Home About us Contact
|
Home About us Contact | ||
|
|
||
Bayesian Formulation (bayesian + formulation)
Selected AbstractsA Bayesian model for estimating the effects of drug use when drug use may be under-reportedADDICTION, Issue 11 2009Garnett P. McMillan ABSTRACT Aims We present a statistical model for evaluating the effects of substance use when substance use might be under-reported. The model is a special case of the Bayesian formulation of the ,classical' measurement error model, requiring that the analyst quantify prior beliefs about rates of under-reporting and the true prevalence of substance use in the study population. Design Prospective study. Setting A diversion program for youths on probation for drug-related crimes. Participants A total of 257 youths at risk for re-incarceration. Measurements The effects of true cocaine use on recidivism risks while accounting for possible under-reporting. Findings The proposed model showed a 60% lower mean time to re-incarceration among actual cocaine users. This effect size is about 75% larger than that estimated in the analysis that relies only on self-reported cocaine use. Sensitivity analysis comparing different prior beliefs about prevalence of cocaine use and rates of under-reporting universally indicate larger effects than the analysis that assumes that everyone tells the truth about their drug use. Conclusion The proposed Bayesian model allows one to estimate the effect of actual drug use on study outcome measures. [source] Estimating the number of ozone peaks in Mexico City using a non-homogeneous Poisson modelENVIRONMETRICS, Issue 5 2008Jorge A. Achcar Abstract In this paper, we consider the problem of estimating the number of times an air quality standard is exceeded in a given period of time. A non-homogeneous Poisson model is proposed to analyse this issue. The rate at which the Poisson events occur is given by a rate function ,(t), t,,,0. This rate function also depends on some parameters that need to be estimated. Two forms of ,(t), t,,,0 are considered. One of them is of the Weibull form and the other is of the exponentiated-Weibull form. The parameters estimation is made using a Bayesian formulation based on the Gibbs sampling algorithm. The assignation of the prior distributions for the parameters is made in two stages. In the first stage, non-informative prior distributions are considered. Using the information provided by the first stage, more informative prior distributions are used in the second one. The theoretical development is applied to data provided by the monitoring network of Mexico City. The rate function that best fit the data varies according to the region of the city and/or threshold that is considered. In some cases the best fit is the Weibull form and in other cases the best option is the exponentiated-Weibull. Copyright © 2007 John Wiley & Sons, Ltd. [source] A Bayesian approach to estimating tectonic stress from seismological dataGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2007Richard Arnold SUMMARY Earthquakes are conspicuous manifestations of tectonic stress, but the non-linear relationships between the stresses acting on a fault plane, its frictional slip, and the ensuing seismic radiation are such that a single earthquake by itself provides little information about the ambient state of stress. Moreover, observational uncertainties and inherent ambiguities in the nodal planes of earthquake focal mechanisms preclude straightforward inferences about stress being drawn on the basis of individual focal mechanism observations. However, by assuming that each earthquake in a small volume of the crust represents a single, uniform state of stress, the combined constraints imposed on that stress by a suite of focal mechanism observations can be estimated. Here, we outline a probabilistic (Bayesian) technique for estimating tectonic stress directions from primary seismological observations. The Bayesian formulation combines a geologically motivated prior model of the state of stress with an observation model that implements the physical relationship between the stresses acting on a fault and the resultant seismological observation. We show our Bayesian formulation to be equivalent to a well-known analytical solution for a single, errorless focal mechanism observation. The new approach has the distinct advantage, however, of including (1) multiple earthquakes, (2) fault plane ambiguities, (3) observational errors and (4) any prior knowledge of the stress field. Our approach, while computationally demanding in some cases, is intended to yield reliable tectonic stress estimates that can be confidently compared with other tectonic parameters, such as seismic anisotropy and geodetic strain rate observations, and used to investigate spatial and temporal variations in stress associated with major faults and coseismic stress