic situations; for instance, coverage probabilities of confidence intervals can be substantially below the nominal level. The main reason is that these inference methods rely on large sample approximations even though the number of synthesized studies is usually small or moderate in practice. In this article, we solve this problem using a unified inference method based on Monte Carlo conditioning for broad application to random effects meta-analysis. The developed method provides improved confidence intervals with coverage probabilities that are closer to the nominal level than standard methods. As specific applications, we provide new inference procedures for three types of meta-analysis: conventional univariate meta-analysis for pairwise treatment comparisons, meta-analysis of diagnostic test accuracy, and multiple treatment comparisons via network meta-analysis. We also illustrate the practical effectiveness of these methods via real data applications and simulation studies.

We introduce a novel methodology for robust Bayesian estimation with robust divergence (e.g., density power divergence or γ-divergence), indexed by tuning parameters. It is well known that the posterior density induced by robust divergence gives highly robust estimators against outliers if the tuning parameter is appropriately and carefully chosen. In a Bayesian framework, one way to find the optimal tuning parameter would be using evidence (marginal likelihood). However, we theoretically and numerically illustrate that evidence induced by the density power divergence does not work to select the optimal tuning parameter since robust divergence is not regarded as a statistical model. To overcome the problems, we treat the exponential of robust divergence as an unnormalisable statistical model, and we estimate the tuning parameter by minimising the Hyvarinen score. We also provide adaptive computational methods based on sequential Monte Carlo samplers, enabling us to obtain the optimal tuning parameter and samples from posterior distributions simultaneously. The empirical performance of the proposed method through simulations and an application to real data are also provided.

While K-means is known to be a standard clustering algorithm, its performance may be compromised due to the presence of outliers and high-dimensional noisy variables. This paper proposes adaptively robust and sparse K-means clustering (ARSK) to address these practical limitations of the standard K-means algorithm. For robustness, we introduce a redundant error component for each observation, and this additional parameter is penalized using a group sparse penalty. To accommodate the impact of high-dimensional noisy variables, the objective function is modified by incorporating weights and implementing a penalty to control the sparsity of the weight vector. The tuning parameters to control the robustness and sparsity are selected by Gap statistics. Through simulation experiments and real data analysis, we demonstrate the proposed method’s superiority to existing algorithms in identifying clusters without outliers and informative variables simultaneously.

We develop a new robust geographically weighted regression method in the presence of outliers. We embed the standard geographically weighted regression in robust objective function based on γ-divergence. A novel feature of the proposed approach is that two tuning parameters that control robustness and spatial smoothness are automatically tuned in a data-dependent manner. Further, the proposed method can produce robust standard error estimates and give us a reasonable quantity for local outlier detection. We demonstrate that the proposed method is superior to the existing robust geographically weighted regression through simulation and data analysis.

Empirical Bayes (EB) small area estimation based on the well-known Fay-Herriot model may produce unreliable estimates when outlying areas exist. Existing robust methods against outliers or model misspecification are generally inefficient when the assumed distribution is plausible. This article proposes a simple modification of the standard EB methods with adaptively balancing robustness and efficiency. The proposed method uses (Formula presented.) -divergence instead of the marginal log-likelihood and optimizes a tuning parameter controlling robustness by pursuing the efficiency of EB confidence intervals for areal parameters. We provide an asymptotic theory of the proposed method under both the correct specification of the assumed distribution and the existence of outlying areas. We investigate the numerical performance of the proposed method through simulations and two applications to small area estimation of average crime numbers.

Model-assisted estimation based on complex survey data is an important practical problem in survey sampling. When there are many auxiliary variables, selecting the significant variables associated with the study variable is necessary to achieve an efficient estimation of the population parameters of interest. In this study, we formulate a regularized regression estimator in a Bayesian inference framework using the penalty function as the shrinkage prior for model selection. The proposed Bayesian approach enables both efficient point estimates and valid credible intervals. Lastly, we compare the results from two limited simulation studies with those of existing frequentist methods.

This study is concerned with estimating the inequality measures associated with the underlying hypothetical income distribution from the times series grouped data on the income proportions. We adopt the Dirichlet likelihood approach where the parameters of the Dirichlet likelihood are set to the differences between the Lorenz curve of the hypothetical income distribution for the consecutive income classes and propose a state-space model which combines the transformed parameters of the Lorenz curve through a time series structure. The present article also studies the possibility of extending the likelihood model by considering a generalized version of the Dirichlet distribution where the mean is modeled based on the Lorenz curve with an additional hierarchical structure. The simulated data and real data on the Japanese monthly income survey confirmed that the proposed approach produces more efficient estimates on the inequality measures than the existing method that estimates the model independently without time series structures.

Statistical inference with nonresponse is quite challenging, especially when the response mechanism is nonignorable. In this case, the validity of statistical inference depends on untestable correct specification of the response model. To avoid the misspecification, we propose semiparametric Bayesian estimation in which an outcome model is parametric, but the response model is semiparametric in that we do not assume any parametric form for the nonresponse variable. We adopt penalized spline methods to estimate the unknown function. We also consider a fully nonparametric approach to modeling the response mechanism by using radial basis function methods. Using Pólya–gamma data augmentation, we developed an efficient posterior computation algorithm via Gibbs sampling in which most full conditional distributions can be obtained in familiar forms. The performance of the proposed method is demonstrated in simulation studies and an application to longitudinal data.

Meta-analysis is widely used to integrate results from multiple experiments to obtain generalized insights. Since meta-analysis datasets are often heteroscedastic due to varying subgroups and temporal heterogeneity arising from experiments conducted at different time points, the typical meta-analysis approach, which assumes homoscedasticity, fails to adequately address this heteroscedasticity among experiments. This paper proposes a new Bayesian estimation method that simultaneously shrinks estimates of the means and variances of experiments using a hierarchical Bayesian approach while accounting for time effects through a Gaussian process. This method connects experiments via the hierarchical framework, enabling “borrowing strength” between experiments to achieve high-precision estimates of each experiment’s mean. The method can flexibly capture potential time trends in datasets by modeling time effects with the Gaussian process. We demonstrate the effectiveness of the proposed method through simulation studies and illustrate its practical utility using a real marketing promotions dataset.

Many marketing applications, including credit card incentive programs, offer rewards to customers who exceed specific spending thresholds to encourage increased consumption. Quantifying the causal effect of these thresholds on customers is crucial for effective marketing strategy design. Although regression discontinuity design is a standard method for such causal inference tasks, its assumptions can be violated when customers, aware of the thresholds, strategically manipulate their spending to qualify for the rewards. To address this issue, we propose a novel framework for estimating the causal effect under threshold manipulation. The main idea is to model the observed spending distribution as a mixture of two distributions: one representing customers strategically affected by the threshold, and the other representing those unaffected. To fit the mixture model, we adopt a two-step Bayesian approach consisting of modeling nonbunching customers and fitting a mixture model to a sample around the threshold. We show posterior contraction of the resulting posterior distribution of the causal effect under large samples. Furthermore, we extend this framework to a hierarchical Bayesian setting to estimate heterogeneous causal effects across customer subgroups, allowing for stable inference even with small subgroup sample sizes. We demonstrate the effectiveness of our proposed methods through simulation studies and illustrate their practical implications using a real-world marketing dataset.