We provide a review of the Bayesian transformed Gaussian random field model which can be used for the analysis of continuous geostatistical data that display non-Gaussian features. We describe the formulation of the model and its main properties, as well as Bayesian inference and prediction using Monte Carlo methods. The publicly available software btg for the implementation of the model is illustrated by means of spatial and temporal data.

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Pharmacokinetics aims to clarify the kinetics of a drug administered in a human body, by the time course of drug disposition, composed of absorption, distribution, metabolization, and excretion. As a tool for this clarification, a compartment model is often used in practice. In this paper, we considered the diagnostics about the validity of statistical inference of the compartment models. We utilized the relative curvature measure as this diagnostic tool and investigated its appropriateness by some pharmacokinetic literatures and a simulation study. In investigation of the pharmacokinetic literatures, we applied this relative curvature measure and assessed the degree of nonlinearity underlying in the compartment models. Then, we focused on the heteroscedasticity of the blood drug concentration data as the deviation of them from the assumption on the ordinary statistical model, and examined the effects of the heteroscedasticity on this measure. Intending to improve the deviation from this assumption and to evaluate it quantitatively, we utilized the power-transformation approach and presented the relative curvature measure depending on this approach. As a result, in the power-transformation approach, the heteroscedasticity of the blood drug concentration data and the skewness of the distribution of them were improved and the nonlinearity depending on the parameters in the model was decreased. Furthermore, we utilized some diagnostic measures that are concomitant with the relative curvature depending on the power-transformation approach and could understand the properties of the compartment models, without being affected by the heteroscedasticity of the blood drug concentration data. In the simulation study, we assumed the situation where the blood drug concentration data were heteroscedastic, and evaluated the effects of the sample size of the blood drug concentration data, the variability, and the sampling type, on the relative curvature measure. Consequently, it was shown that the parameter-effects curvature for the powertransformation approach was not affected by the heteroscedasticity of the blood drug concentration data. It was suggested that the relative curvature measure could provide productive knowledge for the diagnostics for the statistical inference of compartment models in pharmacokinetics.

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The paper proposes a hybrid regression analysis with neural networks and the classical linear model which possesses both sufficient forecasting accuracy and interpretability. The proposed method utilizes outputs of hidden units in the initially fitted neural network model as additional explanatory variables of the consequent stepwise linear multiple regression, where sigmoid function is used for the output function of the hidden layer of the three layers feed-forward neural networks.
We applied the proposed method to construction of a prediction model for the volume of the water supply in Districts 23, Tokyo to clarify our idea and the effectiveness of the method. Our approach automatically accounts unexpected structural changes in the output variable, i.e. the volume of the water supply, which seems to be related to the water leakage. The water leakage measurements were not observed before 1985 due to the inappropriate measurement method. When such bias from the measurement is adjusted by including the corresponding output from the neural networks, not only did the multiple correlation coefficient of the linear regression model increase drastically, but also the sign conditions of the regression coefficients became consistent. This means the proposed hybrid approach attains the interpretability of the data analysis.

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