Allan Seheult

Bayesian Forecasting for Complex Systems Using Computer Simulators

Although computer models are often used for forecasting future outcomes of complex systems, the uncertainties in such forecasts are not usually treated formally. We describe a general Bayesian approach for using a computer model or simulator of a complex system to forecast system outcomes. The approach is based on constructing beliefs derived from a combination of expert judgments and experiments on the computer model. These beliefs, which are systematically updated as we make runs of the computer model, are used for either Bayesian or Bayes linear forecasting for the system. Issues of design and diagnostics are described in the context of forecasting. The methodology is applied to forecasting for an active hydrocarbon reservoir.

Trimmed L-moments

Classical estimation methods (least squares, the method of moments and maximum likelihood) work well in regular cases such as the exponential family, but outliers can have undue influence on these methods. We define population trimmed L-moments (TL-moments) and corresponding sample TL-moments as robust generalisations of population and sample L-moments. TL-moments assign zero weight to extreme observations, they are easy to compute, their sample variances and covariances can be obtained in closed form, and they are more robust than L-moments are to the presence of outliers. Moreover, a population TL-moment may be well defined where the corresponding population L-moment does not exist: for example, the first population TL-moment is well defined for a Cauchy distribution, but the first population L-moment, the population mean, does not exist. The sample TL-mean is compared with other robust estimators of location.

Constructing partial prior specifications for models of complex physical systems

Summary. Many large scale problems, particularly in the physical sciences, are solved using complex, high dimensional models whose outputs, for a given set of inputs, are expensive and time consuming to evaluate. The complexity of such problems forces us to focus attention on those limited aspects of uncertainty which are directly relevant to the tasks for which the model will be used. We discuss methods for constructing the relevant partial prior specifications for these uncertainties, based on the prior covariance structure. Our approach combines two sources of prior knowledge. First, we elicit both qualitative and quantitative prior information based on expert prior judgments, using computer-based elicitation tools for organizing the complex collection of assessments in a systematic way. Secondly, we test and refine these judgments using detailed experiments based on versions of the model which are cheaper to evaluate. Although the approach is quite general, we illustrate it in the context of matching hydrocarbon reservoir history.

Exact variance structure of sample L-moments

Population L-moments have been proposed as alternatives to central moments for describing distribution location, dispersion and shape, and their sample estimates are unbiased. However, only asymptotic variances and covariances of their estimates have been reported. In this article, we derive expressions for exact variances and covariances of sample L-moments for any sample size n in terms of first- and second-order moments of order statistics from small sample sizes which do not depend on n. Various applications of these result are discussed. We also derive distribution-free unbiased estimators of the variances and covariances of sample L-moments, and report the results of a simulation study to investigate and compare the sampling distributions of standardised L-moments using exact, asymptotic and estimated standard errors. In particular, a new test of symmetry is investigated. Also, approximate standard errors of ratios of sample L-moments, used to estimate ratios of population L-moments analogous to classical scaled measures of skewness and kurtosis, are exemplified.

New approaches to assessing the risk of groundwater contamination by pesticides

Because of the large range of circumstances (such as soil-type, climatic zone, and local agricultural practice) in which pesticides are applied, it is impossible to test fully the environmental fate of a new pesticide being considered for registration. Thus, risk assessors should make best use of modern techniques and all relevant information to make their assessments. This paper discusses the use of statistical methods which use pesticide chemical properties to predict environmental fate. Using US data, a logistic regression approach can be used to estimate the probability that a compound leaches to groundwater based on adsorption (Koc) and degradation (DT50) parameters. An advantage is that both properties are already required to be measured as part of the present pesticide registration process. For UK groundwater monitoring, precise pesticide soil properties are not measured. However, further methods using UK data also indicate that polluting and non-polluting compounds may be distinguished on the basis of these chemical properties. The techniques presented can be used in conjunction with pesticide usage statistics to inform the selection of priority pollutants, to enable monitoring programmes to become more focused, to assess the risk associated with new compounds, and to identify those at high risk of contaminating groundwater.

Control charts based on linear combinations of order statistics

The last 20 years have seen an increasing emphasis on statistical process control as a practical approach to reducing variability in industrial applications. Control charts are used to detect problems such as outliers or excess variability in subgroup means that may have a special cause. We describe an approach to the computation of control limits for exponentially weighted moving average control charts where the usual statistics in classical charts are replaced by linear combinations of order statistics; in particular, the trimmed mean and Ginis mean difference instead of the mean and range, respectively. Control limits are derived, and simulated average run length experiments show the trimmed control charts to be less influenced by extreme observations than their classical counterparts, and lead to tighter control limits. An example is given that illustrates the benefits of the proposed charts. parameters; see, for example, Hunter (1986) and Montgomery (1996). On the other hand, EWMA charts have been shown to be more efficient than Shewharttype charts in detecting small shifts in the process mean; see, for example, Ng & Case (1989), Crowder (1989), Lucas & Saccucci (1990), Amin & Searcy (1991) and Wetherill & Brown (1991). In fact, the EWMA control chart has become popular for monitoring a process mean; see Hunter (1986) for a good discussion. More recently, EWMA charts have been developed for monitoring process variability;

A Bayesian approach to the analysis of environmental fate and behaviour data for pesticide registration

With the harmonisation of data requirements for pesticide registration under EC Directive 91/414 there is need for progress on the techniques used to analyse such data and so help make consistent the judgements applied by national regulatory authorities. This paper proposes a Bayesian technique for combining data from environmental fate and behaviour studies of pesticides in soil. The method uses expert knowledge, based on degradation and adsorption data, and logistic regression methods to form a prior probability distribution for the probability that a given compound leaches. Results from lysimeter experiments are used update the prior knowledge. Data for the compounds bentazone and triclopyr are used to illustrate the techniques. The advantages of the methodology and its implications for the pesticide registration procedure are discussed in the light of possible advances using modern Bayesian statistical techniques and mathematical models.

Minium bias or least squares estriation

The minimum bias estimator of B1 in the model js here compared with the ordinary least squares estimator, the criterion of comparison being the integrated mean squared error of the corresponding estimator of η. The two estimators are shown to be extremes within a natural class and conditions are also given for the preference of one estimator over the other.

Pseudo-likelihood estimation for a class of spatial Markov chains

We consider a class of finite state, two-dimensional Markov chains which can produce a rich variety of patterns and whose simulation is very fast. A parameterization is chosen to make the process nearly spatially homogeneous. We use a form of pseudo-likelihood estimation which results in quick determination of estimate. Parameters associated with boundary cells are estimated separately. We derive the asymptotic distribution of the maximum pseudo-likelihood estimates and show that the usual form of the variance matrix has to be modified to take account of local dependence. Standard error calculations based on the modified asymptotic variance are supported by a simulation study. The procedure is applied to an eight-state permeability pattern from a section of hydrocarbon reservoir rock.