Showing papers on "Bayesian probability published in 1979"

A Predictive Approach to Model Selection

Abstract: This article offers a synthesis of Bayesian and sample-reuse approaches to the problem of high structure model selection geared to prediction. Similar methods are used for low structure models. Nested and nonnested paradigms are discussed and examples given.

Bayesian analysis of some outlier problems in time series

Abstract: SUMMARY Two models, the aberrant innovation model and the aberrant observation model, are considered to characterize outliers in time series. The approach adopted here allows for a small probability a that any given observation is 'bad' and in this set-up the inference about the parameters of an autoregressive model is considered.

On Outlier Rejection Phenomena in Bayes Inference

Abstract: SUMMARY Inference is considered for a location parameter given a random sample. Outliers are not explicitly modelled, but rejection of extreme observations occurs naturally in any Bayesian analysis of data from distributions with suitably thick tails. For other distributions outlier rejection behaviour can never occur. These phenomena motivate new definitions of outlier-proneness and outlier-resistance. The definitions and methodology are Bayesian but the conclusions also have meaning for nonBayesians because they are proved for arbitrary prior distributions. Thus, for example, the t distribution is said to be outlier-prone because it is shown that any admissible inference procedure applied to a t sample will effectively ignore extreme outlying observations regardless of prior information. On the other hand, the normal distribution, for example, is said to be outlier-resistant because it never allows outlier rejection, regardless of prior information.

On solutions of Bayesian games

Abstract: The theory of Bayesian games, as developped by W. Boge, is axiomatically treated. A direct access to the system of complete reflections is shown. Solutions for these games are defined and characterizations for their existence are given.

A Generalization of the Bayesian Steady Forecasting Model

Abstract: SUMMARY The Bayesian Steady Forecasting model is generalized to a very wide class of processes other than the normal by defining the time series on the decision space. Examples of such processes are presented including a Beta-Binomial process, a Poisson-Gamma process and a Student-t sample distribution steady model. Simple updating relations are given for most of the processes discussed.

The impossibility of bayesian group decision making with separate aggregation of beliefs and values

Abstract: 2Bayesian paradigm. Following it, probability assessments and utility functions are defined independently. It seems reasonable to suggest that groups adopt a similar approach.3 That is, the group should deal separately with the two areas of potential disagreement. By some prescribed procedure, the group aggregates the individual probability assessments into a group probability assessment. Similarly, a group utility function is constructed by aggregating individual utility functions. The group probability assessment and utility function are multiplied in the usual manner to give expected utilities. The action offering the highest expected utility is chosen.4 Most real world decision processes, we recognize, make less than conscientious attempts to separate beliefs from values, either in debate or at time of decision.5

Empirical Bayes Estimation of a Binomial Parameter Via Mixtures of Dirichlet Processes

Abstract: The theory of Dirichlet processes is applied to the empirical Bayes estimation problem in the binomial case. The approach is Bayesian rather than being empirical Bayesian. When the prior is a Dirichlet process the posterior is a mixture of Dirichlet processes. Explicit estimators are given for the case of 2 and 3 parameters and compared with other empirical Bayes estimators by way of examples. Since the number of calculations become enormous when the number of parameters gets larger than 2 or 3 we propose two approximations for estimators of a particular parameter and compare their performance using examples.

Bayesian analysis of the linear model with spatial dependence

Abstract: This paper develops a Bayesian analysis of the linear regression model with spatial dependence in the disturbances. The existing literature in spatial econometrics has been based entirely on sampling theory approaches (e. g. Neyman-Pearson and maximum likelihood) to statistical inference, and the Bayesian perspective has not been explored for spatial estimation. In contrast, the mainstream of econometric work has been influenced by the Bayesian approach to statistical inference during the last ten years, largely through the texts and papers of Zellner and Box (Zellner, 1971; Box and Tiao, 1973) and their associates and students. Bayesian methods have been fruitfully applied to the analysis and estimation of a wide range of econometric problems, such as simultaneous equations (Chetty, 1968), production functions (Tsurumi and Tsurumi, 1976; Zellner and Richard, 1973), distributed lag models (Zellner and Geisel, 1970), the linear model with serially correlated errors (Zellner and Tiao, 1965), and the linear model with non-normal errors (Box and Tiao, 1962).

Long-range earthquake forecasting based on a single predictor

Abstract: Summary. For a long-term predictor from which a joint distribution of earthquake occurrence time and magnitude has been obtained, and also a record of past successes, false alarms and failures, Bayesian statistical methods yield predictive information of the kind needed as a basis for decision-making on precautionary measures. The information is presented in terms of risk refinement, intensity probability and success probability. After the event the relative likelihood that a prediction was a success or failure can be estimated. Comparisons can also be made of the performance of different forecasting models. The application of these methods is illustrated by an example based on the proposed swarm-magnitude predictor.

Multiparameter Univariate Bayesian Analysis

Abstract: Bayesian analysis using Monte Carlo integration is a powerful method for univariate inference. This approach makes possible multiparameter flexibility within families of univariate distributions. These distributions are defined in this article by increasing spline functions superimposed on probability paper coordinate systems. Smoothing is controlled by the prior distribution. The prior distribution also can express uncertainties about the form of the tails when extrapolation beyond the range of the data is required. The handling of difficult forms of data (e.g., quantal response data) is straightforward. Posterior distributions for functions of the parameters can be easily computed.