perturbations. [source] A new Bayesian formulation for Holt's exponential smoothingJOURNAL OF FORECASTING, Issue 3 2009Robert R. Andrawis Abstract In this paper we propose a Bayesian forecasting approach for Holt's additive exponential smoothing method. Starting from the state space formulation, a formula for the forecast is derived and reduced to a two-dimensional integration that can be computed numerically in a straightforward way. In contrast to much of the work for exponential smoothing, this method produces the forecast density and, in addition, it considers the initial level and initial trend as part of the parameters to be evaluated. Another contribution of this paper is that we have derived a way to reduce the computation of the maximum likelihood parameter estimation procedure to that of evaluating a two-dimensional grid, rather than applying a five-variable optimization procedure. Simulation experiments confirm that both proposed methods give favorable performance compared to other approaches. Copyright © 2008 John Wiley & Sons, Ltd. [source] The Bayesian choice of crop variety and fertilizer doseJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 1 2002Chris M Theobald Recent contributions to the theory of optimizing fertilizer doses in agricultural crop production have introduced Bayesian ideas to incorporate information on crop yield from several environments and on soil nutrients from a soil test, but they have not used a fully Bayesian formulation. We present such a formulation and demonstrate how the resulting Bayes decision procedure can be evaluated in practice by using Markov chain Monte Carlo methods. The approach incorporates expert knowledge of the crop and of regional and local soil conditions and allows a choice of crop variety as well as of fertilizer level. Alternative dose,response functions are expressed in terms of a common interpretable set of parameters to facilitate model comparisons and the specification of prior distributions. The approach is illustrated with a set of yield data from spring barley nitrogen,response trials and is found to be robust to changes in the dose,response function and the prior distribution for indigenous soil nitrogen. [source] Bayesian Inference in Semiparametric Mixed Models for Longitudinal DataBIOMETRICS, Issue 1 2010Yisheng Li Summary We consider Bayesian inference in semiparametric mixed models (SPMMs) for longitudinal data. SPMMs are a class of models that use a nonparametric function to model a time effect, a parametric function to model other covariate effects, and parametric or nonparametric random effects to account for the within-subject correlation. We model the nonparametric function using a Bayesian formulation of a cubic smoothing spline, and the random effect distribution using a normal distribution and alternatively a nonparametric Dirichlet process (DP) prior. When the random effect distribution is assumed to be normal, we propose a uniform shrinkage prior (USP) for the variance components and the smoothing parameter. When the random effect distribution is modeled nonparametrically, we use a DP prior with a normal base measure and propose a USP for the hyperparameters of the DP base measure. We argue that the commonly assumed DP prior implies a nonzero mean of the random effect distribution, even when a base measure with mean zero is specified. This implies weak identifiability for the fixed effects, and can therefore lead to biased estimators and poor inference for the regression coefficients and the spline estimator of the nonparametric function. We propose an adjustment using a postprocessing technique. We show that under mild conditions the posterior is proper under the proposed USP, a flat prior for the fixed effect parameters, and an improper prior for the residual variance. We illustrate the proposed approach using a longitudinal hormone dataset, and carry out extensive simulation studies to compare its finite sample performance with existing methods. [source] A Bayesian approach to the evolution of perceptual and cognitive systemsCOGNITIVE SCIENCE - A MULTIDISCIPLINARY JOURNAL, Issue 3 2003Wilson S. Geisler Abstract We describe a formal framework for analyzing how statistical properties of natural environments and the process of natural selection interact to determine the design of perceptual and cognitive systems. The framework consists of two parts: a Bayesian ideal observer with a utility function appropriate for natural selection, and a Bayesian formulation of Darwin's theory of natural selection. Simulations of Bayesian natural selection were found to yield new insights, for example, into the co-evolution of camouflage, color vision, and decision criteria. The Bayesian framework captures and generalizes, in a formal way, many of the important ideas of other approaches to perception and cognition. [source] | ||||||||||