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Register a new userBayesian Fusion of Data Partitioned Particle Estimates
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Added by
Jem Corcoran
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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We present a Bayesian data fusion method to approximate a posterior distribution from an ensemble of particle estimates that only have access to subsets of the data. Our approach relies on approximate probabilistic inference of model parameters through Monte Carlo methods, followed by an update and resample scheme related to multiple importance sampling to combine information from the initial estimates. We show the method is convergent in the particle limit and directly suited to application on multi-sensor data fusion problems by demonstrating efficacy on a multi-sensor Keplerian orbit determination problem and a bearings-only tracking problem.
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In this paper, we propose a Bayesian approach to obtain a sparse representation of the effect of a categorical predictor in regression type models. As the effect of a categorical predictor is captured by a group of level effects, sparsity cannot only be achieved by excluding single irrelevant level effects but also by excluding the whole group of effects associated to a predictor or by fusing levels which have essentially the same effect on the response. To achieve this goal, we propose a prior which allows for almost perfect as well as almost zero dependence between level effects a priori. We show how this prior can be obtained by specifying spike and slab prior distributions on all effect differences associated to one categorical predictor and how restricted fusion can be implemented. An efficient MCMC method for posterior computation is developed. The performance of the proposed method is investigated on simulated data. Finally, we illustrate its application on real data from EU-SILC.
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We develop a novel hybrid method for Bayesian network structure learning called partitioned hybrid greedy search (pHGS), composed of three distinct yet compatible new algorithms: Partitioned PC (pPC) accelerates skeleton learning via a divide-and-conquer strategy, $p$-value adjacency thresholding (PATH) effectively accomplishes parameter tuning with a single execution, and hybrid greedy initialization (HGI) maximally utilizes constraint-based information to obtain a high-scoring and well-performing initial graph for greedy search. We establish structure learning consistency of our algorithms in the large-sample limit, and empirically validate our methods individually and collectively through extensive numerical comparisons. The combined merits of pPC and PATH achieve significant computational reductions compared to the PC algorithm without sacrificing the accuracy of estimated structures, and our generally applicable HGI strategy reliably improves the estimation structural accuracy of popular hybrid algorithms with negligible additional computational expense. Our empirical results demonstrate the superior empirical performance of pHGS against many state-of-the-art structure learning algorithms.
We introduce the UPG package for highly efficient Bayesian inference in probit, logit, multinomial logit and binomial logit models. UPG offers a convenient estimation framework for balanced and imbalanced data settings where sampling efficiency is ensured through Markov chain Monte Carlo boosting methods. All sampling algorithms are implemented in C++, allowing for rapid parameter estimation. In addition, UPG provides several methods for fast production of output tables and summary plots that are easily accessible to a broad range of users.
Due to the ease of modern data collection, applied statisticians often have access to a large set of covariates that they wish to relate to some observed outcome. Generalized linear models (GLMs) offer a particularly interpretable framework for such an analysis. In these high-dimensional problems, the number of covariates is often large relative to the number of observations, so we face non-trivial inferential uncertainty; a Bayesian approach allows coherent quantification of this uncertainty. Unfortunately, existing methods for Bayesian inference in GLMs require running times roughly cubic in parameter dimension, and so are limited to settings with at most tens of thousand parameters. We propose to reduce time and memory costs with a low-rank approximation of the data in an approach we call LR-GLM. When used with the Laplace approximation or Markov chain Monte Carlo, LR-GLM provides a full Bayesian posterior approximation and admits running times reduced by a full factor of the parameter dimension. We rigorously establish the quality of our approximation and show how the choice of rank allows a tunable computational-statistical trade-off. Experiments support our theory and demonstrate the efficacy of LR-GLM on real large-scale datasets.
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