35 research outputs found
Bayesian Estimation Under Informative Sampling
Bayesian analysis is increasingly popular for use in social science and other
application areas where the data are observations from an informative sample.
An informative sampling design leads to inclusion probabilities that are
correlated with the response variable of interest. Model inference performed on
the observed sample taken from the population will be biased for the population
generative model under informative sampling since the balance of information in
the sample data is different from that for the population. Typical approaches
to account for an informative sampling design under Bayesian estimation are
often difficult to implement because they require re-parameterization of the
hypothesized generating model, or focus on design, rather than model-based,
inference. We propose to construct a pseudo-posterior distribution that
utilizes sampling weights based on the marginal inclusion probabilities to
exponentiate the likelihood contribution of each sampled unit, which weights
the information in the sample back to the population. Our approach provides a
nearly automated estimation procedure applicable to any model specified by the
data analyst for the population and retains the population model
parameterization and posterior sampling geometry. We construct conditions on
known marginal and pairwise inclusion probabilities that define a class of
sampling designs where consistency of the pseudo posterior is
guaranteed. We demonstrate our method on an application concerning the Bureau
of Labor Statistics Job Openings and Labor Turnover Survey.Comment: 24 pages, 3 figure
Pseudo Bayesian Estimation of One-way ANOVA Model in Complex Surveys
We devise survey-weighted pseudo posterior distribution estimators under
2-stage informative sampling of both primary clusters and secondary nested
units for a one-way ANOVA population generating model as a simple canonical
case where population model random effects are defined to be coincident with
the primary clusters. We consider estimation on an observed informative sample
under both an augmented pseudo likelihood that co-samples random effects, as
well as an integrated likelihood that marginalizes out the random effects from
the survey-weighted augmented pseudo likelihood. This paper includes a
theoretical exposition that enumerates easily verified conditions for which
estimation under the augmented pseudo posterior is guaranteed to be consistent
at the true generating parameters. We reveal in simulation that both approaches
produce asymptotically unbiased estimation of the generating hyperparameters
for the random effects when a key condition on the sum of within cluster
weighted residuals is met. We present a comparison with frequentist EM and a
methods that requires pairwise sampling weights.Comment: 46 pages, 9 figure
Variable Selection for Nonparametric Gaussian Process Priors: Models and Computational Strategies
This paper presents a unified treatment of Gaussian process models that
extends to data from the exponential dispersion family and to survival data.
Our specific interest is in the analysis of data sets with predictors that have
an a priori unknown form of possibly nonlinear associations to the response.
The modeling approach we describe incorporates Gaussian processes in a
generalized linear model framework to obtain a class of nonparametric
regression models where the covariance matrix depends on the predictors. We
consider, in particular, continuous, categorical and count responses. We also
look into models that account for survival outcomes. We explore alternative
covariance formulations for the Gaussian process prior and demonstrate the
flexibility of the construction. Next, we focus on the important problem of
selecting variables from the set of possible predictors and describe a general
framework that employs mixture priors. We compare alternative MCMC strategies
for posterior inference and achieve a computationally efficient and practical
approach. We demonstrate performances on simulated and benchmark data sets.Comment: Published in at http://dx.doi.org/10.1214/11-STS354 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org