1,721,161 research outputs found
A Bayesian nonparametric model for count functional data
Full text linkCount functional data arise in a variety of applications, including longitudinal, spatial and imaging studies measuring functional count responses for each subject under study. The literature on statistical models for dependent count data is dominated by models built from hierarchical Poisson components. The Poisson assumption is not warranted in many applications, and hierarchical Poisson models make restrictive assumptions about over-dispersion in marginal distributions.This article discuss a class of nonparametric Bayes count functional data models introduced in Canale and Dunson (2012), which are constructed through rounding real-valued underlying processes. Computational algorithms are developed using Markov chain Monte Carlo and the methods are illustrated through application to asthma inhaler usage
Enriched Stick Breaking Processes for Functional Data
No full textIn many applications involving functional data, prior information is available about the proportion of curves having different attributes. It is not straightforward to include such information in existing procedures for functional data analysis. Generalizing the functional Dirichlet process (FDP), we propose a class of stick-breaking priors for distributions of functions. These priors incorporate functional atoms drawn from a Gaussian process. The stick-breaking weights are specified to allow user-specified prior probabilities for curve at- tributes, with hyperpriors accommodating uncertainty. Compared with the FDP, the random distribution is enriched for curves having attributes known to be common. Theoretical prop- erties are considered, methods are developed for posterior computation, and the approach is illustrated using data on temperature curves in menstrual cycles
A Bayesian nonparametric model for data on different scales of measure; an application to customer base management of telecommunications companies.
Full text linkTo analyse telecommunications marketing data which are usually made of discrete and continuous observations we consider a general framework to jointly model continuous, count and categorical variables under a nonparametric prior, which is induced through rounding latent variables having an unknown density with respect to Lebesgue measure. The approach is applied to model the joint density of traffic data for a portion of customers of an European mobile phone operator
Enriched Stick Breaking Processes for Functional Data
No full textIn many applications involving functional data, prior information is available about
the proportion of curves having different attributes. It is not straightforward to include
such information in existing procedures for functional data analysis. Generalizing the func-
tional Dirichlet process (FDP), we propose a class of stick-breaking priors for distributions
of functions. These priors incorporate functional atoms drawn from constrained stochastic
processes. The stick-breaking weights are specified to allow user-specified prior probabili-
ties for curve attributes, with hyperpriors accommodating uncertainty. Compared with the
FDP, the random distribution is enriched for curves having attributes known to be common.
Theoretical properties are considered, methods are developed for posterior computation, and
the approach is illustrated using data on temperature curves in menstrual cycles
Bayesian Kernel Mixtures for Counts
Full text linkAlthough Bayesian nonparametric mixture models for continuous data are well developed, the literature on related approaches for count data is limited. A common strategy is to use a mixture of Poissons, which unfortunately is quite restrictive in not accounting for distributions with variance less than the mean. Other approaches include mixing multinomials, which requires finite support, and using a Dirichlet process prior with a Poisson base measure, which does not allow for smooth deviations from the Poisson. We propose broad class of alternative models, nonparametric mixtures of rounded continuous kernels. We develop an efficient Gibbs sampler for posterior computation, and perform a simulation study to assess performance. Focusing on the rounded Gaussian case, we generalize the modeling framework to account for multivariate count data, joint modeling with continuous and categorical variables, and other complications. We illustrate our methods through applications to a developmental toxicity study and marketing data. Supplemental material is available onlin
Locally adaptive Bayesian covariance regression
No full textMultivariate time series data arise in many applied domains, and it is often crucial
to obtain a good characterization of how the covariance among the dierent variables
changes over time. Certainly this is the case in nancial applications in which co-
variance can change dramatically during times of nancial crisis, revealing dierent
associations among assets and countries than occur in a healthier economic climate.
Our focus is on developing models that allow the covariance to vary
exibly over con-
tinuous time, and additionally accommodate locally adaptive smoothing of the covari-
ance. Locally adaptive smoothing to accommodate varying smoothness in a trajectory
over time has been well studied, but such approaches have not yet been developed for
time-varying covariance matrices to our knowledge. To address this gap, we generalize
recently develop methods for Bayesian covariance regression to incorporate random
dictionary elements with locally varying smoothness. Using a dierential equation rep-
resentation, we additionally develop a fast computational approach via MCMC, with
online algorithms also considered. The performance of the models is assessed through
simulation studies and the methods are applied to nancial time series
Nonparametric Bayes modelling of count processes
Full text linkData on count processes arise in a variety of applications, including longitudinal, spatial and
imaging studies measuring count responses. The literature on statistical models for dependent
count data is dominated by models built from hierarchical Poisson components. The Poisson
assumption is not warranted in many applied contexts, and hierarchical Poisson models make
restrictive assumptions about overdispersion in marginal distributions. In this article we propose
a class of nonparametric Bayes count process models, constructed through rounding real-valued
underlying processes. The proposed class of models accommodates situations in which separate
count-valued functional data are observed for each subject under study. Theoretical results on
large support and posterior consistency are established, and computational algorithms are developed based on the Markov chain Monte Carlo approach. The methods are evaluated via simulation studies and illustrated by application to longitudinal tumor counts and to asthma inhaler
usage
Locally Adaptive Factor Processes for Multivariate Time Series
No full textIn modeling multivariate time series, it is important to allow time-varying smoothness in the
mean and covariance process. In particular, there may be certain time intervals exhibiting
rapid changes and others in which changes are slow. If such time-varying smoothness is not
accounted for, one can obtain misleading inferences and predictions, with over-smoothing
across erratic time intervals and under-smoothing across times exhibiting slow variation.
This can lead to mis-calibration of predictive intervals, which can be substantially too
narrow or wide depending on the time. We propose a locally adaptive factor process for
characterizing multivariate mean-covariance changes in continuous time, allowing locally
varying smoothness in both the mean and covariance matrix. This process is constructed
utilizing latent dictionary functions evolving in time through nested Gaussian processes and
linearly related to the observed data with a sparse mapping. Using a di
↵
erential equation
representation, we bypass usual computational bottlenecks in obtaining MCMC and online
algorithms for approximate Bayesian inference. The performance is assessed in simulations
and illustrated in a financial application
Bayesian multivariate mixed-scale density estimation
Full text linkAlthough continuous density estimation has received abundant attention in the Bayesian nonparametrics literature, there is limited theory on multivariate mixed scale density estimation. In this note, we consider a general framework to jointly model continuous, count and categorical variables under a nonparametric prior, which is induced through rounding latent variables having an unknown density with respect to Lebesgue measure. For the proposed class of priors, we provide sufficient conditions for large support, strong consistency and rates of posterior contraction. These conditions allow one to convert sufficient conditions obtained in the setting of multivariate continuous density estimation to the mixed scale case. To illustrate the procedure, a rounded multivariate nonparametric mixture of Gaussians is introduced and applied to a crime and communities dataset
Locally Adaptive Bayesian Multivariate Time Series
No full textIn modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If such locally adaptive smoothness is not accounted for, one can obtain misleading inferences and predictions, with over-smoothing across erratic time intervals and under-smoothing across times exhibiting slow variation. This can lead to miscalibration of predictive intervals, which can be substantially too narrow or wide depending on the time. We propose a continuous multivariate stochastic process for time series having locally varying smoothness in both the mean and covariance matrix. This process is constructed utilizing latent dictionary functions in time, which are given nested Gaussian process priors and linearly related to the observed data through a sparse mapping. Using a differential equation representation, we bypass usual computational bottlenecks in obtaining MCMC and online algorithms for approximate Bayesian inference. The performance is assessed in simulations and illustrated in a financial application
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