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Inference Problems (inference + problem)
Selected AbstractsStopping-time resampling for sequential Monte Carlo methodsJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2005Yuguo Chen Summary., Motivated by the statistical inference problem in population genetics, we present a new sequential importance sampling with resampling strategy. The idea of resampling is key to the recent surge of popularity of sequential Monte Carlo methods in the statistics and engin-eering communities, but existing resampling techniques do not work well for coalescent-based inference problems in population genetics. We develop a new method called ,stopping-time resampling', which allows us to compare partially simulated samples at different stages to terminate unpromising partial samples and to multiply promising samples early on. To illustrate the idea, we first apply the new method to approximate the solution of a Dirichlet problem and the likelihood function of a non-Markovian process. Then we focus on its application in population genetics. All our examples show that the new resampling method can significantly improve the computational efficiency of existing sequential importance sampling methods. [source] Bayesian source detection and parameter estimation of a plume model based on sensor network measurements,APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 4 2010Chunfeng Huang Abstract We consider a network of sensors that measure the intensities of a complex plume composed of multiple absorption,diffusion source components. We address the problem of estimating the plume parameters, including the spatial and temporal source origins and the parameters of the diffusion model for each source, based on a sequence of sensor measurements. The approach not only leads to multiple-source detection, but also the characterization and prediction of the combined plume in space and time. The parameter estimation is formulated as a Bayesian inference problem, and the solution is obtained using a Markov chain Monte Carlo algorithm. The approach is applied to a simulation study, which shows that an accurate parameter estimation is achievable. Copyright © 2010 John Wiley & Sons, Ltd. [source] Estimating the Intensity of a Spatial Point Process from Locations Coarsened by Incomplete GeocodingBIOMETRICS, Issue 1 2008Dale L. Zimmerman Summary The estimation of spatial intensity is an important inference problem in spatial epidemiologic studies. A standard data assimilation component of these studies is the assignment of a geocode, that is, point-level spatial coordinates, to the address of each subject in the study population. Unfortunately, when geocoding is performed by the standard automated method of street-segment matching to a georeferenced road file and subsequent interpolation, it is rarely completely successful. Typically, 10,30% of the addresses in the study population, and even higher percentages in particular subgroups, fail to geocode, potentially leading to a selection bias, called geographic bias, and an inefficient analysis. Missing-data methods could be considered for analyzing such data; however, because there is almost always some geographic information coarser than a point (e.g., a Zip code) observed for the addresses that fail to geocode, a coarsened-data analysis is more appropriate. This article develops methodology for estimating spatial intensity from coarsened geocoded data. Both nonparametric (kernel smoothing) and likelihood-based estimation procedures are considered. Substantial improvements in the estimation quality of coarsened-data analyses relative to analyses of only the observations that geocode are demonstrated via simulation and an example from a rural health study in Iowa. [source] Prospects and challenges for parametric models in historical biogeographical inferenceJOURNAL OF BIOGEOGRAPHY, Issue 7 2009Richard H. Ree Abstract In historical biogeography, phylogenetic trees have long been used as tools for addressing a wide range of inference problems, from explaining common distribution patterns of species to reconstructing ancestral geographic ranges on branches of the tree of life. However, the potential utility of phylogenies for this purpose has yet to be fully realized, due in part to a lack of explicit conceptual links between processes underlying the evolution of geographic ranges and processes of phylogenetic tree growth. We suggest that statistical approaches that use parametric models to forge such links will stimulate integration and propel hypothesis-driven biogeographical inquiry in new directions. We highlight here two such approaches and describe how they represent early steps towards a more general framework for model-based historical biogeography that is based on likelihood as an optimality criterion, rather than having the traditional reliance on parsimony. The development of this framework will not be without significant challenges, particularly in balancing model complexity with statistical power, and these will be most apparent in studies of regions with many component areas and complex geological histories, such as the Mediterranean Basin. [source] Stopping-time resampling for sequential Monte Carlo methodsJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2005Yuguo Chen Summary., Motivated by the