Stochastic Decision Rules Research Articles

Worst-Case Stealthy Attacks on Stochastic Event-Based State Estimation

This article considers the worst-case stealthy attack strategies on stochastic event-based state estimation. Smart sensors equipped with local event-triggered Kalman filters are used to transmit innovations. Contrary to classic Kalman filters, the transmitted innovation screened by the stochastic decision rule does not follow a Gaussian distribution. A type of distribution called complete Gaussian crater is defined and analyzed, which is essential for designing stealthy attacks. The evolution of the estimation error covariance under attacks is obtained. Stealthy attacks that yield the greatest estimation errors under constraints on transmission rates and probability distributions are obtained and analyzed. The system performance degradation caused by different attacks is evaluated via simulations.

On Determining Firing Delay Time of Transitions for Petri Net Based Signaling Pathways by Introducing Stochastic Decision Rules

Parameter determination is important in modeling and simulating biological pathways including signaling pathways. Parameters are determined according to biological facts obtained from biological experiments and scientific publications. However, such reliable data describing detailed reactions are not reported in most cases. This prompted us to develop a general methodology of determining the parameters of a model in the case of that no information of the underlying biological facts is provided. In this study, we use the Petri net approach for modeling signaling pathways, and propose a method to determine firing delay times of transitions for Petri net models of signaling pathways by introducing stochastic decision rules. Petri net technology provides a powerful approach to modeling and simulating various concurrent systems, and recently have been widely accepted as a description method for biological pathways. Our method enables to determine the range of firing delay time which realizes smooth token flows in the Petri net model of a signaling pathway. The availability of this method has been confirmed by the results of an application to the interleukin-1 induced signaling pathway.

Fuzzy adaptive management of social and ecological carrying capacities for protected areas

Commonly used methods of evaluating the degree of consistency of protected area ecosystems with social and ecological carrying capacities are likely to result in decision errors. This occurs because such methods do not account for imprecision and uncertainty in inferring the degree of ecosystem consistency from an observed ecosystem indicator. This paper proposes a fuzzy adaptive management approach to determine whether a protected area ecosystem is consistent with ecological and social carrying capacities and, if not, to identify management actions that are most likely to achieve consistency when there is uncertainty about the current degree of consistency and how alternative management actions are likely to influence that consistency. The proposed approach is illustrated using a hypothetical example that uses an ecosystem indicator that reflects combinations of different levels of user satisfaction and conservation of threatened and endangered species. Application of the proposed fuzzy adaptive management approach requires a protected area manager to: (1) identify alternative management actions for achieving ecosystem consistency with social and ecological carrying capacities in each of several management zones in a protected area; (2) randomly assign alternative management actions to management zones; (3) define fuzzy sets for the ecosystem indicator and degree of ecosystem consistency, and fuzzy relations between the ecosystem indicator and the degree of ecosystem consistency; (4) monitor the indicator in each management zone; (5) define fuzzy sets based on the observed indicator in each management zone; and (6) combine the fuzzy sets defined on the observed indicator and the fuzzy relations between the indicator and the degree of ecosystem consistency to reach conclusions about the most likely degree of consistency for alternative management actions in each management zone. The fuzzy adaptive management approach proposed here is advantageous when the benefits of avoiding the decision errors inherent with crisp and stochastic decision rules outweigh the added cost of implementing the approach.

Patterns of Consumption in a Discrete Choice Model with Asymmetric Interactions

We study the consumption behaviour of an asymmetric network of heterogeneous agents in the framework of discrete choice models with stochastic decision rules. We assume that the interactions among agents are uniquely specified by their ``social distance'' and consumption is driven by peering, distinction and aspiration effects. The utility of each agent is positively or negatively affected by the choices of other agents and consumption is driven by peering, imitation and distinction effects. The dynamical properties of the model are explored, by numerical simulations, using three different evolution algorithms with: parallel, sequential and random-sequential updating rules. We analyze the long-time behaviour of the system which, given the asymmetric nature of the interactions, can either converge into a fixed point or a periodic attractor. We discuss the role of symmetric versus asymmetric contributions to the utility function and also that of idiosyncratic preferences, costs and memory in the consumption decision of the agents.

