arXiv subjects

Sylvia Frühwirth-Schnatter

Publications and source records attributed to Sylvia Frühwirth-Schnatter.

27 records · Page 2Linked to original sources

arXiv2020

Shrinkage in the Time-Varying Parameter Model Framework Using the R Package shrinkTVP

Time-varying parameter (TVP) models are widely used in time series analysis to flexibly deal with processes which gradually change over time. However, the risk of overfitting in TVP models is well known. This issue can be dealt with using appropriate global-local shrinkage priors, which pull time-varying parameters towards static ones. In this paper, we introduce the R package shrinkTVP (Knaus, Bitto-Nemling, Cadonna, and Frühwirth-Schnatter 2019), which provides a fully Bayesian implementation of shrinkage priors for TVP models, taking advantage of recent developments in the literature, in particular that of Bitto and Frühwirth-Schnatter (2019). The package shrinkTVP allows for posterior simulation of the parameters through an efficient Markov Chain Monte Carlo (MCMC) scheme. Moreover, summary and visualization methods, as well as the possibility of assessing predictive performance through log predictive density scores (LPDSs), are provided. The computationally intensive tasks have been implemented in C++ and interfaced with R. The paper includes a brief overview of the models and shrinkage priors implemented in the package. Furthermore, core functionalities are illustrated, both with simulated and real data.

econ.EM↗

arXiv2019

Triple the gamma -- A unifying shrinkage prior for variance and variable selection in sparse state space and TVP models

Time-varying parameter (TVP) models are very flexible in capturing gradual changes in the effect of a predictor on the outcome variable. However, in particular when the number of predictors is large, there is a known risk of overfitting and poor predictive performance, since the effect of some predictors is constant over time. We propose a prior for variance shrinkage in TVP models, called triple gamma. The triple gamma prior encompasses a number of priors that have been suggested previously, such as the Bayesian lasso, the double gamma prior and the Horseshoe prior. We present the desirable properties of such a prior and its relationship to Bayesian Model Averaging for variance selection. The features of the triple gamma prior are then illustrated in the context of time varying parameter vector autoregressive models, both for simulated datasets and for a series of macroeconomics variables in the Euro Area.

econ.EM↗

arXiv2018

From here to infinity - sparse finite versus Dirichlet process mixtures in model-based clustering

In model-based-clustering mixture models are used to group data points into clusters. A useful concept introduced for Gaussian mixtures by Malsiner Walli et al (2016) are sparse finite mixtures, where the prior distribution on the weight distribution of a mixture with $K$ components is chosen in such a way that a priori the number of clusters in the data is random and is allowed to be smaller than $K$ with high probability. The number of cluster is then inferred a posteriori from the data. The present paper makes the following contributions in the context of sparse finite mixture modelling. First, it is illustrated that the concept of sparse finite mixture is very generic and easily extended to cluster various types of non-Gaussian data, in particular discrete data and continuous multivariate data arising from non-Gaussian clusters. Second, sparse finite mixtures are compared to Dirichlet process mixtures with respect to their ability to identify the number of clusters. For both model classes, a random hyper prior is considered for the parameters determining the weight distribution. By suitable matching of these priors, it is shown that the choice of this hyper prior is far more influential on the cluster solution than whether a sparse finite mixture or a Dirichlet process mixture is taken into consideration.

stat.ME↗

arXiv2018

Mixtures of Experts Models

Mixtures of experts models provide a framework in which covariates may be included in mixture models. This is achieved by modelling the parameters of the mixture model as functions of the concomitant covariates. Given their mixture model foundation, mixtures of experts models possess a diverse range of analytic uses, from clustering observations to capturing parameter heterogeneity in cross-sectional data. This chapter focuses on delineating the mixture of experts modelling framework and demonstrates the utility and flexibility of mixtures of experts models as an analytic tool.

