Application Of Bayesian Decision Theory Research Articles

NON-FACTIVE KOLMOGOROV CONDITIONALIZATION

Abstract Kolmogorov conditionalization is a strategy for updating credences based on propositions that have initial probability 0. I explore the connection between Kolmogorov conditionalization and Dutch books. Previous discussions of the connection rely crucially upon a factivity assumption: they assume that the agent updates credences based on true propositions. The factivity assumption discounts cases of misplaced certainty, i.e., cases where the agent invests credence 1 in a falsehood. Yet misplaced certainty arises routinely in scientific and philosophical applications of Bayesian decision theory. I prove a non-factive Dutch book theorem and converse Dutch book theorem for Kolmogorov conditionalization. The theorems do not rely upon the factivity assumption, so they establish that Kolmogorov conditionalization has unique pragmatic virtues that persist even in cases of misplaced certainty.

Necessity of Multiple Rounds of Nucleic Acid Detection: Application of Bayesian Decision Theory in Real Life

Bayesian Decision is a risk-based decision that uses the Bayesian formula to combine prior probability with conditional probability, which helps people make more mathematically logical inferences in the continuous updating of data and facts. In this paper, Bayesian Decision will be applied to analyze the necessity of multiple rounds of nucleic acid detection in middle and high risk areas up against the epidemic. Besides, data processing will be conducted in positive patients and negative patients. Then Bayesian factor is introduced to simplify the calculation to draw the corresponding conclusions, and the practical application value of Bayesian Decision is prospected.

Analysis of Application Status of Bayesian Decision

There are many applications of Bayesian decision theory in computer science and mathematical modeling. Because of how it works, the algorithm can evaluate possible outcomes and choose a course of action. Decisions are made in the face of ambiguity and incomplete information in every area of human activity. When making a choice, it is common for the outcomes and their worth to the decision maker to rely on factors outside their control. Bayesian decision theory is devoted to solving these sorts of decision-making difficulties. Using Bayesian decision theory has benefited engineering, economics, business, public policy, and even AI. Examining recent literature in the field, this study delves into how Bayesian decision theory might be used for tasks including mistake detection, risk assessment, and route planning. The study’s findings demonstrate the value and utility of using Bayesian decision theory, and the authors hope that its presentation will stimulate the use of a similar approach in the future.

When to give aspirin to prevent preeclampsia: application of Bayesian decision theory

There is good evidence that first-trimester assessment of the risk for preterm preeclampsia and treatment of the high-risk group with aspirin reduces the incidence of preterm preeclampsia. Furthermore, there is evidence that aspirin is associated with an increased risk of maternal and neonatal hemorrhagic complications. Against this background, there are ongoing debates whether aspirin should be recommended for all women or to a subpopulation of women predicted to be at increased risk of developing preeclampsia. Moreover, if a strategy of the prediction and prevention of preterm preeclampsia is to be used, what method should be used for the prediction, and what risk cutoff should be used to decide on who to treat? This study aimed to compare the policies of universal treatment, stratified treatment, and no treatment with aspirin. Decisions about aspirin prophylaxis were considered from the perspective of the Bayesian decision theory. Using this approach, the treatment policies were evaluated for risks of preterm preeclampsia, effects of aspirin, and trade-offs between the harms and benefits of the treatment. Evidence on the risk of preterm preeclampsia was taken from the Screening programme for pre-eclampsia study, which was a first-trimester screening study for the prediction of preeclampsia. Evidence of the effect of aspirin was taken from the Aspirin for Evidence-Based Preeclampsia Prevention trial, which was a trial of aspirin vs placebo in the prevention of preterm preeclampsia. The trade-off between the benefits and harms of aspirin was specified by addressing the question, "What is the maximum number of women that should be treated to prevent 1 case of preterm preeclampsia?" The number can be considered as an exchange rate between the harms and benefits of using aspirin to prevent preterm PE. Given the uncertainty about the harms associated with aspirin, the treatment policies were compared across a wide range of exchange rates. For exchange rates between 10 and 1000 women treated with aspirin to prevent 1 case of preterm preeclampsia, the net benefit achieved from the risk assessment and targeted treatment of women at high risk of preterm preeclampsia was higher than that from women with no treatment or women with universal treatment with aspirin. Universal treatment with aspirin should be avoided. Risk-based screening should be used, and the cutoff for taking aspirin should be determined from the consideration of the trade-off between the benefits and harms and detection, false-positive, and screen-positive rates.

An Improved Dutch Book Theorem for Conditionalization

Lewis proved a Dutch book theorem for Conditionalization. The theorem shows that an agent who follows any credal update rule other than Conditionalization is vulnerable to bets that inflict a sure loss. Lewis’s theorem is tailored to factive formulations of Conditionalization, i.e. formulations on which the conditioning proposition is true. Yet many scientific and philosophical applications of Bayesian decision theory require a non-factive formulation, i.e. a formulation on which the conditioning proposition may be false. I prove a Dutch book theorem tailored to non-factive Conditionalization. I also discuss the theorem’s significance.

