arXiv subjects

Gregor Kastner

Publications and source records attributed to Gregor Kastner.

17 recordsLinked to original sources

arXiv2025

Repulsive mixtures via the sparsity-inducing partition prior

We introduce a novel prior distribution for modelling the weights in mixture models based on a generalisation of the Dirichlet distribution, the Selberg Dirichlet distribution. This distribution contains a repulsive term, which naturally penalises values that lie close to each other on the simplex, thus encouraging few dominating clusters. The repulsive behaviour induces additional sparsity on the number of components. We refer to this construction as sparsity-inducing partition (SIP) prior. By highlighting differences with the conventional Dirichlet distribution, we present relevant properties of the SIP prior and demonstrate their implications across a variety of mixture models, including finite mixtures with a fixed or random number of components, as well as repulsive mixtures. We propose an efficient posterior sampling algorithm and validate our model through an extensive simulation study as well as an application to a biomedical dataset describing children's Body Mass Index and eating behaviour.

stat.ME↗

arXiv2025

A note on simulation methods for the Dirichlet-Laplace prior

Bhattacharya et al. (2015, Journal of the American Statistical Association 110(512): 1479-1490) introduce a novel prior, the Dirichlet-Laplace (DL) prior, and propose a Markov chain Monte Carlo (MCMC) method to simulate posterior draws under this prior in a conditionally Gaussian setting. The original algorithm samples from conditional distributions in the wrong order, i.e., it does not correctly sample from the joint posterior distribution of all latent variables. This note details the issue and provides two simple solutions: A correction to the original algorithm and a new algorithm based on an alternative, yet equivalent, formulation of the prior. This corrigendum does not affect the theoretical results in Bhattacharya et al. (2015).

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arXiv2024

Bayesian nonparametric partial clustering: Quantifying the effectiveness of agricultural subsidies across Europe

The global climate has underscored the need for effective policies to reduce greenhouse gas emissions from all sources, including those resulting from agricultural expansion, which is regulated by the Common Agricultural Policy (CAP) across the European Union (EU). To assess the effectiveness of these mitigation policies, statistical methods must account for the heterogeneous impact of policies across different countries. We propose a Bayesian approach that combines the multinomial logit model, which is suitable for compositional land-use data, with a Bayesian nonparametric (BNP) prior to cluster regions with similar policy impacts. To simultaneously control for other relevant factors, we distinguish between cluster-specific and global covariates, coining this approach the Bayesian nonparametric partial clustering model. We develop a novel and efficient Markov Chain Monte Carlo (MCMC) algorithm, leveraging recent advances in the Bayesian literature. Using economic, geographic, and subsidy-related data from 22 EU member states, we examine the effectiveness of policies influencing land-use decisions across Europe and highlight the diversity of the problem. Our results indicate that the impact of CAP varies widely across the EU, emphasizing the need for subsidies to be tailored to optimize their effectiveness.

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arXiv2022

Bayesian modeling and clustering for spatio-temporal areal data: An application to Italian unemployment

Spatio-temporal areal data can be seen as a collection of time series which are spatially correlated according to a specific neighboring structure. Incorporating the temporal and spatial dimension into a statistical model poses challenges regarding the underlying theoretical framework as well as the implementation of efficient computational methods. We propose to include spatio-temporal random effects using a conditional autoregressive prior, where the temporal correlation is modeled through an autoregressive mean decomposition and the spatial correlation by the precision matrix inheriting the neighboring structure. Their joint distribution constitutes a Gaussian Markov random field, whose sparse precision matrix enables the usage of efficient sampling algorithms. We cluster the areal units using a nonparametric prior, thereby learning latent partitions of the areal units. The performance of the model is assessed via an application to study regional unemployment patterns in Italy. When compared to other spatial and spatio-temporal competitors, the proposed model shows more precise estimates and the additional information obtained from the clustering allows for an extended economic interpretation of the unemployment rates of the Italian provinces.

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arXiv2022

Forecasting macroeconomic data with Bayesian VARs: Sparse or dense? It depends!

