Showing papers on "Bayesian inference published in 1981"
TL;DR: In the face of uncertainty, all available information should be used to make inferences or decisions as mentioned in this paper, when probability distributions for an uncertain quantity are obtained from experts, models, or models.
Abstract: Inferences or decisions in the face of uncertainty should be based on all available information. Thus, when probability distributions for an uncertain quantity are obtained from experts, models, or...
456 citations
TL;DR: In this paper, the authors illustrate Bayesian and empirical Bayesian techniques that can be used to summarize the evidence in such data about differences among treatments, thereby obtaining improved estimates of the treatment effect in each experiment, including the one having the largest observed effect.
Abstract: Many studies comparing new treatments to standard treatments consist of parallel randomized experiments. In the example considered here, randomized experiments were conducted in eight schools to determine the effectiveness of special coaching programs for the SAT. The purpose here is to illustrate Bayesian and empirical Bayesian techniques that can be used to help summarize the evidence in such data about differences among treatments, thereby obtaining improved estimates of the treatment effect in each experiment, including the one having the largest observed effect. Three main tools are illustrated: 1) graphical techniques for displaying sensitivity within an empirical Bayes framework, 2) simple simulation techniques for generating Bayesian posterior distributions of individual effects and the largest effect, and 3) methods for monitoring the adequacy of the Bayesian model specification by simulating the posterior predictive distribution in hypothetical replications of the same treatments in the same eig...
263 citations
TL;DR: The paper shows that on this Bayesian basis it is possible to build a consistent theory of system identification and considers problems of one-shot and real-time identification, estimation and prediction in closed control loop, redundant and unidentifiable parameters, time-varying parameters and adaptivity.
234 citations
TL;DR: In this paper, the analysis of transformation of observations in the linear model with normal errors proposed by Box & Cox (1964) is considered, and a different choice of noninformative unnormed prior is advocated, which is not outcome dependent.
Abstract: SUMMARY The analysis of transformation of observations in the linear model with normal errors proposed by Box & Cox (1964) is considered. A different choice of noninformative unnormed prior is advocated, which is not outcome dependent. This new selection of prior leads to a formal identity between likelihood and Bayesian inference, both for the estimation of the best transformation to normality and for the presence of homoscedasticity and additivity under this transformation. Extension to a related problem is mentioned.
66 citations
TL;DR: This note proves the following proposition: if the assumptions made in deriving Duda et al.'s scheme are satisfied, together with the additional assumptions that the space of hypotheses is mutually exclusive and exhaustive, then no updating can take place.
64 citations
TL;DR: Application of Bayes' theorem using data collected provides an insight based upon probabilities and odds in the way preoperative conditions and operative results affect the ultimate treatment result.
29 citations
TL;DR: In this article, it is shown that the posterior probability of a likelihood region has a simple frequency interpretation as a mean conditional confidence level, and that the central multivariate normal model is considered as an example.
Abstract: According to an invariance principle, for some models having a certain group structure, there is a uniquely defined prior representing ignorance, which is called the inner prior. It is shown that the corresponding posterior probability of a likelihood region has a simple frequency interpretation as a mean conditional confidence level. The central multivariate normal model is considered as an example.
25 citations
01 Jan 1981
TL;DR: A need for philosophers of science to examine statistical theorizing in science is indicated, since inference and explanation in economics is often statistical in nature.
Abstract: At a recent conference on problems in economics the following problem was raised:
Econometricians like to think of themselves as scientists, and their methods as scientific. Students of the philosophy of science, on the other hand, have not had any notable success in relating the formal concepts of scientific method or the logic of scientific explanation and theory construction to either the method or the theory of econometrics [3, p. 238].
This should not be taken to mean that the theory and practice of economics and econometrics is not scientific. It rather points to the need for a greater effort among philosophers to tie their analyses to actual scientific practice. More specifically, it indicates a need for philosophers of science to examine statistical theorizing in science, since inference and explanation in economics is often statistical in nature.
20 citations
01 Dec 1981
TL;DR: The authors argued that both averaging and conservatism in the Bayesian task occur because subjects produce their judgments by using an adjustment strategy that is qualitatively equivalent to averaging, and two experiments were presented that support this view by showing qualitative errors in the direction of revisions in Bayesian inference that are well-accounted for by the simple adjustment strategy.
Abstract: : Two empirically well supported research findings in the judgment literature are that (1) human judgments often appear to follow an averaging rule, and (2) judgments in Bayesian inference tasks are usually conservative relative to optimal judgments. This paper argues that both averaging and conservatism in the Bayesian task occur because subjects produce their judgments by using an adjustment strategy that is qualitatively equivalent to averaging. Two experiments are presented that support this view by showing qualitative errors in the direction of revisions in the Bayesian task that are well-accounted for by the simple adjustment strategy. Two additional results are also discussed: (1) a tendency for subjects in one experiment to evaluate sample evidence according to representativeness rather than according to relative likelihood, and (2) a strong recency effect that may reflect the influence of the internal representation of sample information during the judgment process. (Author)
18 citations
TL;DR: A dynamic model for determining the proper stopping point using decision theory under risk with changing utilities is used as the basis for a Bayesian model of user scanning behavior, which has implications for retrieval systems design and evaluation.
