32,557 research outputs found
parallelMCMCcombine: An R Package for Bayesian Methods for Big Data and Analytics
Recent advances in big data and analytics research have provided a wealth of
large data sets that are too big to be analyzed in their entirety, due to
restrictions on computer memory or storage size. New Bayesian methods have been
developed for large data sets that are only large due to large sample sizes;
these methods partition big data sets into subsets, and perform independent
Bayesian Markov chain Monte Carlo analyses on the subsets. The methods then
combine the independent subset posterior samples to estimate a posterior
density given the full data set. These approaches were shown to be effective
for Bayesian models including logistic regression models, Gaussian mixture
models and hierarchical models. Here, we introduce the R package
parallelMCMCcombine which carries out four of these techniques for combining
independent subset posterior samples. We illustrate each of the methods using a
Bayesian logistic regression model for simulation data and a Bayesian Gamma
model for real data; we also demonstrate features and capabilities of the R
package. The package assumes the user has carried out the Bayesian analysis and
has produced the independent subposterior samples outside of the package. The
methods are primarily suited to models with unknown parameters of fixed
dimension that exist in continuous parameter spaces. We envision this tool will
allow researchers to explore the various methods for their specific
applications, and will assist future progress in this rapidly developing field.Comment: for published version see:
http://www.plosone.org/article/fetchObject.action?uri=info%3Adoi%2F10.1371%2Fjournal.pone.0108425&representation=PD
Sample- and segment-size specific Model Selection in Mixture Regression Analysis
As mixture regression models increasingly receive attention from both theory and practice, the question of selecting the correct number of segments gains urgency. A misspecification can lead to an under- or oversegmentation, thus resulting in flawed management decisions on customer targeting or product positioning.
This paper presents the results of an extensive simulation study that examines the performance of commonly used information criteria in a mixture regression context with normal data. Unlike with previous studies, the performance is evaluated at a broad range of sample/segment size combinations being the most critical factors for the effectiveness of the criteria from both a theoretical and practical point of view. In order to assess the absolute performance of each criterion with respect to chance, the performance is reviewed against so called chance criteria, derived from discriminant analysis.
The results induce recommendations on criterion selection when a certain sample size is given and help to judge what sample size is needed in order to guarantee an accurate decision based on a certain criterion respectively
Sparsity-Promoting Bayesian Dynamic Linear Models
Sparsity-promoting priors have become increasingly popular over recent years
due to an increased number of regression and classification applications
involving a large number of predictors. In time series applications where
observations are collected over time, it is often unrealistic to assume that
the underlying sparsity pattern is fixed. We propose here an original class of
flexible Bayesian linear models for dynamic sparsity modelling. The proposed
class of models expands upon the existing Bayesian literature on sparse
regression using generalized multivariate hyperbolic distributions. The
properties of the models are explored through both analytic results and
simulation studies. We demonstrate the model on a financial application where
it is shown that it accurately represents the patterns seen in the analysis of
stock and derivative data, and is able to detect major events by filtering an
artificial portfolio of assets
- …