stat.ME↗

arXiv2018

Achieving Shrinkage in a Time-Varying Parameter Model Framework

Shrinkage for time-varying parameter (TVP) models is investigated within a Bayesian framework, with the aim to automatically reduce time-varying parameters to static ones, if the model is overfitting. This is achieved through placing the double gamma shrinkage prior on the process variances. An efficient Markov chain Monte Carlo scheme is developed, exploiting boosting based on the ancillarity-sufficiency interweaving strategy. The method is applicable both to TVP models for univariate as well as multivariate time series. Applications include a TVP generalized Phillips curve for EU area inflation modelling and a multivariate TVP Cholesky stochastic volatility model for joint modelling of the returns from the DAX-30 index.

stat.ME↗

arXiv2017

Efficient Bayesian Inference for Multivariate Factor Stochastic Volatility Models

We discuss efficient Bayesian estimation of dynamic covariance matrices in multivariate time series through a factor stochastic volatility model. In particular, we propose two interweaving strategies (Yu and Meng, Journal of Computational and Graphical Statistics, 20(3), 531-570, 2011) to substantially accelerate convergence and mixing of standard MCMC approaches. Similar to marginal data augmentation techniques, the proposed acceleration procedures exploit non-identifiability issues which frequently arise in factor models. Our new interweaving strategies are easy to implement and come at almost no extra computational cost; nevertheless, they can boost estimation efficiency by several orders of magnitude as is shown in extensive simulation studies. To conclude, the application of our algorithm to a 26-dimensional exchange rate data set illustrates the superior performance of the new approach for real-world data.

stat.CO↗

arXiv2017

Ancillarity-Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Estimation of Stochastic Volatility Models

Bayesian inference for stochastic volatility models using MCMC methods highly depends on actual parameter values in terms of sampling efficiency. While draws from the posterior utilizing the standard centered parameterization break down when the volatility of volatility parameter in the latent state equation is small, non-centered versions of the model show deficiencies for highly persistent latent variable series. The novel approach of ancillarity-sufficiency interweaving has recently been shown to aid in overcoming these issues for a broad class of multilevel models. In this paper, we demonstrate how such an interweaving strategy can be applied to stochastic volatility models in order to greatly improve sampling efficiency for all parameters and throughout the entire parameter range. Moreover, this method of "combining best of different worlds" allows for inference for parameter constellations that have previously been infeasible to estimate without the need to select a particular parameterization beforehand.

stat.ME↗

arXiv2016

Model-based clustering based on sparse finite Gaussian mixtures

In the framework of Bayesian model-based clustering based on a finite mixture of Gaussian distributions, we present a joint approach to estimate the number of mixture components and identify cluster-relevant variables simultaneously as well as to obtain an identified model. Our approach consists in specifying sparse hierarchical priors on the mixture weights and component means. In a deliberately overfitting mixture model the sparse prior on the weights empties superfluous components during MCMC. A straightforward estimator for the true number of components is given by the most frequent number of non-empty components visited during MCMC sampling. Specifying a shrinkage prior, namely the normal gamma prior, on the component means leads to improved parameter estimates as well as identification of cluster-relevant variables. After estimating the mixture model using MCMC methods based on data augmentation and Gibbs sampling, an identified model is obtained by relabeling the MCMC output in the point process representation of the draws. This is performed using $K$-centroids cluster analysis based on the Mahalanobis distance. We evaluate our proposed strategy in a simulation setup with artificial data and by applying it to benchmark data sets.

stat.ME↗

arXiv2016

Identifying Mixtures of Mixtures Using Bayesian Estimation

The use of a finite mixture of normal distributions in model-based clustering allows to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by imposing constraints on the model or by using post-processing procedures. Within the Bayesian framework we propose a different approach based on sparse finite mixtures to achieve identifiability. We specify a hierarchical prior where the hyperparameters are carefully selected such that they are reflective of the cluster structure aimed at. In addition this prior allows to estimate the model using standard MCMC sampling methods. In combination with a post-processing approach which resolves the label switching issue and results in an identified model, our approach allows to simultaneously (1) determine the number of clusters, (2) flexibly approximate the cluster distributions in a semi-parametric way using finite mixtures of normals and (3) identify cluster-specific parameters and classify observations. The proposed approach is illustrated in two simulation studies and on benchmark data sets.

stat.ME↗