Semi-infinite relaxation of joint chance constraints in chance-constrained programming Part 1. Zero-order stochastic decision rules†

A new class of semi-infinite deterministic (‘determinizations’) dominants and relaxations of joint chance-constraints in chance-constrained programming is developed and specialized to zero-order stochastic decision rule situations. Tight constraint relaxations are obtained where only the partial information of means and variances is known. The tight non-linear semi-infinite relaxations are related to an accessible finite subsystem. When the chance constraints involve linear inequalities, for a large class, the non-linear tight system is proved equivalent to a linear program. Its solutions for the Prekopa-Szantai reservoir construction examples agree well with theirs

Sequential female choice and the previous male effect in sticklebacks

Female choice, identified as a major force in sexual selection theory, has recently been demonstrated in a number of species. These tests concentrated on simultaneous choice situations although females have to compare males sequentially in most territorial species, which is the more demanding task. Here it is shown that female three-spined sticklebacks, Gasterosteus aculeatus L., rate sequentially presented males according to their brightness. With increasing costs of sampling the females become less choosy. Furthermore, a male's attractiveness has a significant effect on the female's rating of the next male; a given male is rated higher when preceded by a duller male than by a brighter one and vice versa. Female sticklebacks use a stochastic decision rule in sequential mate choice that is attuned to the attractiveness of the present and previously encountered male. This demonstration of a “previous male effect” not only indicates an efficient mechanism for finding the best of a number of males but also extends the applicability of sexual selection theory.

Identification and Estimation Issues for a Causal Earnings Model

In this paper, I postulate a causal, or structural, model of corporate earnings and present a theoretical analysis of various empirical issues related to the identification and estimation of time-series earnings models.' The postulated model describing corporate earnings is derived endogenously by specifying a model of the firm's production and invest ment structure and its inventory accounting rule. The main characteristic of this model is that the firm uses linear stochastic decision rules to determine its production, inventory, and capital investment levels. Such decision rules are frequently postulated in the economics literature. Using the theoretical properties of the derived earnings model, I then address estimation and forecasting issues in a general manner without actually doing the estimation. Starting with Dopuch and Watts [1972], much of the empirical research in accounting on the structural (i.e., time-series) properties of earnings numbers has first postulated a linear, stochastic, time-series model as the underlying earnings-generating process, and then identified and estimated the model using a sample of realized earnings numbers. These accounting studies usually have the goal of estimating an expectation model to generate expected or forecasted earnings. This type of end

Models for Allocating Police Preventive Patrol Effort

This paper develops models that maximize the expected number of occasions per unit of time that a police patrol unit enters a street segment during the time that a crime is visible. Constraints are added that insure a minimum patrol coverage to all streets. The successive visits from street-to-street form a Markov chain. The solution that maximizes the objective function gives a stochastic decision rule which is used with Monte Carlo techniques to generate a random patrol schedule. The problem is posed with one car and several cars patrolling the same region.

Dissection Methods for Solutions in Chance Constrained Programming Problems Under Discrete Distributions

Under the assumption of discrete distributions for the random variables involved, deterministic equivalent problems are derived for a general class of chance constrained (but not necessarily linear) programming problems. These permit the explicit solution of such problems for all or most types of optimal stochastic decision rules which are of interest, including optimal multistage rules and not restricted to the class of linear rules. The formulation given encompasses certain cases of stochastic programming with recourse, and the deterministic equivalents derived for these reduce to well-known versions available in the literature.

Solution theorems in probabilistic programming: A linear programming approach

Abstract : For some years research on solution theorems in probabilistic programming has been dormant. The obvious consequences of formal similarities to deterministic mathematical programming problems had been rapidly exhausted by researchers. Currently, however, the deeper study which was taking place during the 'dormant period' has begun to produce results. On the one hand theorems characterizing optimal classes of stochastic decision rules for various general change-constrained problems have been obtained. On the other hand, a great amount of effort has been expended on the special class of problems called linear programming problems under uncertainty, usually 2-stage and under still more special assumptions. The general objective of these specializations has been to attain results and thereby to gain insight and technique to reapproach more fruitfully the more important and general but more recondite probabilistic programming problems. To this end, few abstractions or devices, from finite-dimensional Banach spaces to the Kakutani fixed-point theorem appear to have gone untried, except, perhaps, the ancient one of study and correlation of the existent results of other researchers. It is the purpose of this paper to provide some such correlation and a redirection so that these simpler probabilistic programming problems may be overcome in all generality with new, simpler methods which offer some promise of extension to the more involved chance constrained (and other probabilistic) models.

Chance-Constrained Programming

A new conceptual and analytical vehicle for problems of temporal planning under uncertainty, involving determination of optimal (sequential) stochastic decision rules is defined and illustrated by means of a typical industrial example. The paper presents a method of attack which splits the problem into two non-linear (or linear) programming parts, (i) determining optimal probability distributions, (ii) approximating the optimal distributions as closely as possible by decision rules of prescribed form.