Statistical analysis of very high-dimensional data sets of hierarchically structured binary variables with missing data: An application to marine corps readiness evaluations

The present analysis deals with very high-dimensional data sets, each one containing close to 900 binary variables. Each data set corresponds to an evaluation of one complex system. These data sets are characterized by large portions of missing data where, moreover, the unobserved variables are not the same in different evaluations. Thus, the problems which confront the statistical analysis are those of multivariate binary data analysis, where the number of variables is much larger than the sample size and in which missing data varies with the sample elements. The variables, however, are hierarchically structured and the problem of clustering variables to groups does not exist in the present study. In order to motivate the statistical problem under consideration, the Marine Corps Combat Readiness Evaluation System (MCCRES) is described for infantry battalions and then used for exposition. The present article provides a statistical model for data from MCCRES and develops estimation and prediction procedures which utilize the dependence structure. The E-M algorithm is applied to obtain maximum-likelihood estimates of the parameters of interest. Numerical examples illustrate the proposed methods.     

Minimizing costs of sequential and parallel personnel testing programs

We consider groups of tests for personnel selection purposes in which each test has a known a priori probability of being failed, such failure resulting in outright rejection and termination of testing. Each test has a fixed cost and given duration. We consider the minimization of the total expected cost due to both the fixed costs and the delay costs when the tests may be conducted sequentially or in parallel. In the latter situation, a heuristic algorithm is proposed and illustrated.     

Optimal stopping problems for differential equations perturbed by a poisson process

We investigate a class of optimal stopping problems for dynamical systems described by one-dimensional differential equations with an additive Poisson disturbance. The rate of the disturbance may depend upon the current state of the system. A dynamic programming equation for the optimal stopping cost is derived along with conditions which must be met at the boundary of the optimal stopping set. These boundary conditions depend upon whether or not the stopping set may be entered by smooth motion.     

Economic impact and the notion of compensated procurement

The paper consists essentially of two parts. In the first part a linear economic impact model is presented whose structure is based on subcontracting flows. The structural coefficients are defined in terms of flows per area. The model is derived from two identities that are analogous to the income and expenditure identities of national income accounting. The parameters are prime contracts and when one or several of the prime contracts are changed, the model determines the impacts of such changes on the various regions that have been selected. The impacts can be combined with regional multipliers to derive changes in regional income and regional employment. Fragmentary data for this kind of model have been collected on a one-time basis by DOD in 1965 and some results based on the data are presented. The second part of the paper is concerned with normative economics. A scheme is suggested, called compensated procurement, that outlines how the Department of Defense might employ the impact model in a macroeconomic setting. The basic idea is that a stabilization fund be established to finance an array of potential projects which are contracted for to balance sudden shifts in defense demand. Only short-run stabilization is advocated.     

Landmarks in defense literature

Achtung-Panzer! By Major General Heinz Guderian, Translated by Christopher Duffy with Introduction and Notes by Paul Harris. (Arms & Armour Press £16.99. ISBN 1-85409-138-7, 220 pages)     

A two-phase procedure for allotting geostationary orbital locations to communications satellites

We consider the problem of allotting locations in the geostationary orbit to communication satellites, subject to angle of elevation and electromagnetic interference constraints. An optimization framework is used as a means of finding feasible allotment plans. Specifically, we present a two-phase solution procedure for the satellite location problem (SLP). The objective in SLP is to allot geostationary orbital locations to satellites so as to minimize the sum of the absolute differences between the locations prescribed for the satellites and corresponding specified desired locations. We describe two heuristics, an ordering procedure and a k-permutation algorithm, that are used in tandem to find solutions to SLP. Solutions to a worldwide example problem with 183 satellites serving 208 service areas are summarized.     

A linear programming approach to geometric programs

A cutting plane method, based on a geometric inequality, is described as a means of solving geometric programs. While the method is applied to the primal geometric program, it is shown to retain the geometric programming duality relationships. Several methods of generating the cutting planes are discussed and illustrated on some example problems.     

Minimax trees,paths, and cut sets

The notions of minimax paths, trees, and cut sets are defined for undirected graphs; and relationships between these entities are established. Simple solution procedures based on these relationships are presented.     

Toward a study of bidding processes part IV - games with unknown costs

This paper represents a continuation of three previous papers [1-.3] in the study of competitive bidding processes. It treats the case where a bidder's knowledge of his competitor's cost i s given by a probability distribution over a certain interval. The results obtained extend the work of Vickrey [4] to the case where the cost intervals a r e not necessarily symmetric.