High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature

Although the Bock–Aitkin likelihood-based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations, a serious limitation of the method is its reliance on fixed-point Gauss-Hermite (G-H) quadrature in the solution of the likelihood equations and likelihood-ratio tests. When the number of latent dimensions is large, computational considerations require that the number of quadrature points per dimension be few. But with large numbers of items, the dispersion of the likelihood, given the response pattern, becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space. In this paper, we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data. In particular, we show that adaptive G-H quadrature, combined with mean and covariance adjustments at each iteration of an EM algorithm, produces an accurate fast-converging solution with as few as two points per dimension. Evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of upto eight dimensions. Unlike an earlier application of adaptive Gibbs sampling to this problem by Meng and Schilling, the simulations also confirm the validity of the present method in calculating likelihood-ratio chi-square statistics for determining the number of factors required in the model. Finally, we apply the method to a sample of real data from a test of teacher qualifications.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43596/1/11336_2003_Article_1141.pd

Implementable Algorithm for Stochastic Optimization Using Sample Average Approximations

We develop an implementable algorithm for stochastic optimization problems involving probability functions. Such problems arise in the design of structural and mechanical systems. The algorithm consists of a nonlinear optimization algorithm applied to sample average approximations and a precision-adjustment rule. The sample average approximations are constructed using Monte Carlo simulations or importance sampling techniques. We prove that the algorithm converges to a solution with probability one and illustrate its use by an example involving a reliability-based optimal design.Research Associateship Program at the National Research CouncilTaisei Chair in Civil Engineering at UC BerkeleyNational Science Foundation under Grant ECS-9900985Research Associateship Program at the National Research CouncilTaisei Chair in Civil Engineering at UC BerkeleyNational Science Foundation under Grant ECS-990098

Extensions of Stochastic Optimization Results from Problems with Simple to Problems with Complex Failure Probability Functions

We derive an implementable algorithm for solving nonlinear stochastic optimization problems with failure probability constraints using sample average approximations. The paper extends prior results dealing with a failure probability expressed by a single measure to the case of failure probability expressed in terms of multiple performance measures. We also present a new formula for the failure probability gradient. A numerical example addressing the optimal design of a reinforced concrete highway bridge illustrates the algorithm.This work was sponsored by the Research Associateship Program, National Research Council

Efficient Sample Sizes in Stochastic Nonlinear Programming

Journal of Computational and Applied Mathematics, Vol. 217, pp. 301-310.We consider a class of stochastic nonlinear programs for which an approximation to a locally optimal solution is speci_ed in terms of a fractional reduction of the initial cost error. We show that such an approximate solution can be found by approximately solving a sequence of sample average approximations. The key issue in this approach is the determination of the required sequence of sample average approximations as well as the number of iterations to be carried out on each sample average approximation in this sequence. We show that one can express this requirement as an idealized optimization problem whose cost function is the computing work required to obtain the required error reduction. The speci_cation of this idealized optimization problem requires the exact knowledge of a few problems and algorithm parameters. Since the exact values of these parameters are not known, we use estimates, which can be updated as the computation progresses. We illustrate our approach using two numerical examples from structural engineering design

Reliability-based optimal design using sample average approximations

The article of record as published may be found at http://dx.doi.org/10.1016/j.probengmech.2004.03.001An algorithm for reliability-based optimal design is developed using sampling techniques for estimating the failure probability. The algorithm applies a new method for sensitivity calculations of the failure probability. Initially, the estimates of the failure probability are coarse. As the algorithm progresses towards an optimal design, the number of sample points is increased in an adaptive way leading to better estimates of the failure probability. The algorithm is proven to converge to an optimal design. The applicability of the algorithm is shown in an example from the area of highway bridge design.Research Associateship Program at the National Research CouncilTaisei Chair in Civil Engineering at UC BerkeleyNational Science Foundation grant ECS-9900985Research Associateship Program at the National Research CouncilTaisei Chair in Civil Engineering at UC BerkeleyNational Science Foundation grant ECS-990098