On the proper formulation of conditionalization

Conditionalization is a norm that governs the rational reallocation of credence. I distinguish between factive and non-factive formulations of Conditionalization. Factive formulations assume that the conditioning proposition is true. Non-factive formulations allow that the conditioning proposition may be false. I argue that non-factive formulations provide a better foundation for philosophical and scientific applications of Bayesian decision theory. I furthermore argue that previous formulations of Conditionalization, factive and non-factive alike, have almost universally ignored, downplayed, or mishandled a crucial causal aspect of Conditionalization. To formulate Conditionalization adequately, one must explicitly address the causal structure of the transition from old credences to new credences. I offer a formulation of Conditionalization that takes these considerations into account, and I compare my preferred formulation with some prominent formulations found in the literature.

Application of Bayesian Decision Theory Based on Prior Information in the Multi-Objective Optimization Problem

General multi-objective optimization methods are hard to obtain prior inform ation, how to utilize prior information has been a challenge. This paper analyzes the characteristics of Bayesian decision-making based on maximum entropy principle and prior information, especially in case that how to effectively improve decision-making reliability in deficiency of reference samples. The paper exhibits effectiveness of the proposed method using the real application of multi-frequency offset estimation in distributed multiple-input multiple-output system. The simulation results demonstrate Bayesian decision-making based on prior information has better global searching capability when sampling data is deficient.

Application of Bayesian Decision Theory Based on Prior Information in the Multi-Objective Optimization Problem

Application of Bayesian Decision Theory Based on Prior Information in the Multi-Objective Optimization Problem

Disease Cycle Approach to Plant Disease Prediction

Plant disease cycles represent pathogen biology as a series of interconnected stages of development including dormancy, reproduction, dispersal, and pathogenesis. The progression through these stages is determined by a continuous sequence of interactions among host, pathogen, and environment. The stages of the disease cycle form the basis of many plant disease prediction models. The relationship of temperature and moisture to disease development and pathogen reproduction serve as the basis for most contemporary plant disease prediction systems. Pathogen dormancy and inoculum dispersal are considered less frequently. We found extensive research efforts evaluating the performance of prediction models as part of operation disease management systems. These efforts appear to be greater than just a few decades ago, and include novel applications of Bayesian decision theory. Advances in information technology have stimulated innovations in model application. This trend must accelerate to provide the disease management strategies needed to maintain global food supplies.

Predictive strategic marketing management decisions in small firms

PurposeThe purpose of this paper is to suggest a framework for sales forecasting more suitable for smaller firms. The authors examine the sales forecasting practices of small firms and then proceed to discuss the application of Bayesian decision theory in the production of sales forecasts, a method arguably more suited to the smaller firm. The authors suggest that many small firm entrepreneurs are inherently “Bayesian” in their thinking approach to predicting events in that they often rely on subjective estimates at least for initial starting values.Design/methodology/approachA triangulated approach which uses qualitative group discussions and thematic content analysis, a reasonably large‐scale questionnaire sample survey administered by post and analysed using descriptive statistics and non‐parametric tests of association and a case study approach based on the authors own consultancy activities to illustrate the practical application of the forecasting model suggested.FindingsThat many small firms use no formal sales forecasting framework at all. That the majority of small firm owners and/or managers rate sales forecasting skills very low in their list of priorities when given a choice of course to attend at subsidised rates. That there is no significant difference in the importance small firm owners and/or managers attach to formal sales forecasting skills.Research limitations/implicationsInformation has been gained from one geographic area in the north of England although the results may have a wider application to all small firms in the UK and elsewhere. Only the region's six most important industry sectors were included as stratification variables in the sample survey. Other regions will have a different mix of industries and will be stratified differently.Originality/valueThe article addresses the sales forecasting needs of small firms specifically within the marketing for small business context and offers a realistic option with a clear rationale.

Applications of Bayesian Decision Theory to Sequential Mastery Testing

The purpose of this paper is to formulate optimal sequential rules for mastery tests. The framework for the approach is derived from Bayesian sequential decision theory. Both a threshold and linear loss structure are considered. The binomial probability distribution is adopted as the psychometric model involved. Conditions sufficient for sequentially setting optimal cutting scores are presented. Optimal sequential rules will be derived for the case of a subjective beta distribution representing prior true level of functioning. An empirical example of sequential mastery esting for concept-learning in medicine concludes the paper.

Applications of Bayesian Decision Theory to Sequential Mastery Testing

The purpose of this paper is to formulate optimal sequential rules for mastery tests. The framework for this approach is derived from empirical Bayesian decision theory. Both a threshold and linear loss structure are considered. The binomial probability distribution is adopted as the psychometric model involved. Conditions sufficient for sequentially setting optimal cutting scores are presented. Optimal sequential rules will be derived for the case of a beta distribution representing prior true level functioning. An empirical example of sequential mastery testing for concept-learning in medicine concludes the paper.

