Bayesian Revision Research Articles

Interaction between Productivity and Measurement

INTRODUCTION Measurement often appears far from benign. Close to home we have the systemwide, at times corrosive effects of student evaluations and popular press rankings. Modern medicine exhibits cycles of advances in measurement, e.g., blood chemistry, followed by development of pharmaceuticals designed to improve those measures. Many are the stories of the athlete more interested in personal than team glory. And then there is the unfolding case of earnings, where we encounter developments in financial engineering and organizational arrangements that seem to have no purpose beyond improving the earnings measure. Economically, we are accustomed to measures being simply a source of information, where Bayesian revision in decision making or valuation and optimal contracting in trading arrangements determine the information’s effect on organizational and individual behavior. Although subtleties surface in a multitask setting, and we know ‘‘bad’’ information can drive out ‘‘good’’ information (e.g., Holmstrom and Milgrom 1991), it seems the story is deeper. A commitment to produce a particular set of measures has the potential to affect the organization’s behavior, to affect productivity, in ways that go beyond traditional information effects. Here we put forward and analyze one such setting. Exactly how the act of measurement produces effects beyond mere information effects is an open question. Our approach is to look to the physical sciences, where measurement is far from benign, and to import the natural effect of measurement in that setting to a human organization. We do not claim this

A statistical framework for strategic decision making with AHP: Probability assessment and Bayesian revision

A probability assessment framework is outlined for an organizational decision involving a conditioning event (CE). The decision may, for example, involve a new-product launch (strategic decision) dependent on the outcome of market research (CE). The framework illustrates how Bayesian revision could be employed as related “news” arrives intermittently to revise current probabilities prior to decision implementation. A unique contribution of this paper is its utilization of the analytic hierarchy process to ascertain a set of consistent and coherent probabilities for the event/sample spaces at all stages of the decision process.

Modeling Costs and Cost-Effectiveness of Different CMV Management Strategies in Liver Transplant Recipients as a Support for Current and Future Decision Making

Objectives To develop a generic decision-analytic model to predict health and economic outcomes of different management options for cytomegalovirus (CMV) infection and disease in liver transplant patients. Methods and Data The model considers different CMV management strategies, thereby emphasizing the important difference between infection and disease. The first strategy starts with prophylaxis prior to transplantation, followed by preemptive treatment if infection, based on positive CMV diagnostic tests, is confirmed. The second strategy is a preemptive strategy consisting of only testing followed by preemptive treatment. Finally, in the wait-and-treat strategy, antiviral treatment is only started when clinical signs of CMV disease appear. Management and resource-use data were obtained from clinical experts in large transplant centers in France, Germany, and the United Kingdom. Cost data were collected from the health care payer's perspective. A Bayesian revision technique was applied to distinguish effectiveness of current management options for CMV infection vs. CMV disease, an aspect that is currently underreported in literature. Results CMV prophylaxis in liver transplant recipients is generally more cost-effective than preemptive and wait-and-treat strategies. In order of importance, changes in drug costs, drug efficacy, specificity of CMV testing, cost of hospitalization, probability of CMV relapse and baseline CMV risk are the most important factors influencing the cost-effectiveness. Conclusion This model describes different strategies applied for management of CMV in liver transplant patients and is useful both for current decision making, optimal disease management, and assessment of future research targets.

Perceptual-cognitive universals as reflections of the world

The universality, invariance, and elegance of principles governing the universe may be reflected in principles of the minds that have evolved in that universe--provided that the mental principles are formulated with respect to the abstract spaces appropriate for the representation of biologically significant objects and their properties. (1) Positions and motions of objects conserve their shapes in the geometrically fullest and simplest way when represented as points and connecting geodesic paths in the six-dimensional manifold jointly determined by the Euclidean group of three-dimensional space and the symmetry group of each object. (2) Colors of objects attain constancy when represented as points in a three-dimensional vector space in which each variation in natural illumination is canceled by application of its inverse from the three-dimensional linear group of terrestrial transformations of the invariant solar source. (3) Kinds of objects support optimal generalization and categorization when represented, in an evolutionarily-shaped space of possible objects, as connected regions with associated weights determined by Bayesian revision of maximum-entropy priors.

