[1] The aim of this research is to estimate the parameters of a large-scale numerical model of a geothermal reservoir using Markov chain Monte Carlo (MCMC) sampling, within the framework of Bayesian inference. All feasible parameters that are consistent with the measured data are summarized by the posterior distribution, and hence parameter estimation and uncertainty quantification are both given by calculating expected values of statistics of interest over the posterior distribution. It appears to be computationally infeasible to use the standard Metropolis-Hastings algorithm (MH) to sample the high dimensional computationally expensive posterior distribution. To improve the sampling efficiency, a new adaptive delayed-acceptance MH algorithm (ADAMH) is implemented to adaptively build a stochastic model of the error introduced by the use of a reduced-order model. This use of adaptivity differs from existing adaptive MCMC algorithms that tune proposal distributions of the Metropolis-Hastings algorithm (MH), though ADAMH also implements that technique. For the 3-D geothermal reservoir model we present here, ADAMH shows a great improvement in the computational efficiency of the MCMC sampling, and promising results for parameter estimation and uncertainty quantification are obtained. This algorithm could offer significant improvement in computational efficiency when implementing sample-based inference in other large-scale inverse problems.

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In a replication of a series of studies conducted by Sue and colleagues in the mid-1970s, demographic and service data were retrieved for the Seattle-King County area from the Washington Mental Health Information System. Caucasian clients were compared against Asian, black, Hispanic, and Native American client groups, and, where possible, against the findings reported earlier by Sue. These clients were compared in terms of basic demographic characteristics, characteristics of staff providing the services, dropout rates, and average number of services received. The most notable findings are (a) that failure-to-return rates are dramatically lower for the current sample than for Sue's and not greatly different for minorities than for Caucasians, (b) that variability in failure-to-return rates is most strongly related to level of functioning and not related to minority status, and (c) that although Asian Americans still average fewer services than Caucasians (other minorities do not differ significantly), the mean number of services had increased substantially for all groups but more for minorities than for Caucasians.

The stability of natural convective flow in a porous medium heated both uniformly and non-uniformly from below is studied in order to determine the possibility of oscillatory and other unsteady flows, and to explore the conditions under which they may occur. The results of the numerical work are directly comparable with experiments using a Hele Shaw cell and also, in the uniformly heated case, with the results of Combarnous & Le Fur (1969) and Caltagirone, Cloupeau & Combarnous (1971). It is shown that for the uniformly heated problem there exist, in certain cases, two distinct possible modes of flow, one of which is fluctuating, the other being steady. However in the non-uniformly heated case the boundary conditions force the solution into a unique mode of flow which is regularly oscillatory when there is considerable non-uniformity in the heat input at the lower boundary, provided that the Rayleigh number is sufficiently high.

Previous solutions of the idealized saltwater intrusion problem known as the Henry problem are discussed, and possible reasons for the observed discrepancies between them are given. High‐accuracy finite difference techniques are used to solve the nondimensionalized equations governing the problem, and a fine grid is used so that the solutions obtained contain only very small truncation errors. Such errors are investigated by means of grid refinement. Comparison of past results with the present solutions indicate, first, the presence of significant inaccuracy in certain earlier results and, second, the effects of numerical dispersion in other previous solutions calculated using relatively few grid points.

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Elective surgery cancellation is a significant problem with far-reaching consequences. While multifactorial in aetiology, increased bed usage by medical specialties is one important factor. This study has implications for doctors, training, administrators and patients.