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The main goal of this paper is to describe a new multistage Monte Carlo (MMC) simulation method for solving influence diagrams using local computation. Global methods have been proposed by others that sample from the joint probability distribution of all the variables in the influence diagram. However, for influence diagrams having many variables, the state space of all variables grows exponentially, and the sample sizes required for good estimates may be too large to be practical. In this paper, we develop a MMC method, which samples only a small set of chance variables for each decision node in the influence diagram. MMC is akin to methods developed for exact solution of influence diagrams in that we limit the number of chance variables sampled at any time. Because influence diagrams model each chance variable with a conditional probability distribution, the MMC method lends itself well to influence diagram representations.

We develop a method for constructing confidence regions on the mean vectors of multivariate processes that is based on a vector autoregressive (VAR) representation of the data-generating process. A confidence-region-construction algorithm for a general autoregressive model is given. We establish the asymptotic validity of the confidence-region estimator (that is, the exact achievement of nominal coverage probability as the sample size tends to infinity) when the output process is a stationary vector autoregressive process of known, finite order. With respect to confidence-region volume, coverage probability, and execution time, we carry out an experimental performance comparison of VAR versus the methods of Bonferroni Batch Means (BBM), Multivariate Batch Means (MBM), and Multivariate Spectral Analysis (SPA). The experimental results indicate that (i) VAR delivered confidence regions with the smallest volume; (ii) BBM delivered confidence regions with the largest volume, the highest coverage and the smallest execution time; (iii) in small samples, all of the methods might yield confidence-region estimators whose coverage differs significantly from the nominal level; and (iv) in large samples for which the sample autocorrelation function indicates a vector autoregressive dependence structure, VAR is a viable technique for simulation output analysis.

A model for measuring the efficiency of Decision Making Units (=DMU's) is presented, along with related methods of implementation and interpretation. The term DMU is intended to emphasize an orientation toward managed entities in the public and/or not-for-profit sectors. The proposed approach is applicable to the multiple outputs and designated inputs which are common for such DMU's. A priori weights, or imputations of a market-price-value character are not required. A mathematical programming model applied to observational data provides a new way of obtaining empirical estimates of extrernal relations—such as the production functions and/or efficient production possibility surfaces that are a cornerstone of modern economics. The resulting extremal relations are used to envelop the observations in order to obtain the efficiency measures that form a focus of the present paper. An illustrative application utilizes data from Program Follow Through (=PFT). A large scale social experiment in public school education, it was designed to test the advantages of PFT relative to designated NFT (=Non-Follow Through) counterparts in various parts of the U.S. It is possible that the resulting observations are contaminated with inefficiencies due to the way DMU's were managed en route to assessing whether PFT (as a program) is superior to its NFT alternative. A further mathematical programming development is therefore undertaken to distinguish between “management efficiency” and “program efficiency.” This is done via procedures referred to as Data Envelopment Analysis (=DEA) in which one first obtains boundaries or envelopes from the data for PFT and NFT, respectively. These boundaries provide a basis for estimating the relative efficiency of the DMU's operating under these programs. These DMU's are then adjusted up to their program boundaries, after which a new inter-program envelope is obtained for evaluating the PFT and NFT programs with the estimated managerial inefficiencies eliminated. The claimed superiority of PFT fails to be validated in this illustrative application. Our DEA approach, however, suggests the additional possibility of new approaches obtained from PFT-NFT combinations which may be superior to either of them alone. Validating such possibilities cannot be done only by statistical or other modelings. It requires recourse to field studies, including audits (e.g., of a U.S. General Accounting Office variety) and therefore ways in which the results of a DEA approach may be used to guide such further studies (or audits) are also indicated.