arXiv subjects

Sylvia Frühwirth-Schnatter

Publications and source records attributed to Sylvia Frühwirth-Schnatter.

At least 19 recordsLinked to original sources

arXiv2026

The generalized lower triangular process prior

In the analysis of multivariate data, factor models represent a powerful technique for both reducing dimensionality and facilitating qualitative understanding of the latent determinants governing the observed data. Interpretability, however, is often hindered by the non-identifiability of factor loading matrices due to rotational invariance. A prevailing strategy to address this issue is to consider positive lower triangular structures. A relaxation of the latter condition has been recently proposed in the literature with the so called generalized lower triangular structure. However, its Bayesian implementation presents substantial challenges, requiring complex reversible-jump algorithms and making prior elicitation difficult because of the limited interpretability of the model parameters. In this paper, we introduce a generalized lower triangular process prior that allows both global and within-component sparsity structures for learning both the number of factors and possible sparsity structures within the vector of observations. The proposed approach provides straightforward prior parameters elicitation exploiting possibly different prior information on the rank and sparsity characteristics. We also explore connections with the Indian buffet process, providing further insight into the sparsity structure induced by the proposed prior. Posterior computation can be performed resorting to a Gibbs sampler with Metropolis-Hastings moves. The efficacy of the proposed method is demonstrated through comprehensive simulations and the analysis of the Big Five Personality Test data.

stat.ME↗

arXiv2026

CliPS -- How to identify cluster distributions in Bayesian mixture models

We propose the CliPS procedure when fitting Bayesian mixture models in the context of model-based clustering to identify the cluster distributions while simultaneously assessing the suitability of a cluster solution and validating the cluster structure. The procedure relies on the point process representation of a mixture model and is based on the assumption that a suitable cluster solution requires the clusters to be distinguishable with respect to a low-dimensional functional of the component-specific parameters of the mixture. CliPS maps the component-specific MCMC draws to the point process representation and identifies clusters there, exploiting that, while data distributions usually overlap, the posterior of these functionals are more and more separated for increasing sample size. We outline the procedure and illustrate its use on several model-based clustering examples.

stat.ME↗

arXiv2026

Marginal Data Augmentation for Efficient Bayesian Modeling of Counts and Rates with a Demographic Application

Count data models are ubiquitous in many fields, yet Bayesian data augmentation algorithms for such models frequently encounter challenges with Markov chain Monte Carlo efficiency. Posterior simulation is especially demanding when modeling data with a high proportion of zero outcomes. In this paper, we address this issue by introducing a marginal data augmentation approach for semi-parametric Bayesian count data regression models, based on a working parameter that rescales latent outcomes corresponding to zero-count observations. This strategy alleviates the strong posterior dependencies that typically reduce the efficiency of standard data augmentation schemes and leads to substantial gains in sampling efficiency. Synthetic data examples and simulation studies are used to demonstrate the improvements in mixing compared to conventional sampling methods. A demographic application using latent factor analysis to model subnational mortality counts in Austria further underscores the broader applicability of the proposed methodology.

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arXiv2025

Cover It Up! Bipartite Graphs Uncover Identifiability in Sparse Factor Analysis

Despite the popularity of factor models with sparse loading matrices, little attention has been given to formally address identifiability of these models beyond standard rotation-based identification such as the positive lower triangular constraint. To fill this gap, we present a counting rule on the number of nonzero factor loadings that is sufficient for achieving generic uniqueness of the variance decomposition in the factor representation. This is formalized in the framework of sparse matrix spaces and some classical elements from graph and network theory. Furthermore, we provide a computationally efficient tool for verifying the counting rule. Our methodology is illustrated for real data in the context of post-processing posterior draws in Bayesian sparse factor analysis.

econ.EM↗

arXiv2025

The Dynamic Triple Gamma Prior as a Shrinkage Process Prior for Time-Varying Parameter Models

