32 research outputs found
Statistical inference with anchored Bayesian mixture of regressions models: A case study analysis of allometric data
No full textWe present an illustrative study in which we use a mixture of regressions
model to improve on an ill-fitting simple linear regression model relating log
brain mass to log body mass for 100 placental mammalian species. The slope of
the model is of particular scientific interest because it corresponds to a
constant that governs a hypothesized allometric power law relating brain mass
to body mass. We model these data using an anchored Bayesian mixture of
regressions model, which modifies the standard Bayesian Gaussian mixture by
pre-assigning small subsets of observations to given mixture components with
probability one. These observations (called anchor points) break the relabeling
invariance (or label-switching) typical of exchangeable models.
In the article, we develop a strategy for selecting anchor points using tools
from case influence diagnostics. We compare the performance of three anchoring
methodson the allometric data and in simulated settings
Subsampling the Gibbs sampler: variance reduction
No full textSubsampling the output of a Gibbs sampler in a non-systematic fashion can improve the efficiency of marginal estimators if the subsampling strategy is tied to the actual updates made. We illustrate this point by example, approximation, and asymptotics. The results hold both for random-scan and fixed-scan Gibbs samplers.Bayesian analysis Efficiency Estimation Markov chains Monte Carlo Stationary time series
Inferences on Lung Cancer Mortality Rates Based on Reference Priors Under Partial Ordering
No full textmelt: Multiple Empirical Likelihood Tests in R
No full textEmpirical likelihood enables a nonparametric, likelihood-driven style of inference without relying on assumptions frequently made in parametric models. Empirical likelihood-based tests are asymptotically pivotal and thus avoid explicit studentization. This paper presents the R package melt that provides a unified framework for data analysis with empirical likelihood methods. A collection of functions are available to perform multiple empirical likelihood tests for linear and generalized linear models in R. The package melt offers an easy-to-use interface and flexibility in specifying hypotheses and calibration methods, extending the framework to simultaneous inferences. Hypothesis testing uses a projected gradient algorithm to solve constrained empirical likelihood optimization problems. The core computational routines are implemented in C++, with OpenMP for parallel computation
Regularized Exponentially Tilted Empirical Likelihood for Bayesian Inference
No full textBayesian inference with empirical likelihood faces a challenge as the
posterior domain is a proper subset of the original parameter space due to the
convex hull constraint. We propose a regularized exponentially tilted empirical
likelihood to address this issue. Our method removes the convex hull constraint
using a novel regularization technique, incorporating a continuous exponential
family distribution to satisfy a Kullback-Leibler divergence criterion. The
regularization arises as a limiting procedure where pseudo-data are added to
the formulation of exponentially tilted empirical likelihood in a structured
fashion. We show that this regularized exponentially tilted empirical
likelihood retains certain desirable asymptotic properties of (exponentially
tilted) empirical likelihood and has improved finite sample performance.
Simulation and data analysis demonstrate that the proposed method provides a
suitable pseudo-likelihood for Bayesian inference. The implementation of our
method is available as the R package retel. Supplementary materials for this
article are available online
