SUMMARY A computer algorithm for tidal analysis is developed, based on a Bayesian method proposed by Ishiguro et al. (1983). The basic assumption of the method is smoothness of the drift. This assumption is represented in the form of prior probability in the Bayesian model. Once the prior distribution is determined, the parameters used in the analysis model are obtained by maximizing the posterior distribution of the parameters. For the given data, ABIC (Akaike's Bayesian Information Criterion, Akaike 1980) is used to select the optimum values of the hyperparameters of the prior distribution and combination of parameters. The program, BAYTAP‐G, can be adapted to tidal data which includes such irregularities as drift, occasional steps and disturbances caused by meteorological influences. The applicability of this program is examined using simulated data and real strain data.

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In population pharmacokinetic studies, one of the main objectives is to estimate population pharmacokinetic parameters specifying the population distributions of pharmacokinetic parameters. Confidence intervals for population pharmacokinetic parameters are generally estimated by assuming the asymptotic normality, which is a large-sample property, that is, a property which holds for the cases where sample sizes are large enough. In actual clinical trials, however, sample sizes are limited and not so large in general. Likelihood functions in population pharmacokinetic modelling include a multiple integral and are quite complicated. We hence suspect that the sample sizes of actual trials are often not large enough for assuming the asymptotic normality and that the asymptotic confidence intervals underestimate the uncertainties of the estimates of population pharmacokinetic parameters. As an alternative to the asymptotic normality approach, we can employ a bootstrap approach. This paper proposes a bootstrap standard error approach for constructing confidence intervals for population pharmacokinetic parameters. Comparisons between the asymptotic and bootstrap confidence intervals are made through applications to a simulated data set and an actual phase I trial.

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The purpose of the present paper is to propose a practical procedure for the estimation of the binary response curve. The procedure is based on a model which approximates the response curve by a finely segmented piecewise constant function. To obtain a stable estimate we assume a prior distribution of the parameters of the model. The prior distribution has several parameters (hyper-parameters) which are chosen to minimize an information criterion ABIC. The procedure is applicable to data consisting of observations of a binary response variable and a single explanatory variable. The practical utility of the procedure is demonstrated by examples of applications to the dose response curve estimation, to the intensity function estimation of a point process and to the analysis of social survey data. The application of the procedure to the discriminant analysis is also briefly discussed.