Many existing shrinkage approaches for time-varying parameter (TVP) models assume constant innovation variances across time points, inducing sparsity by shrinking these variances toward zero. However, this assumption falls short when states exhibit large jumps or structural changes, as often seen in empirical time series analysis. To address this, we propose the dynamic triple gamma prior -- a stochastic process that induces time-dependent shrinkage by modeling dependence among innovations while retaining a well-known triple gamma marginal distribution. This framework encompasses various special and limiting cases, including the horseshoe shrinkage prior, making it highly flexible. We derive key properties of the dynamic triple gamma that highlight its dynamic shrinkage behavior and develop an efficient Markov chain Monte Carlo algorithm for posterior sampling. The proposed approach is evaluated through sparse covariance modeling and forecasting of the returns of the EURO STOXX 50 index, demonstrating favorable forecasting performance.

econ.EM↗

arXiv2024

Without Pain -- Clustering Categorical Data Using a Bayesian Mixture of Finite Mixtures of Latent Class Analysis Models

We propose a Bayesian approach for model-based clustering of multivariate categorical data where variables are allowed to be associated within clusters and the number of clusters is unknown. The approach uses a two-layer mixture of finite mixtures model where the cluster distributions are approximated using latent class analysis models. A careful specification of priors with suitable hyperparameter values is crucial to identify the two-layer structure and obtain a parsimonious cluster solution. We outline the Bayesian estimation based on Markov chain Monte Carlo sampling with the telescoping sampler and describe how to obtain an identified clustering model by resolving the label switching issue. Empirical demonstrations in a simulation study using artificial data as well as a data set on low back pain indicate the good clustering performance of the proposed approach, provided hyperparameters are selected which induce sufficient shrinkage.

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arXiv2023

Dynamic Mixture of Finite Mixtures of Factor Analysers with Automatic Inference on the Number of Clusters and Factors

Mixtures of factor analysers (MFA) models represent a popular tool for finding structure in data, particularly high-dimensional data. While in most applications the number of clusters, and especially the number of latent factors within clusters, is mostly fixed in advance, in the recent literature models with automatic inference on both the number of clusters and latent factors have been introduced. The automatic inference is usually done by assigning a nonparametric prior and allowing the number of clusters and factors to potentially go to infinity. The MCMC estimation is performed via an adaptive algorithm, in which the parameters associated with the redundant factors are discarded as the chain moves. While this approach has clear advantages, it also bears some significant drawbacks. Running a separate factor-analytical model for each cluster involves matrices of changing dimensions, which can make the model and programming somewhat cumbersome. In addition, discarding the parameters associated with the redundant factors could lead to a bias in estimating cluster covariance matrices. At last, identification remains problematic for infinite factor models. The current work contributes to the MFA literature by providing for the automatic inference on the number of clusters and the number of cluster-specific factors while keeping both cluster and factor dimensions finite. This allows us to avoid many of the aforementioned drawbacks of the infinite models. For the automatic inference on the cluster structure, we employ the dynamic mixture of finite mixtures (MFM) model. Automatic inference on cluster-specific factors is performed by assigning an exchangeable shrinkage process (ESP) prior to the columns of the factor loading matrices. The performance of the model is demonstrated on several benchmark data sets as well as real data applications.

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arXiv2023

Ultimate Pólya Gamma Samplers -- Efficient MCMC for possibly imbalanced binary and categorical data

Modeling binary and categorical data is one of the most commonly encountered tasks of applied statisticians and econometricians. While Bayesian methods in this context have been available for decades now, they often require a high level of familiarity with Bayesian statistics or suffer from issues such as low sampling efficiency. To contribute to the accessibility of Bayesian models for binary and categorical data, we introduce novel latent variable representations based on Pólya-Gamma random variables for a range of commonly encountered logistic regression models. From these latent variable representations, new Gibbs sampling algorithms for binary, binomial, and multinomial logit models are derived. All models allow for a conditionally Gaussian likelihood representation, rendering extensions to more complex modeling frameworks such as state space models straightforward. However, sampling efficiency may still be an issue in these data augmentation based estimation frameworks. To counteract this, novel marginal data augmentation strategies are developed and discussed in detail. The merits of our approach are illustrated through extensive simulations and real data applications.

stat.CO↗

arXiv2023

Efficient Bayesian Modeling of Binary and Categorical Data in R: The UPG Package

In this vignette, we introduce the UPG package for 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 marginal data augmentation. UPG provides several methods for fast production of output tables and summary plots that are easily accessible to a broad range of users.