statistical inference problem in population genetics, we present a new sequential importance sampling with resampling strategy. The idea of resampling is key to the recent surge of popularity of sequential Monte Carlo methods in the statistics and engin-eering communities, but existing resampling techniques do not work well for coalescent-based inference problems in population genetics. We develop a new method called ,stopping-time resampling', which allows us to compare partially simulated samples at different stages to terminate unpromising partial samples and to multiply promising samples early on. To illustrate the idea, we first apply the new method to approximate the solution of a Dirichlet problem and the likelihood function of a non-Markovian process. Then we focus on its application in population genetics. All our examples show that the new resampling method can significantly improve the computational efficiency of existing sequential importance sampling methods. [source] Using Difference-Based Methods for Inference in Regression with Fractionally Integrated ProcessesJOURNAL OF TIME SERIES ANALYSIS, Issue 6 2007Wen-Jen Tsay Abstract., This paper suggests a difference-based method for inference in the regression model involving fractionally integrated processes. Under suitable regularity conditions, our method can effectively deal with the inference problems associated with the regression model consisting of nonstationary, stationary and intermediate memory regressors, simultaneously. Although the difference-based method provides a very flexible modelling framework for empirical studies, the implementation of this method is extremely easy, because it completely avoids the difficult problems of choosing a kernel function, a bandwidth parameter, or an autoregressive lag length for the long-run variance estimation. The asymptotic local power of our method is investigated with a sequence of local data-generating processes (DGP) in what Davidson and MacKinnon [Canadian Journal of Economics. (1985) Vol. 18, pp. 38,57] call ,regression direction'. The simulation results indicate that the size control of our method is excellent even when the sample size is only 100, and the pattern of power performance is highly consistent with the theoretical finding from the asymptotic local power analysis conducted in this paper. [source] Shrinkage drift parameter estimation for multi-factor Ornstein,Uhlenbeck processesAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 2 2010Sévérien Nkurunziza Abstract We consider some inference problems concerning the drift parameters of multi-factors Vasicek model (or multivariate Ornstein,Uhlebeck process). For example, in modeling for interest rates, the Vasicek model asserts that the term structure of interest rate is not just a single process, but rather a superposition of several analogous processes. This motivates us to develop an improved estimation theory for the drift parameters when homogeneity of several parameters may hold. However, the information regarding the equality of these parameters may be imprecise. In this context, we consider Stein-rule (or shrinkage) estimators that allow us to improve on the performance of the classical maximum likelihood estimator (MLE). Under an asymptotic distributional quadratic risk criterion, their relative dominance is explored and assessed. We illustrate the suggested methods by analyzing interbank interest rates of three European countries. Further, a simulation study illustrates the behavior of the suggested method for observation periods of small and moderate lengths of time. Our analytical and simulation results demonstrate that shrinkage estimators (SEs) provide excellent estimation accuracy and outperform the MLE uniformly. An over-ridding theme of this paper is that the SEs provide powerful extensions of their classical counterparts. Copyright © 2009 John Wiley & Sons, Ltd. [source] A Bayesian Semiparametric Survival Model with Longitudinal MarkersBIOMETRICS, Issue 2 2010Song Zhang Summary We consider inference for data from a clinical trial of treatments for metastatic prostate cancer. Patients joined the trial with diverse prior treatment histories. The resulting heterogeneous patient population gives rise to challenging statistical inference problems when trying to predict time to progression on different treatment arms. Inference is further complicated by the need to include a longitudinal marker as a covariate. To address these challenges, we develop a semiparametric model for joint inference of longitudinal data and an event time. The proposed approach includes the possibility of cure for some patients. The event time distribution is based on a nonparametric Pólya tree prior. For the longitudinal data we assume a mixed effects model. Incorporating a regression on covariates in a nonparametric event time model in general, and for a Pólya tree model in particular, is a challenging problem. We exploit the fact that the covariate itself is a random variable. We achieve an implementation of the desired regression by factoring the joint model for the event time and the longitudinal outcome into a marginal model for the event time and a regression of the longitudinal outcomes on the event time, i.e., we implicitly model the desired regression by modeling the reverse conditional distribution. [source] | ||||||||||