Sample Size Determination for Phase II Clinical Trials Based on Bayesian Decision Theory

This paper describes an application of Bayesian decision theory to the determination of sample size for phase II clinical studies. The approach uses the method of backward induction to obtain group sequential designs that are optimal with respect to some specified gain function. A gain function is proposed focussing on the financial costs of, and potential profits from, the drug development programme. On the basis of this gain function, the optimal procedure is also compared with an alternative Bayesian procedure proposed by Thall and Simon. The latter method, which tightly controls type I error rate, is shown to lead to an expected gain considerably smaller than that from the optimal test. Gain functions with respect to which Thall and Simon's boundary is optimal are sought and it is shown that these can only be of the form considered, that is, with constant cost for phase III study and cost of the phase II study proportional to the sample size, if potential profit increases over time.

Applications of Bayesian decision theory to intelligent tutoring systems

The purpose of this paper is to consider some applications of Bayesian decision theory to intelligent tutoring systems. In particular, it will be indicated how the problem of adapting the appropriate amount of instruction to the changing nature of student's capabilities during the learning process can be situated within the general framework of Bayesian decision theory. Two basic elements of this approach will be used to improve instructional decision making in intelligent tutoring systems. First, it is argued that in many decision-making situations the linear loss model is a realistic representation of the losses actually incurred. Second, it is shown that the psychometric model relating observed test scores to the true level of functioning can be represented by Kelley's regression line from classical test theory. Optimal decision rules will be derived using these two features.

An Application of Bayesian Decision Theory to the Design and Inspection of Marine Structures

Life of structures which are subject to fatigue failures involves high degree of uncertainty and risk. In order to design such systems it is necessary to take into account several stochastic elements. As the structure ages, the relationship among initial cost, inspections, maintenance and reliability level becomes important, and it has to be studied in order to achieve a good design from the cost-effectiveness point of view. This paper analyses this relationship and proposes a method to take the best decision among a set of alternatives regarding structural dimensions using a new class of Bayesian loss functions that are based on the concepts of under and over design.

A decision-theoretic approach to planning, perception, and control

The application of Bayesian decision theory as a framework for designing high-level robotic control systems is discussed. The approach to building planning and control systems integrates sensor fusion, prediction, and sequential decision making. The system explicitly uses the value of sensor information as well as the value of actions that facilitate further sensing. A stochastic decision model and a model for mobile-target localization used in the control system are described. A control system implemented to drive a small mobile robot equipped with eight sonar transducers with a maximum range of six meters and a visual processing system capable of identifying moving targets in its visual field and reporting their motion relative to the robot is also discussed. >

An Application of Bayesian Decision Theory to Decentralized Control of Job Scheduling

There is a wide spectrum of techniques that can be aptly named decentralized control. However, certain functions in distributed operating systems, e.g., scheduling, operate under such demanding requirements that no known optimal control solutions exist. It has been shown that heuristics are necessary. This paper presents a heuristic for the effective cooperation of multiple decentralized components of a job scheduling function. An especially useful feature of the heuristic is that it can dynamically adapt to the quality of the state information being processed. Extensive simulation results show the utility of this heuristic. The simulation results are compared to several analytical models and a baseline simulation model. The heuristic itself is based on the application of Bayesian decision theory. Bayesian decision theory was used because its principles can be applied as a systematic approach to complex decision making under conditions of imperfect knowledge, and it can run relatively cheaply in real time.

Toward a Cognitive Spatial Theory

Our knowledge of the external world impinges upon our actions, and our acts affect our knowledge. The relationship between behavior and knowledge is mutual or circular, and exceedingly complex. In this paper we simplify and compartmentalize this mutual relationship and focus particularly on the elementary observation that where one lives, where one travels, and what one does affects what one knows of and understands about the world. In what way can we account for this observation? Models have been constructed which attempt to explain how an individual acquires information relevant to behavior and how that information affects behavior. Thus, Webber [14, pp. 110-14] provides normative models of the manner in which a profit maximizing firm collects the information basic to decisions about plant location; Burnett [2, 3] models the choice of shops by people who are gradually acquiring information about a retail system; Golledge and Brown [6] have indicated some of the uses of decision theory in examining market behavior; and King and Golledge [8] have illustrated some applications of Bayesian decision theory to such situations. In all these cases, the information gathered is relevant to the way in which the individual behaves-behavior changes as the amount and quality of available information increases. Here we focus attention on behavior, and

An Application of Statistical Decision Theory to Commercial Turkey Production

This article provides an empirical application of Bayesian decision theory to management decisions under uncertainty. The empirical problem is one of choice between contract and independent production of turkeys. The major random variables affecting incomes are product prices and mortality rates. The optimal action is first determined where only prior probabilities of the states of nature are available. Optimal strategies are then determined where a price‐forecasting model is available and posterior probabilities of the states are determined. The value of the additional information provided by the price‐forecasting model is substantial. Simulated growth in firm net worth is faster and more stable when the price‐forecasting model is used.