3,939 research outputs found
Restricted Covariance Priors with Applications in Spatial Statistics
We present a Bayesian model for area-level count data that uses Gaussian
random effects with a novel type of G-Wishart prior on the inverse
variance--covariance matrix. Specifically, we introduce a new distribution
called the truncated G-Wishart distribution that has support over precision
matrices that lead to positive associations between the random effects of
neighboring regions while preserving conditional independence of
non-neighboring regions. We describe Markov chain Monte Carlo sampling
algorithms for the truncated G-Wishart prior in a disease mapping context and
compare our results to Bayesian hierarchical models based on intrinsic
autoregression priors. A simulation study illustrates that using the truncated
G-Wishart prior improves over the intrinsic autoregressive priors when there
are discontinuities in the disease risk surface. The new model is applied to an
analysis of cancer incidence data in Washington State.Comment: Published at http://dx.doi.org/10.1214/14-BA927 in the Bayesian
Analysis (http://projecteuclid.org/euclid.ba) by the International Society of
Bayesian Analysis (http://bayesian.org/
Robust Classification of Functional and Quantitative Image Data Using Functional Mixed Models
This paper describes how to perform classification of complex, high-dimensional functional data using the functional mixed model (FMM) framework. The FMM relates a functional response to a set of predictors through functional fixed and random effects, which allows it to account for various factors and between-function correlations. Classification is performed through training the model treating class as one of the fixed effects, and then predicting on the test data using posterior predictive probabilities of class. Through a Bayesian scheme, we are able to adjust for factors affecting both the functions and the class designations. While the method we present can be applied to any FMM-based method, we provide details for two specific Bayesian approaches: the Gaussian, wavelet-based functional mixed model (G-WFMM) and the robust, wavelet-based functional mixed model (R-WFMM). Both methods perform modeling in the wavelet space, which yields parsimonious representations for the functions, and can naturally adapt to local features and complex nonstationarities in the functions. The R-WFMM allows potentially heavier tails for features of the functions indexed by particular wavelet coefficients, leading to a down weighting of outliers that makes the method robust to outlying functions or regions of functions. The models are applied to a pancreatic cancer mass spectroscopy data set and compared with some other recently developed functional classification methods
Covariance pattern mixture models for the analysis of multivariate heterogeneous longitudinal data
We propose a novel approach for modeling multivariate longitudinal data in
the presence of unobserved heterogeneity for the analysis of the Health and
Retirement Study (HRS) data. Our proposal can be cast within the framework of
linear mixed models with discrete individual random intercepts; however,
differently from the standard formulation, the proposed Covariance Pattern
Mixture Model (CPMM) does not require the usual local independence assumption.
The model is thus able to simultaneously model the heterogeneity, the
association among the responses and the temporal dependence structure. We focus
on the investigation of temporal patterns related to the cognitive functioning
in retired American respondents. In particular, we aim to understand whether it
can be affected by some individual socio-economical characteristics and whether
it is possible to identify some homogenous groups of respondents that share a
similar cognitive profile. An accurate description of the detected groups
allows government policy interventions to be opportunely addressed. Results
identify three homogenous clusters of individuals with specific cognitive
functioning, consistent with the class conditional distribution of the
covariates. The flexibility of CPMM allows for a different contribution of each
regressor on the responses according to group membership. In so doing, the
identified groups receive a global and accurate phenomenological
characterization.Comment: Published at http://dx.doi.org/10.1214/15-AOAS816 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Bayesian Deep Net GLM and GLMM
Deep feedforward neural networks (DFNNs) are a powerful tool for functional
approximation. We describe flexible versions of generalized linear and
generalized linear mixed models incorporating basis functions formed by a DFNN.
The consideration of neural networks with random effects is not widely used in
the literature, perhaps because of the computational challenges of
incorporating subject specific parameters into already complex models.
Efficient computational methods for high-dimensional Bayesian inference are
developed using Gaussian variational approximation, with a parsimonious but
flexible factor parametrization of the covariance matrix. We implement natural
gradient methods for the optimization, exploiting the factor structure of the
variational covariance matrix in computation of the natural gradient. Our
flexible DFNN models and Bayesian inference approach lead to a regression and
classification method that has a high prediction accuracy, and is able to
quantify the prediction uncertainty in a principled and convenient way. We also
describe how to perform variable selection in our deep learning method. The
proposed methods are illustrated in a wide range of simulated and real-data
examples, and the results compare favourably to a state of the art flexible
regression and classification method in the statistical literature, the
Bayesian additive regression trees (BART) method. User-friendly software
packages in Matlab, R and Python implementing the proposed methods are
available at https://github.com/VBayesLabComment: 35 pages, 7 figure, 10 table
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