Reliability-Based Optimal Design: Problem Formulations, Algorithms and Application

Algorithms for solving three classes of reliability-based optimal design problems are presented. The algorithms address design problems for structural components, series systems, and a portfolio of series systems, where the objective and/or constraint functions involve probability terms. The proposed approach employs reformulations of the problems, in which probability terms are replaced by better-behaving functions. The reformulated problems can be solved by existing semi-infinite optimization algorithms, An important advantage of the approach is that the required reliability and optimization calculations are completely decoupled, thus allowing flexibility in the choice of the optimization algorithm and the reliability method. A comprehensive numerical example demonstrates applications of the proposed algorithms.Taisei Chair in Civil Engineering at UC BerkeleyNational Science Foundation under grant ECS-9900985UC Berkeley Space Sciences LaboratoryLockheed Martin Advanced Technology Center Mini-grant ProgramTaisei Chair in Civil Engineering at UC BerkeleyNational Science Foundation under grant ECS-9900985UC Berkeley Space Sciences LaboratoryLockheed Martin Advanced Technology Center Mini-grant Progra

On the Optimal Detection of an Underwater Intruder in a Channel using Unmanned Underwater Vehicles

Naval Research Logistics, Vol. 58, No. 8, pp. 804-820

Plantaricins - biosynthesis, mode of action and potential in ensuring food safety

Scharakteryzowano właściwości, strukturę oraz spektrum aktywności plantarycyn wytwarzanych przez niektóre szczepy Lactobacillus. Przedstawiono ich klasyfikację, mechanizm biosyntezy, modele działania na inne bakterie oraz stabilność. Plantarycyny są dość różnorodne pod względem właściwości fizykochemicznych, struktury i spektrum aktywności przeciwdrobnoustrojowej. Szczepy Lactobacillus plantarum zdolne do syntezy plantarycyn należą do mikroorganizmów najczę- ściej obecnych w fermentowanych produktach spożywczych, a także w napojach i innych wyrobach z dodatkiem mleka. Budowa cząsteczek, ich stabilność oraz mechanizm działania sprawiają, że plantary- cyny charakteryzują się skutecznym działaniem bakteriobójczym. Ze względu na niewielką oporność organizmów patogennych na te substancje mogą być one alternatywą dla wielu stosowanych obecnie związków o działaniu przeciwdrobnoustrojowym. Plantarycyny wpływają na zahamowanie wzrostu drob- noustrojów chorobotwórczych, a w konsekwencji na poprawę zdrowia człowieka. Z uwagi na coraz więk- sze zainteresowanie produktami naturalnymi plantarycyny mogą w przyszłości znaleźć zastosowanie w różnych gałęziach przemysłu. Wyniki badań dotyczące ich wykorzystania mogą stać się podstawą do projektowania efektywnych preparatów probiotycznych, kultur starterowych do produkcji fermentowanej żywności czy nowych metod zabezpieczania żywności, co w konsekwencji wpłynie na poprawę zdrowia i jakości życia człowieka

Understanding the effects of social selfishness on the performance of heterogeneous opportunistic networks

Given a number of patrollers, the channel patrol problem consists of determining the periodic trajectories that the patrollers must trace out so as to maximize the probability of detection of the intruder. We formulate this problem as an optimal control problem. We assume that the patrollers' sensors are imperfect and that their motions are subject to turn-rate constraints, and that the intruder travels straight down a channel, with constant speed. Using discretization of time and space, we approximate the optimal control problem with a large-scale nonlinear programming problem which we solve to obtain an approximately stationary solution and a corresponding optimized trajectory for each patroller. In numerical tests, we obtain new insight--not easily obtained using geometric calculations--into efficient patrol trajectory designs for up to two patrollers in a narrow channel where interaction between the patrollers is unavoidable due to their limited turn rate.Partially supported by ONR MURI "Computational methods for collaborative motion" (CoMotion), and ARO MURI "Scalable SWARMS of autonomous robots and mobile sensors: (SWARMS). Also AFOSR Young Investigator grant F1ATA08337G003Approved for public release; distribution is unlimited