Richard J. Beckman

A comparison of three methods for selecting values of input variables in the analysis of output from a computer code

Two types of sampling plans are examined as alternatives to simple random sampling in Monte Carlo studies. These plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function.

CREATING SYNTHETIC BASELINE POPULATIONS

To develop activity-based travel models using microsimulation, individual travelers and households must be considered. Methods for creating baseline synthetic populations of households and persons using 1990 census data are given. Summary tables from the Census Bureau STF-3A are used in conjunction with the Public Use Microdata Sample (PUMS), and Iterative Proportional Fitting (IPF) is applied to estimate the proportion of households in a block group or census tract with a desired combination of demographics. Households are generated by selection of households from the associated PUMS according to these proportions. The tables of demographic proportions which are exploited here to make household selections from the PUMS may be used in traditional modeling. The procedures are validated by creating pseudo census tracts from PUMS samples and considering the joint distribution of the size of households and the number of vehicles in the households. It is shown that the joint distributions created by these methods do not differ substantially from the true values. Additionally the effects of small changes in the procedure, such as imputation of additional demographics and adding partial counts to the constructed demographic tables are discussed in the paper.

Diagnostics for mixed-model analysis of variance

We describe a new method for assessment of model inadequacy in maximum-likelihood mixed-model analysis of variance. In particular, we discuss its use in diagnosing perturbations from the usual assumption of constant error variance and from the assumption that each realization of a given random factor has been drawn from the same normal population. Computer implementation of the procedure is described, and an example is presented, involving the analysis of filter cartridges used with commercial respirators.

A New Family of Probability Distributions with Applications to Monte Carlo Studies

Abstract A new probability distribution is presented that offers considerable potential for providing stochastic inputs to Monte Carlo simulation studies. The distribution includes the exponential power family as a special case. An efficient computational strategy is proposed for random variate generation. An example for testing the hypothesis of unit variance illustrates the advantages of the proposed distribution.

Maximum likelihood estimation for the beta distribution

A fast method of calculating the two-parameter maximum-likelihood estimates of the beta distribution is given which does not require starting values and is generally free from convergence problems.

The Distribution of an Arbitrary Studentized Residual and the Effects of Updating in Multiple Regression

Abstract It is shown that in multiple regression the quantity has a t distribution with n − p − 1 degrees of freedom, where τn is the nth studentized residual. The effects on the residuals and the sum of the squared residuals by adding a new data point to a multiple regression problem are investigated.

Monte Carlo estimation under different distributions using the same simulation

Two methods for reducing the computer time necessary to investigate changes in distribution of random inputs to large simulation computer codes are presented. The first method produces unbiased estimators of functions of the output variable under the new distribution of the inputs. The second method generates a subset of the original outputs that has a distribution corresponding to the new distribution of inputs. Efficiencies of the two methods are examined.

Testing for Two-Phase Regressions

The critical values for testing for a two-phase regression are given by simulation methods. The dependence of the test on the values of the independent variable is investigated. and a comparison is made between the critical values of the simulation and those given by using Bonferronis inequality.

Two-sided tolerance limits for balanced random-effects ANOVA models

In this article, we derive two-sided approximate β-content tolerance limits for multiway balanced random-effects models. We provide factors, obtained from numerical integration, that can be used to obtain β-content tolerance intervals. We describe methods for extending the results to nested models and discuss the use of the tabled tolerance factors for exact intervals for simple random samples when we have an independent estimate of the variance. We demonstrate the procedure with an experimental design used to evaluate the firing time precision in a high-explosives system.

Approximate one-sided tolerance bounds on the number of failures using Poisson regression

Safety studies of a nuclear reactor often center their interest on the probable number, of component failures in a time span of duration To . Using the asymptotic normality of the estimator from Poisson regression, we develop approximate upper tolerance bounds for the distribution of the number of failures. Tables are given for easy computation of such bounds when the bound itself is less than 50. An example consisting of 90 failure records for nuclearreactor valve types provides illustration of the tolerance bound computations and dataanalytic techniques for validating a Poisson regression model.