Search results for "Bay"
showing 10 items of 1187 documents
A Bayesian Sequential Look at u-Control Charts
2005
We extend the usual implementation of u-control charts (uCCs) in two ways. First, we overcome the restrictive (and often inadequate) assumptions of the Poisson model; next, we eliminate the need for the questionable base period by using a sequential procedure. We use empirical Bayes(EB) and Bayes methods and compare them with the traditional frequentist implementation. EB methods are somewhat easy to implement, and they deal nicely with extra-Poisson variability (and, at the same time, informally check the adequacy of the Poisson assumption). However, they still need the base period. The sequential, full Bayes approach, on the other hand, also avoids this drawback of traditional u-charts. T…
Bayesian analysis and design for comparison of effect-sizes
2002
Comparison of effect-sizes, or more generally, of non-centrality parameters of non-central t distributions, is a common problem, especially in meta-analysis. The usual simplifying assumptions of either identical or non-related effect-sizes are often too restrictive to be appropriate. In this paper, the effect-sizes are modeled as random effects with t distributions. Bayesian hierarchical models are used both to design and analyze experiments. The main goal is to compare effect-sizes. Sample sizes are chosen so as to make accurate inferences about the difference of effect-sizes and also to convincingly solve the testing of equality of effect-sizes if such is the goal.
Asymptotic optimality of myopic information-based strategies for Bayesian adaptive estimation
2016
This paper presents a general asymptotic theory of sequential Bayesian estimation giving results for the strongest, almost sure convergence. We show that under certain smoothness conditions on the probability model, the greedy information gain maximization algorithm for adaptive Bayesian estimation is asymptotically optimal in the sense that the determinant of the posterior covariance in a certain neighborhood of the true parameter value is asymptotically minimal. Using this result, we also obtain an asymptotic expression for the posterior entropy based on a novel definition of almost sure convergence on "most trials" (meaning that the convergence holds on a fraction of trials that converge…
Correcting for non-ignorable missingness in smoking trends
2015
Data missing not at random (MNAR) is a major challenge in survey sampling. We propose an approach based on registry data to deal with non-ignorable missingness in health examination surveys. The approach relies on follow-up data available from administrative registers several years after the survey. For illustration we use data on smoking prevalence in Finnish National FINRISK study conducted in 1972-1997. The data consist of measured survey information including missingness indicators, register-based background information and register-based time-to-disease survival data. The parameters of missingness mechanism are estimable with these data although the original survey data are MNAR. The u…
Conditionally heteroscedastic intensity-dependent marking of log Gaussian Cox processes
2009
Spatial marked point processes are models for systems of points which are randomly distributed in space and provided with measured quantities called marks. This study deals with marking, that is methods of constructing marked point processes from unmarked ones. The focus is density-dependent marking where the local point intensity affects the mark distribution. This study develops new markings for log Gaussian Cox processes. In these markings, both the mean and variance of the mark distribution depend on the local intensity. The mean, variance and mark correlation properties are presented for the new markings, and a Bayesian estimation procedure is suggested for statistical inference. The p…
Poisson Regression with Change-Point Prior in the Modelling of Disease Risk around a Point Source
2003
Bayesian estimation of the risk of a disease around a known point source of exposure is considered. The minimal requirements for data are that cases and populations at risk are known for a fixed set of concentric annuli around the point source, and each annulus has a uniquely defined distance from the source. The conventional Poisson likelihood is assumed for the counts of disease cases in each annular zone with zone-specific relative risk and parameters and, conditional on the risks, the counts are considered to be independent. The prior for the relative risk parameters is assumed to be piecewise constant at the distance having a known number of components. This prior is the well-known cha…
A Bayesian analysis of classical hypothesis testing
1980
The procedure of maximizing the missing information is applied to derive reference posterior probabilities for null hypotheses. The results shed further light on Lindley’s paradox and suggest that a Bayesian interpretation of classical hypothesis testing is possible by providing a one-to-one approximate relationship between significance levels and posterior probabilities.
Breaking the curse of dimensionality in quadratic discriminant analysis models with a novel variant of a Bayes classifier enhances automated taxa ide…
2013
Macroinvertebrate samples are commonly used in biomonitoring to study changes on aquatic ecosystems. Traditionally, specimens are identified manually to taxa by human experts being time-consuming and cost intensive. Using the image data of 35 taxa and 64 features, we propose a novel variant of the quadratic discriminant analysis for breaking the curse of dimensionality in quadratic discriminant analysis models. Our variant, called a random Bayes array (RBA), uses bagging and random feature selection similar to random forest. We explore several variations of RBA. We consider three classification (i.e taxa identification) decisions: majority vote, averaged posterior probabilities, and a novel…
Bayesian subcohort selection for longitudinal covariate measurements in follow‐up studies
2022
We propose an approach for the planning of longitudinal covariate measurements in follow-up studies where covariates are time-varying. We assume that the entire cohort cannot be selected for longitudinal measurements due to financial limitations, and study how a subset of the cohort should be selected optimally, in order to obtain precise estimates of covariate effects in a survival model. In our approach, the study will be designed sequentially utilizing the data collected in previous measurements of the individuals as prior information. We propose using a Bayesian optimality criterion in the subcohort selections, which is compared with simple random sampling using simulated and real follo…
What Bayesians Expect of Each Other
1991
Abstract Our goal is to study general properties of one Bayesian's subjective beliefs about the behavior of another Bayesian's subjective beliefs. We consider two Bayesians, A and B, who have different subjective distributions for a parameter θ, and study Bayesian A's expectation of Bayesian B's posterior distribution for θ given some data Y. We show that when θ can take only two values, Bayesian A always expects Bayesian B's posterior distribution to lie between the prior distributions of A and B. Conditions are given under which a similar result holds for an arbitrary real-valued parameter θ. For a vector parameter θ we present useful expressions for the mean vector and covariance matrix …