Hydrologic uncertainty processor for probabilistic river stage forecasting: precipitation-dependent model

The hydrologic uncertainty processor (HUP) is a component of the Bayesian forecasting system (BFS) which produces a short-term probabilistic river stage forecast (PRSF) based on a probabilistic quantitative precipitation forecast (PQPF). The task of the HUP is to quantify the hydrologic uncertainty under the hypothesis that there is no precipitation uncertainty. The hydrologic uncertainty is the aggregate of all uncertainties arising from sources other than those quantified by the PQPF. The precipitation-dependent HUP has two branches, each conditional on the hypothesized occurrence or nonoccurrence of precipitation during the period covered by the PQPF (here 24 h). Under each hypothesis, the time series of river stages (here at 24-h steps) is modeled a priori as a Markov process of order one with nonstationary transition distributions. The families of prior distributions and likelihood functions are all nonstationary (with forecast lead time) and meta-Gaussian (with respect to their multivariate dependence structure). For each lead time, Bayesian revision yields two families of posterior distributions whose mixture, determined by the probability of precipitation occurrence, characterizes the hydrologic uncertainty. Estimation and validation of the HUP are described using data from the operational forecast system (OFS) of the National Weather Service (NWS) for a 1430 km 3 headwater basin.

Hydrologic uncertainty processor for probabilistic river stage forecasting

The hydrologic uncertainty processor (HUP) is a component of the Bayesian forecasting system that produces a short‐term probabilistic river stage forecast based on a probabilistic quantitative precipitation forecast (PQPF). The task of the HUP is to quantify the hydrologic uncertainty under the hypothesis that there is no precipitation uncertainty. The hydrologic uncertainty is the aggregate of all uncertainties arising from sources other than those quantified by the PQPF; these sources include the hydrologic model (model and parameter uncertainties), inputs estimated deterministically (measurement, estimation, and prediction uncertainties), and inputs not forecasted (e.g., precipitation beyond the period covered by the PQPF). Bayesian theory for the HUP is presented, and a meta‐Gaussian model is developed. This parametric model allows for (1) any form of marginal distributions of river stages, (2) a nonlinear and heteroscedastic dependence structure between the model river stage and the actual river stage, and (3) an analytic solution of the Bayesian revision process. Estimation and validation of the model are described using data from the operational forecast system of the National Weather Service for a 1430‐km2 headwater basin.

Action-timing problem with sequential Bayesian belief revision process

We consider the problem of deciding the best action time when observations are made sequentially. Specifically we address a special type of optimal stopping problem where observations are made from state-contingent distributions and there exists uncertainty on the state. In this paper, the decision-maker's belief on state is revised sequentially based on the previous observations. By using the independence property of the observations from a given distribution, the sequential Bayesian belief revision process is represented as a simple recursive form. The methodology developed in this paper provides a new theoretical framework for addressing the uncertainty on state in the action-timing problem context. By conducting a simulation analysis, we demonstrate the value of applying Bayesian strategy which uses sequential belief revision process. In addition, we evaluate the value of perfect information to gain more insight on the effects of using Bayesian strategy in the problem.

Efficiency testing revisited: a foreign exchange market with Bayesian learning

The paper re-examines the efficiency hypothesis in the foreign exchange market. The traditional efficiency-testing equations are reviewed and a more general model is developed that incorporates Bayesian revisions of devaluation expectations. A number of properties regarding the pattern of the coefficients in efficiency-testing equations are established. The empirical estimation of the model by using data from the emerging foreign exchange market in Greece confirms the properties of the theoretical model.

PHASED CAPACITY EXPANSION - USING CONTINUOUS DISTRIBUTIONS TO MODEL PRIOR BELIEFS

ABSTRACT Many current equipment replacement/production capacity expansion decisions carry increasing amounts of performance uncertainty when the alternative processes include technical innovations. In a sequential decision making environment, post-audit information can be used to resolve this uncertainty. In this paper, we demonstrate how three-point, PERT-type estimates can be used to determine continuous prior probability distributions that incorporate the post-audit information in Bayesian revision. Further, we develop the concept of equivalent sample size to insert qualitative judgment into the decision making process. This is initially used to reflect our belief in the estimates' quality, and, subsequently, in an assessment of the quality of the observed sample data. A case study of an actual decision problem is used to illustrate the concepts.

Bayesian analysis of foraging by pigeons (Columba livia).

