Open AccessPosted Content
Effective Reparameterized Importance Sampling for Spatial Generalized Linear Mixed Models with Parametric Links
Evangelos Evangelou,Vivekananda Roy +1 more
- 13 Mar 2018
TL;DR: A generalized importance sampling (GIS) estimator based on multiple Markov chains for an empirical Bayes analysis of SGLMMs and a new method based on Laplace approximation for choosing the multiple importance densities in the GIS estimator.
read more
Abstract: Spatial generalized linear mixed models (SGLMMs) have been popular for analyzing non-Gaussian spatial data observed in a continuous region. These models assume a prescribed link function that relates the underlying spatial random field with the mean response. On the other hand, there are circumstances, such as when the data contain outlying observations, where the use of a prescribed link function can result in a poor fit which can be improved by the use of a parametric link function. In this paper we present different sensible choices of parametric link functions which possess certain desirable properties. It is important to estimate the parameters of the link function, rather than assume a known value. To that end, we present a generalized importance sampling (GIS) estimator based on multiple Markov chains for an empirical Bayes analysis of SGLMMs. It turns out that the GIS estimator, although more efficient than simple importance sampling, can be highly variable when it is used to estimate the parameters of certain link functions. We propose two modified GIS estimators based on suitable reparameterizations (transformations) of the Monte Carlo samples. These transformations are also used to eliminate the well-known separability problem of Geyer's (1994) reverse logistic regression estimator. We also provide a new method based on Laplace approximation for choosing the multiple importance densities (or skeleton points) in the GIS estimator. Finally, we discuss a methodology for selecting models with appropriate link function family, which extends to choosing a spatial correlation function as well. The proposed estimators and methodology are illustrated using both simulation and real data examples.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
•Posted Content
Selection of proposal distributions for generalized importance sampling estimators
TL;DR: In this paper, a geometric space filling coverage criterion, a minimax variance approach, and a maximum entropy approach are proposed for the selection of the proposal distributions for multi-proposal IS estimators.
5
References
Generalized Linear Models
TL;DR: This is the rst book on generalized linear models written by authors not mostly associated with the biological sciences, and it is thoroughly enjoyable to read.
14.7K
A limited-memory algorithm for bound-constrained optimization
Richard H. Byrd,L. Peihuang,Jorge Nocedal +2 more
- 01 Mar 1996
TL;DR: An algorithm for solving large nonlinear optimization problems with simple bounds is described, based on the gradient projection method and uses a limited-memory BFGS matrix to approximate the Hessian of the objective function.
•Book
Model-based Geostatistics
Peter J. Diggle,Jonathan A. Tawn,Rana Moyeed +2 more
- 25 Aug 2008
TL;DR: An overview of model-based geostatistics can be found in this paper, where a generalized linear model is proposed for estimating geometrical properties of geometrically constrained data.
Generalized Linear Models.
Abstract: The purpose of this handout is to briefly show that several seemingly unrelated models are actually all special cases of the generalized linear model. (Indeed, I think most of these techniques were initially developed without people realizing they were interconnected.) We will also briefly introduce the use of factor variables and the margins command, both of which will be used heavily during the course.
2.2K