stat.CO↗

arXiv2023

Generalized Cumulative Shrinkage Process Priors with Applications to Sparse Bayesian Factor Analysis

The paper discusses shrinkage priors which impose increasing shrinkage in a sequence of parameters. We review the cumulative shrinkage process (CUSP) prior of Legramanti et al. (2020), which is a spike-and-slab shrinkage prior where the spike probability is stochastically increasing and constructed from the stick-breaking representation of a Dirichlet process prior. As a first contribution, this CUSP prior is extended by involving arbitrary stick-breaking representations arising from beta distributions. As a second contribution, we prove that exchangeable spike-and-slab priors, which are popular and widely used in sparse Bayesian factor analysis, can be represented as a finite generalized CUSP prior, which is easily obtained from the decreasing order statistics of the slab probabilities. Hence, exchangeable spike-and-slab shrinkage priors imply increasing shrinkage as the column index in the loading matrix increases, without imposing explicit order constraints on the slab probabilities. An application to sparse Bayesian factor analysis illustrates the usefulness of the findings of this paper. A new exchangeable spike-and-slab shrinkage prior based on the triple gamma prior of Cadonna et al. (2020) is introduced and shown to be helpful for estimating the unknown number of factors in a simulation study.

stat.ME↗

arXiv2023

Sparse Bayesian factor analysis when the number of factors is unknown

There has been increased research interest in the subfield of sparse Bayesian factor analysis with shrinkage priors, which achieve additional sparsity beyond the natural parsimonity of factor models. In this spirit, we estimate the number of common factors in the highly implemented sparse latent factor model with spike-and-slab priors on the factor loadings matrix. Our framework leads to a natural, efficient and simultaneous coupling of model estimation and selection on one hand and model identification and rank estimation (number of factors) on the other hand. More precisely, by embedding the unordered generalized lower triangular loadings representation into overfitting sparse factor modelling, we obtain posterior summaries regarding factor loadings, common factors as well as the factor dimension via postprocessing draws from our efficient and customized Markov chain Monte Carlo scheme.

stat.ME↗

arXiv2023

When it counts -- Econometric identification of the basic factor model based on GLT structures

Despite the popularity of factor models with sparse loading matrices, little attention has been given to formally address identifiability of these models beyond standard rotation-based identification such as the positive lower triangular (PLT) constraint. To fill this gap, we review the advantages of variance identification in sparse factor analysis and introduce the generalized lower triangular (GLT) structures. We show that the GLT assumption is an improvement over PLT without compromise: GLT is also unique but, unlike PLT, a non-restrictive assumption. Furthermore, we provide a simple counting rule for variance identification under GLT structures, and we demonstrate that within this model class the unknown number of common factors can be recovered in an exploratory factor analysis. Our methodology is illustrated for simulated data in the context of post-processing posterior draws in Bayesian sparse factor analysis.

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arXiv2022

Bayesian Reconciliation of Return Predictability

This article considers a stable vector autoregressive (VAR) model and investigates return predictability in a Bayesian context. The VAR system comprises asset returns and the dividend-price ratio as proposed in Cochrane (2008), and allows pinning down the question of return predictability to the value of one particular model parameter. We develop a new shrinkage type prior for this parameter and compare our Bayesian approach to ordinary least squares estimation and to the reduced-bias estimator proposed in Amihud and Hurvich (2004). A simulation study shows that the Bayesian approach dominates the reduced-bias estimator in terms of observed size (false positive) and power (false negative). We apply our methodology to annual CRSP value-weighted returns running, respectively, from 1926 to 2004 and from 1953 to 2021. For the first sample, the Bayesian approach supports the hypothesis of no return predictability, while for the second data set weak evidence for predictability is observed.

stat.AP↗

arXiv2022

Sparse Bayesian State-Space and Time-Varying Parameter Models

In this chapter, we review variance selection for time-varying parameter (TVP) models for univariate and multivariate time series within a Bayesian framework. We show how both continuous as well as discrete spike-and-slab shrinkage priors can be transferred from variable selection for regression models to variance selection for TVP models by using a non-centered parametrization. We discuss efficient MCMC estimation and provide an application to US inflation modeling.