In this article, the authors combine models of timing and Bayesian revision of information concerning patch quality to predict foraging behavior. Pigeons earned food by pecking on 2 keys (patches) in an experimental chamber. Food was primed for only 1 of the patches on each trial. There was a constant probability of finding food in a primed patch, but it accumulated only while the animals searched there. The optimal strategy was to choose the better patch first and remain for a fixed duration, thereafter alternating evenly between the patches. Pigeons were nonoptimal in 3 ways: (a) they departed too early, (b) their departure times were variable, and (c) they were biased in their choices after initial departure. The authors review various explanations of these data.

USING DATA FROM EPIDEMIOLOGIC STUDIES TO REVISE PROBABILITIES

Information about the relationship between risk factors and the probability of disease is often reported by an odds ratio, although its use for revising the probability of disease in a clinical setting is not intuitive and requires complex computations. A somewhat better approach is Bayesian probability revision. The authors present a method where likelihood ratios can be obtained from odds ratios, and they present simple computational methods for implementing all of the techniques described.

Trend analysis and prediction procedures for time nonhomogeneous claim processes

The paper focuses on time nonhomogeneous claim occurrence processes. Such processes arise either in a natural way, as a result of modelling (often qualitative-type) assumptions, or when a trend may exist and needs to be allowed for in the model construction. For trend analysis, we use trend representations which are formulated on the basis of an appropriate process characteristic in conjunction with a probabilistic ordering notion. Such trend representations are verified for a given process with respect to assumptions on its stochastic behaviour. Making predictions with regard to quantities of interest such as the time to the next claim or the expected total number of claims in the next year is the other major goal of this work. The predictions are obtained by employing Bayesian revision procedures for different inference models on the claim occurrence process.

Perceptual-cognitive universals as reflections of the world

The universality, invariance, and elegance of principles governing the universe may be reflected in principles of the minds that have evolved in that universe-provided that the mental principles are formulated with respect to the abstract spaces appropriate for the representation of biologically significant objects and their properties. (1)Positions andmotions of objects conserve theirshapes in the geometrically fullest and simplest way when represented as points and connecting geodesic paths in the six-dimensional manifold jointly determined by the Euclidean group of three-dimensional space and the symmetry group of each object. (2)Colors of objects attain constancy when represented as points in a three-dimensional vector space in which each variation in natural illumination is cancelled by application of its inverse from the three-dimensional linear group of terrestrial transformations of the invariant solar source. (3)Kinds of objects support optimal generalization and categorization when represented, in an evolutionarily shaped space of possible objects, as connected regions with associated weights determined by Bayesian revision of maximum-entropy priors.

Single and Multiple Period Decision Models for Analysis of Quality and Quantity of Validation*

ABSTRACTThis paper investigates a single period model for the analysis of the impact of the quality of the validation effort. The single period model uses a Bayesian approach to find that validation is a critical point process. That model is then extended to allow for the uncertainty of the validation process to determine the quality of the underlying model. Some monotonicity results are developed for the model and investigated in light of the process being a critical point process. The model indicates that, consistent with comments from real world settings, the impact of the quality of the validation effort can be substantial.The paper also presents two multiperiod models of the impact of the quantity of the validation effort. In practice, the development of an expert system may follow a recurring multiperiod life cycle, where a prototype is built, the system is validated to determine how well it performs, and based on that performance, is either funded or not funded. The first multiple period model assumes that validation and funding occurs at each point in the PVF budget cycle. The model employs Bayesian revision of probabilities to update the prior probability of obtaining a model with an appropriate level of success. It is found that the critical point for multiperiod problems is different than that for single period problems. This model forms the basis of the second model. The second multiple period model extends the first by assuming that the quantity of validation can be varied. The more validation, the more likely that flaws in the model will be found. Thus, the more validation, the better the understanding of the level of performance of the model.

A Warning Zone Method for the Multiperiod Cost Variance Investigation Problem

ABSTRACTThis paper develops a warning zone approach to make variance investigation decisions for a multiperiod process. The assumed cost generation process varies between an in‐control and out‐of‐control state. These states cannot be directly observed, but must be inferred from the reported cost variances. Using the warning zone method of inference, the manager investigates the process whenever an upper threshold is exceeded or a lower threshold is exceeded for two consecutive periods. A four‐state Markov chain models the resulting decision process. Steady state probabilities are derived for this chain and are used to obtain explicit formulas for the effectiveness and efficiency of the decision process. These formulas permit computation of the cost savings attainable by the warning zone method. Compared to other decision rules, the warning zone method is much simpler than the theoretically optimal Bayesian revision method, but uses more information than the Markovian control limit method. Numerical comparison of results shows that the warning zone method usually captures most of the available cost savings, even in cases where the Markovian control limit method does not perform well.

