Search results for "probability"
showing 10 items of 3417 documents
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…
Is the p-Value a Suitable Basis for the Construction of Measures of Evidence? Comment on “The Role of p-Values in Judging the Strength of Evidence an…
2020
Dr. Gibson has to be congratulated for having enriched the wealth of articles written in response to the ASA statement on p-values of 2016 by a valuable and thoughtful contribution. We particularly...
Isotropic stochastic flow of homeomorphisms on Rd associated with the critical Sobolev exponent
2008
Abstract We consider the critical Sobolev isotropic Brownian flow in R d ( d ≥ 2 ) . On the basis of the work of LeJan and Raimond [Y. LeJan, O. Raimond, Integration of Brownian vector fields, Ann. Probab. 30 (2002) 826–873], we prove that the corresponding flow is a flow of homeomorphisms. As an application, we construct an explicit solution, which is also unique in a certain space, to the stochastic transport equation when the associated Gaussian vector fields are divergence free.
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 …
An introduction to Bayesian reference analysis: inference on the ratio of multinomial parameters
1998
This paper offers an introduction to Bayesian reference analysis, often described as the more successful method to produce non-subjective, model-based, posterior distributions. The ideas are illustrated in detail with an interesting problem, the ratio of multinomial parameters, for which no model-based Bayesian analysis has been proposed. Signposts are provided to the huge related literature.