econ.EM↗

arXiv2022

Spying on the prior of the number of data clusters and the partition distribution in Bayesian cluster analysis

Cluster analysis aims at partitioning data into groups or clusters. In applications, it is common to deal with problems where the number of clusters is unknown. Bayesian mixture models employed in such applications usually specify a flexible prior that takes into account the uncertainty with respect to the number of clusters. However, a major empirical challenge involving the use of these models is in the characterisation of the induced prior on the partitions. This work introduces an approach to compute descriptive statistics of the prior on the partitions for three selected Bayesian mixture models developed in the areas of Bayesian finite mixtures and Bayesian nonparametrics. The proposed methodology involves computationally efficient enumeration of the prior on the number of clusters in-sample (termed as ``data clusters'') and determining the first two prior moments of symmetric additive statistics characterising the partitions. The accompanying reference implementation is made available in the R package 'fipp'. Finally, we illustrate the proposed methodology through comparisons and also discuss the implications for prior elicitation in applications.

stat.ME↗

arXiv2021

Generalized mixtures of finite mixtures and telescoping sampling

Within a Bayesian framework, a comprehensive investigation of mixtures of finite mixtures (MFMs), i.e., finite mixtures with a prior on the number of components, is performed. This model class has applications in model-based clustering as well as for semi-parametric density estimation and requires suitable prior specifications and inference methods to exploit its full potential. We contribute by considering a generalized class of MFMs where the hyperparameter $γ_K$ of a symmetric Dirichlet prior on the weight distribution depends on the number of components. We show that this model class may be regarded as a Bayesian non-parametric mixture outside the class of Gibbs-type priors. We emphasize the distinction between the number of components $K$ of a mixture and the number of clusters $K_+$, i.e., the number of filled components given the data. In the MFM model, $K_+$ is a random variable and its prior depends on the prior on $K$ and on the hyperparameter $γ_K$. We employ a flexible prior distribution for the number of components $K$ and derive the corresponding prior on the number of clusters $K_+$ for generalized MFMs. For posterior inference, we propose the novel telescoping sampler which allows Bayesian inference for mixtures with arbitrary component distributions without resorting to reversible jump Markov chain Monte Carlo (MCMC) methods. The telescoping sampler explicitly samples the number of components, but otherwise requires only the usual MCMC steps of a finite mixture model. The ease of its application using different component distributions is demonstrated on several data sets.

stat.ME↗

arXiv2021

How many data clusters are in the Galaxy data set? Bayesian cluster analysis in action

In model-based clustering, the Galaxy data set is often used as a benchmark data set to study the performance of different modeling approaches. Aitkin (2001) compares maximum likelihood and Bayesian analyses of the Galaxy data set and expresses reservations about the Bayesian approach due to the fact that the prior assumptions imposed remain rather obscure while playing a major role in the results obtained and conclusions drawn. The aim of the paper is to address Aitkin's concerns about the Bayesian approach by shedding light on how the specified priors influence the number of estimated clusters. We perform a sensitivity analysis of different prior specifications for the mixtures of finite mixture model, i.e., the mixture model where a prior on the number of components is included. We use an extensive set of different prior specifications in a full factorial design and assess their impact on the estimated number of clusters for the Galaxy data set. Results highlight the interaction effects of the prior specifications and provide insights into which prior specifications are recommended to obtain a sparse clustering solution. A simulation study with artificial data provides further empirical evidence to support the recommendations. A clear understanding of the impact of the prior specifications removes restraints preventing the use of Bayesian methods due to the complexity of selecting suitable priors. Also, the regularizing properties of the priors may be intentionally exploited to obtain a suitable clustering solution meeting prior expectations and needs of the application.

stat.AP↗

arXiv2021

Factor-augmented Bayesian treatment effects models for panel outcomes

We propose a new, flexible model for inference of the effect of a binary treatment on a continuous outcome observed over subsequent time periods. The model allows to seperate association due to endogeneity of treatment selection from additional longitudinal association of the outcomes and hence unbiased estimation of dynamic treatment effects. We investigate the performance of the proposed method on simulated data and employ it to reanalyse data on the longitudinal effects of a long maternity leave on mothers' earnings after their return to the labour market.

stat.ME↗