Beyond sensitivity, specificity and statistical independence.

Sensitivity and specificity have clear definitions when there is a single test for one disease, and the test is either positive or negative. This paper presents a unified approach for obtaining posterior probabilities (predictive values) when there are more than two test outcomes and/or more than one disease state. In these cases, sensitivity and specificity do not have clear definitions. Three examples from the literature demonstrate how this approach simplifies the presentation of Bayesian revision of prior probabilities. Use of proper care in data collection for the purpose of estimating conditional probabilities can avoid assumptions of statistical independence.

The impact of confidence interval information on probability judgements

Previous efforts to demonstrate the value of confidence interval financial statements for credit evaluation and investment decisions have met with limited success. The present study examined the impact of nonfinancial confidence interval reports on predecisional behavior. A Bayesian revision task was used to investigate the impact of report type, information system uncertainty and decision problem uncertainty on the accuracy of probability judgements. All three variables influenced task performance. Moreover, subjects given confidence interval reports outperformed those who were given single-figure reports when significant information system and decision problem uncertainties were present. The results obtained here suggest several facets of the decision setting which may influence the value of confidence interval financial statements.

On the combinatorial structure of Bayesian learning with imperfect information

Apart from the enumerative nature of event frequencies, the connection between Bayesian theory and combinatories does not seem to be an obvious one. In this paper, I study the underlying combinatorial structure of a particular class of Bayesian revision problems. This class is characterized by two properties. First, the initial Bayesian prior is taken to be Dirichlet. Second, the sequence of observations generated by the stochastic process in question, assumed i.i.d., is taken to convey imperfect information in general. In the body of the paper, I demonstrate that the combinatorial features of interest surface during the application of Bayes' Rule. This gives rise to a sequence of posterior distributions having strong combinatorial attributes. Not unexpectedly, the first moments of the posteriors turn out to have strong combinatorial attributes as well; and these are of special interest. Finally, the analysis serves to generalize the well-known conjugate family property for Dirichlet distributions (see DeGroot [1]) from the case when observations convey perfect information to the case where they convey imperfect information.

Revising Earnings Per Share Forecasts: An Empirical Test

In this study, we postulate that forecasters desire to improve their performance by studying their past forecasting errors. To improve performance, forecasters may measure their past mistakes and revise their forecasts by forecast revision techniques. In an empirical test, forecasts of fifty firms' EPS were prepared by seven forecasting models. The initial forecasts were corrected by the Theil optimal linear correction technique and a Bayesian revision adjustment. Results indicate that the optimal linear correction technique is superior to not correcting for past forecast error.

DISCRETE-TO-BETA: A FORTRAN IV program for converting discrete prior distributions into beta prior distributions

The beta distribution is frequently used when one wants to make Bayesian revisions about priors, as is discussed in Till (1977). The use of continuous rather than discrete priors makes the decision framework less artificial and computationally more efficient. However, unfamiliarity with the beta distribution causes added assessment problems (Corless, 1972; Gentry, Bonczkowski, & Caldwell, in press). Consequently, training in the use of the beta distributions is needed before using the distribution in a decision-making framework. One means of obtaining the needed familiarity with the beta distribution is to provide information on corresponding discrete and beta distributions. The Program. DISCRETE-TO-BETA is a FORTRAN IV program that finds a beta distribution corresponding to the input discrete distribution through the method of moments. The two distributions are plotted so that the user can get a better idea of their correspondence. Input. The program requires the input of the discrete states of the world in decimal form (the hypothesized proportions) and the prior probability that each state is the true one. Output. The program generates the mean and variance of the discrete distribution and the values of the estimates of the beta parameters that provide the same mean and variance values for the beta distribution. The program also plots the distributions. Restriction. Program DISCRETE-TO-BETA is written in FORTRAN N, so any computer system that supports FORTRAN IV can use it. It takes 1.28 sec to run on the IBM 370-158 computer. Availability. A copy of the listing, documentation, and sample of the output can be obtained free of charge by writing to Jim Gentry, College of Business Administration, Oklahoma State University, Stillwater, Oklahoma 74074.