Abstract: A model of a user's scan of the output of an information storage and retrieval system in response to a query is presented. Rules for determining the user's optimal stopping point are discussed and compared. A dynamic model for determining the proper stopping point using decision theory under risk with changing utilities is used as the basis for a Bayesian model of user scanning behavior. An algorithm to implement the Bayesian model is introduced and examples of the model are given. The implications for retrieval systems design and evaluation are discussed.
18 citations
TL;DR: It is shown that the method of reconciliation they have proposed is formally equivalent to that of taking a weighted average of log-odds, with weights proportional to the independent information content of each assessment, and has the advantage of being simple in application.
TL;DR: For partially observable processes with conditional distributions within fixed (parametrized) exponential families for all times t, the parameters of the a-posteriori distributions ξtP(|η1,...,ηt) (ω) can be calculated by a recursive algorithm as mentioned in this paper.
Abstract: For partially observable processes (ξt, ηt) with conditional distributions within fixed (parametrized) exponential families for all times t, the parameters of the a-posteriori distributions ξtP(|η1,...,ηt) (ω) can be calculated by a recursive algorithm. A method to find the algorithm in this situation is given.
01 Nov 1981
TL;DR: An interactive algorithm is proposed for the problem of selecting one of a finite number of alternatives where each is evaluated in terms of a number of conflicting criteria and ultimately implies probability distributions on the utilities of each alternative.
Abstract: An interactive algorithm is proposed for the problem of selecting one of a finite number of alternatives where each is evaluated in terms of a number of conflicting criteria. A simple form of utility function is assumed, and the possibility is modeled probabilistically that the decisionmaker may at any time indicate a preference between alternatives in conflict with his true utility. On this basis, a formal Bayesian inferential procedure is applied to a sequence of pairwise choices between alternatives made by the decisionmaker to yield estimates of the unknown parameters of the utility function. This ultimately implies probability distributions on the utilities of each alternative. The sequence of pairwise comparisons continues until a satisfactorily short list of alternatives remains after elimination of those inferred to be significantly worse than the best.
TL;DR: The objective of the paper is to offer a strategy for progressively specifying a model within that class of linear models, and to display the precise role of each assumption, at offering alternatives to unnecessarily restrictive specifications, and at improving the robustness of the inference procedures the authors discuss.
TL;DR: A simple urn model is presented for earthquake prediction statistics that is equivalent to the Bayesian models of Collins, Guagenti and Scirocco, and Kijko.
Abstract: A simple urn model is presented for earthquake prediction statistics. This model is equivalent to the Bayesian models of Collins (1977), Guagenti and Scirocco (1980), and Kijko (1981).
TL;DR: In this paper, the authors examine conjugate Bayes inference to gain some insight in-to why particularly simple forms may be obtained in some standard statistical models, and they show that simple results often arise as a consequence of group-structural properties possessed by the model.
Abstract: We examine conjugate Bayes inference to gain some insight in-to why particularly simple forms may be obtained in some standard statistical models. The simple results often arise as a conse-quence of group-structural properties possessed by the model. Some examples are presented.
Dissertation•
01 Jan 1981
TL;DR: The work reported here is directed towards simplifying the task of the researcher who wishes to use Bayes' rule as a standard for inferential behavior and of the analyst who wish to use task decomposition in aiding inference.
Abstract: In cascaded inference tasks there is not a direct logical connection between an observable event (datum) and the hypothesis of interest. Instead there is interposed at least one logical reasoning stage, consisting of intervening variables or intermediate event states. This paper is concerned with the modification or extension of Bayes' rule to render it more specific as a normative model for cascaded inference. In particular, the work reported here is directed towards simplifying the task of the researcher who wishes to use Bayes' rule as a standard for inferential behavior and of the analyst who wishes to use task decomposition in aiding inference. This is achieved by the development of some general principles of inference, the use of concepts from graph theory for the representation of inference tasks, and the application of computer technology.
TL;DR: The analysis serves to generalize the well-known conjugate family property for Dirichlet distributions from the case when observations convey perfect information to the case where they convey imperfect information.
01 Jan 1981
TL;DR: In this paper, the authors consider the model in which the failure rate for a device changes when the device is subjected to shocks which occur stochastically over time and show that increasing failure rate distributions can be obtained by making simple models for the effects of shocks.
Abstract: We consider the model in which the failure rate for a device changes when the device is subjected to shocks which occur stochastically over time. We show that increasing failure rate distributions can be obtained by making simple models for the effects of shocks. The results provide a physical motivation for using the Weibull distributions for failure time data. Random failure rates used in Bayesian inference are also obtained in a similar manner by modeling the effects of shocks to be stochastic.
05 Dec 1981
TL;DR: The report presents a summary of the research conducted in the theory and application of time series analysis, in Bayesian methods, and in density estimation and interpolation techniques.
Abstract: : The report presents a summary of the research conducted in the theory and application of time series analysis, in Bayesian methods, and in density estimation and interpolation techniques. (Author)
01 Dec 1981
TL;DR: The connection with statistical inference and recent papers on statistical foundations are discussed and some aids for assessing subjective probability are surveyed.
Abstract: : The assessment of subjective probability is of great interest in risk analysis. Some aids for assessing subjective probability are surveyed. The connection with statistical inference and recent papers on statistical foundations are discussed. (Author)