Gordon M. Kaufman

Bayesian Analysis of the Independent Multinormal Process—Neither Mean Nor Precision Known

Abstract Under the assumption that neither the mean vector nor the variance-covariance matrix are known with certainty, the natural conjugate family of prior densities for the multivariate Normal process is identified. Prior-posterior and preposterior analysis is done assuming that the prior is in the natural conjugate family. A procedure is presented for obtaining non-degenerate joint posterior and preposterior distributions of all parameters even when the number of objective sample observations is less than the number of parameters of the process.

Estimation of Finite Population Properties When Sampling is without Replacement and Proportional to Magnitude

Abstract Geologists often evaluate aggregate volumes of discovered plus undiscovered oil and/or gas in a petroleum basin by use of geologic-volumetric methods. Although sophisticated geological reasoning may be employed, the essential idea behind these methods is simple: estimate (a) the volume of hydrocarbon bearing sediment in the basin, (b) the amount of hydrocarbons present per unit volume of sediment, and (c) the fraction of hydrocarbons present per unit volume that is technologically recoverable. The product of (a) and (b) is interpretable as a point estimate of the sum of amounts of oil and gas in place in individual oil and gas deposits (fields) in the basin. The product of (a), (b), and (c) is a point estimate of amounts of oil and gas recoverable from all individual deposits in the basin.

A Bayesian Analysis of Nonresponse in Dichotomous Processes

Abstract A Bayesian treatment is given of a two-phase sampling problem when sampling is from a double dichotomy, losses are quadratic, and sampling costs are linear. The motivating question is: how does one determine an optimal first phase sample from a dichotomous population given that an optimal follow-up sample of nonrespondents in the first phase is to be taken?

Are wildcat well outcomes dependent or independent

A binary logit model is adapted to the spatial point process represented by outcomes of wildcat wells as a function of drilling history. The probability of success of the (n+1)st wildcat is made dependent on the wells location and on outcomes of wildcats previously drilled within a distanced of the well. This simple model is a device for investigating patterns of dependencies of wildcat well outcomes and for projecting probabilities of drilling success at particular locations. The model is applied to two Canadian petroleum plays.

Sequential climate decisions under uncertainty : an integrated framework

We develop an integrated framework for evaluating sequential greenhouse gas abatement policies under uncertainty. The analysis integrates information concerning the magnitude, timing, and impacts of climate change with data on the likely effectiveness and cost of possible response options. Reduced-scale representations of the global climate system, drawn from the MIT Integrated Global System Model, form the empirical basis of the analysis. The method is illustrated in application to emissions control policies of the form considered under the United Nations Framework Convention on Climate Change.

Successive sampling and software reliability

The connection between successive sampling and exponential order statistics (EOS) models of software failures is highlighted. Maximum likelihood and unbiased estimators designed for successive sampling inference can be applied to software failure data generated by EOS models. They lead naturally to predictive estimators of waiting times to future failures based on an observed software failure history.

The interface between geostatistical modeling of oil and gas discovery and economics

Methods of forecasting future additions to the supply of primary energy resources generated by exploratory effort must be able to measure the consequence for supply of a wide range of tax, cost, regulatory, and leasing policies. Otherwise they are of little practical value. One methodological strategy currently in vogue is to model the response to policy choice of supply in micro units composed of a set of geologically homogeneous deposit types located in a particular geographic area and then compute regional or national supply forecasts by directly aggregating these responses. The forecasting strategy has strengths relative to its alternatives, but it requires data on individual deposits and on the probabilistic properties of the population of deposits to which it belongs. It demands, in addition, that geostatistical modeling and micro-economic theory be tightly linked, that deposit data be presented so as to allow systematic inferences to be made about deposit size distributions, and that expert opinion be expressed as personal or subjective probabilities. The data required for application of this forecasting strategy to large regions is, with a few notable exceptions, not available. The USGS and the GSC have begun work directed to this end in the case of oil and gas. Working backward from the skeleton of a micro-economic model of a generic petroleum play is a useful way to identify what data is needed and in what form. If a correspondence between descriptive geologic attributes and the parameters of deposit size distributions can be identified and a discrete classification of size distribution types generated, then statistical analogies between population of mineral deposits might be created and used in the same fashion as geologic analogies, which are greatly streamlining implementation of a forecasting strategy based on direct aggregation of microunits.

WHAT HAS SEISMIC MISSED

The relative efficiencies of alternative geometric patterns of both discrete borehole and continuous grid line search have been extensively discussed in the mathematical geology literature. However, an equally important problem has received virtually no attention: How to use a sample of properties of geologic anomalies detected by grid line search of a region to estimate systematically both the number and size distribution of geologic anomalies missed by the search. We show how estimation methods developed in the sample survey design literature can be adapted to this problem, and we apply these methods to data describing 94 anomalies identified by a seismic reconnaissance survey.

Optimal Sample Size in Two-Action Problems When the Sample Observations Are Lognormal and the Precision h Is Known

Necessary and sufficient conditions are stated for a sample of size n to be optimal when sampling is Lognormal, the precision h is known, and the terminal decision problem is two act, linear value in the mean of the sampling process. A nomogram for computing optimal sample size is presented.

Statistical Identification and Estimability

This article is reproduced from the previous edition, volume 22, pp. 15025–15031,