A Stepwise Bayesian Procedure

Abstract: Ordinarily a Bayesian estimation procedure uses one prior distribution to obtain a unique estimation rule (its Bayes rule). From the decision theoretical point of view, this procedure can be regarded as a convenient way to obtain admissible decision rules. However, many intuitively appealing, admissible estimation rules cannot be obtained directly in this way. We propose a new mechanism, called the Stepwise Bayesian Procedure (SBP). When the parameter space contains only finitely-many points and the loss function is strictly convex, this SBP can be used to obtain every admissible estimation rule. A relationship between SBP and the limiting Bayes rules is given.

Identification of Learning Disabled Adolescents: A Bayesian Approach

Abstract: The identification of learning disabled adolescents for program placement is a major concern of school personnel. An array of problems are associated with the identification of learning disabled populations ranging from the use of the best differentiating characteristics to the types of measures used. The identification model discussed in this article attempts to address some of these problems. The Bayesian approach is an alternative to traditional methods that rely primarily on psychometric data or classroom/clinical observation for identification decisions.

A bayesian nonparametric estimator of survival probability assuming increasing failure rate

Abstract: Bayesian nonparametric estimators of the survival function, the failure rate function, and the density function are obtainedusing jump processes as prior distributions on the space of increasing failure rate functions. The jump processes are intui-tively appealing and have a meaningful physical interpretation. Examples are given and the estimates are compared with the maxi-mum likelihood estimates. In addition, the Bayesian nonpara-metric estimators are presented for arbitrarily right-censored observations.

Choosing among alternative hydrologic regression models

Abstract: Bayesian theory provides for the explicit accounting of both parameter and model uncertainties. It is used in this work to derive a procedure for discriminating among alternative hydrologic regression models. In particular, the procedure was used to discriminate among alternative exogenous variables in regression models. Controlled experiments with hydrologic models were designed to test the proposed procedure under different assumptions on model prior probabilities, length of sample, and model subset. These examples showed that besides its theoretical advantages, the use of the Bayesian procedure unambiguously selects the correct model in most of the applications.

Bayesian Statistics, Credentialing Examinations, and the Determination of Passing Points.

Abstract: The Bayesian approach to setting passing points presents an attractive alternative to the normative and absolute standard approaches. The Bayesian approach takes into explicit consideration important variables such as loss ratios, well-defined minimum criterion levels, the nature of existing data on candidate competence, and the true level of functioning of a candidate. In this article, the Bayesian approach to setting passing points on credentialing examinations in the health fields is considered in the context of the Normal model. Several theoretical examples are given to demonstrate the mechanics of the Bayesian procedure. The theoretical example is followed by an application of the method to a credentialing examination in one of the allied health professions, in order to determine a ration al passing point.

The Computer-Assisted Data Analysis (CADA) Monitor (1978)

Abstract: This article describes a statistical computing system, the Computer-Assisted Data Analysis (CADA) Monitor, for use in performing interactive statistical data analysis. Especially easy to use because of its conversational nature, CADA includes facilities for data management, evaluation of probability distributions, Bayesian parametric models, Bayesian simultaneous estimation, Bayesian full-rank analysis of variance, and exploratory data analysis. CADA is written in a transportable subset of BASIC, and versions are currently available for a variety of computers.

The dependence of betting strategies on the probability of winning

Abstract: We consider the optimal wagers to be made by a gambler facing cointossing games who desires to maximize the expected value of the utility of his final fortune in a fixed number n of plays. In the case of fixed probability of a win, the optimal bet is shown to be increasing in the probability. In the case of unknown probability of a win, the wager is shown to be monotone in the prior distribution under the monotone likelihood ratio ordering of these distributions. GAMBLING THEORY; BETTING STRATEGIES; MONOTONE POLICIES; ADAPTIVE BETTING; BAYESIAN DECISIONS

An investigation into the properties of Bayesian forecasting models

Abstract: In the early 70's, Harrison and Stevens made a major contribution to the area of statistical forecasting. They adopted a Bayesian approach in conjunction with a fundamental model, first used by Kalman and called the Dynamic Linear Model (DLM). This thesis is concerned with the investigation of the properties of different Bayesian forecasting models and in particular of the Multi State Model (MSM). The latter is important in postulating that no single DLM can adequately describe a process with discontinuities and consequently the system defines a number of models characterising the most likely process states. A small number of parameters are shown to govern the behaviour of the MSM and the relationship between the choice of these parameters. and performance has been examined. It is shown that for a process exhibiting discontinuities, traditional forecasting criteria such as the mean square error are no longer appropriate. An alternative set of performance measures is proposed and used as the main language of understanding the variety of responses of the MSM to different types and sizes of discontinuities. The parameter representing the noise variance of the process is shown to be critical to the performance of both the MSIl and other single state Bayesian models. A number of on line variance estimation methods are proposed and tested on artificial and real data. The methods are shown to be robust and lead to improved performance not only of the MSM but the other Bayesian single state models which of course require a noise variance estimate. Finally, alternative formulations of the MSM are proposed, leading to significant reduction in the computational and storage requirements while at the same time improving the response of the MSM.