Vector autogressions (VARs) are widely applied when it comes to modeling and forecasting macroeconomic variables. In high dimensions, however, they are prone to overfitting. Bayesian methods, more concretely shrinkage priors, have shown to be successful in improving prediction performance. In the present paper, we introduce the semi-global framework, in which we replace the traditional global shrinkage parameter with group-specific shrinkage parameters. We show how this framework can be applied to various shrinkage priors, such as global-local priors and stochastic search variable selection priors. We demonstrate the virtues of the proposed framework in an extensive simulation study and in an empirical application forecasting data of the US economy. Further, we shed more light on the ongoing ``Illusion of Sparsity'' debate, finding that forecasting performances under sparse/dense priors vary across evaluated economic variables and across time frames. Dynamic model averaging, however, can combine the merits of both worlds.

econ.EM↗

arXiv2021

Bayesian Machine Learning meets Formal Methods: An application to spatio-temporal data

We propose an interdisciplinary framework that combines Bayesian predictive inference, a well-established tool in Machine Learning, with Formal Methods rooted in the computer science community. Bayesian predictive inference allows for coherently incorporating uncertainty about unknown quantities by making use of methods or models that produce predictive distributions, which in turn inform decision problems. By formalizing these decision problems into properties with the help of spatio-temporal logic, we can formulate and predict how likely such properties are to be satisfied in the future at a certain location. Moreover, we can leverage our methodology to evaluate and compare models directly on their ability to predict the satisfaction of application-driven properties. The approach is illustrated in an urban mobility application, where the crowdedness in the center of Milan is proxied by aggregated mobile phone traffic data. We specify several desirable spatio-temporal properties related to city crowdedness such as a fault-tolerant network or the reachability of hospitals. After verifying these properties on draws from the posterior predictive distributions, we compare several spatio-temporal Bayesian models based on their overall and property-based predictive performance.

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arXiv2021

On the joint volatility dynamics in dairy markets

The present study investigates the price (co)volatility of four dairy commodities -- skim milk powder, whole milk powder, butter and cheddar cheese -- in three major dairy markets. It uses a multivariate factor stochastic volatility model for estimating the time-varying covariance and correlation matrices by imposing a low-dimensional latent dynamic factor structure. The empirical results support four factors representing the European Union and Oceania dairy sectors as well as the milk powder markets. Factor volatilities and marginal posterior volatilities of each dairy commodity increase after the 2006/07 global (food) crisis, which also coincides with the free trade agreements enacted from 2007 onwards and EU and US liberalization policy changes. The model-implied correlation matrices show increasing dependence during the second half of 2006, throughout the first half of 2007, as well as during 2008 and 2014, which can be attributed to various regional agricultural dairy policies. Furthermore, in-sample value at risk measures (VaRs and CoVaRs) are provided for each dairy commodity under consideration.

econ.GN↗

arXiv2021

Modeling Univariate and Multivariate Stochastic Volatility in R with stochvol and factorstochvol

Stochastic volatility (SV) models are nonlinear state-space models that enjoy increasing popularity for fitting and predicting heteroskedastic time series. However, due to the large number of latent quantities, their efficient estimation is non-trivial and software that allows to easily fit SV models to data is rare. We aim to alleviate this issue by presenting novel implementations of four SV models delivered in two R packages. Several unique features are included and documented. As opposed to previous versions, stochvol is now capable of handling linear mean models, heavy-tailed SV, and SV with leverage. Moreover, we newly introduce factorstochvol which caters for multivariate SV. Both packages offer a user-friendly interface through the conventional R generics and a range of tailor-made methods. Computational efficiency is achieved via interfacing R to C++ and doing the heavy work in the latter. In the paper at hand, we provide a detailed discussion on Bayesian SV estimation and showcase the use of the new software through various examples.

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arXiv2019

Sparse Bayesian vector autoregressions in huge dimensions

We develop a Bayesian vector autoregressive (VAR) model with multivariate stochastic volatility that is capable of handling vast dimensional information sets. Three features are introduced to permit reliable estimation of the model. First, we assume that the reduced-form errors in the VAR feature a factor stochastic volatility structure, allowing for conditional equation-by-equation estimation. Second, we apply recently developed global-local shrinkage priors to the VAR coefficients to cure the curse of dimensionality. Third, we utilize recent innovations to efficiently sample from high-dimensional multivariate Gaussian distributions. This makes simulation-based fully Bayesian inference feasible when the dimensionality is large but the time series length is moderate. We demonstrate the merits of our approach in an extensive simulation study and apply the model to US macroeconomic data to evaluate its forecasting capabilities.

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arXiv2019

Approaches Toward the Bayesian Estimation of the Stochastic Volatility Model with Leverage

The sampling efficiency of MCMC methods in Bayesian inference for stochastic volatility (SV) models is known to highly depend on the actual parameter values, and the effectiveness of samplers based on different parameterizations varies significantly. We derive novel algorithms for the centered and the non-centered parameterizations of the practically highly relevant SV model with leverage, where the return process and innovations of the volatility process are allowed to correlate. Moreover, based on the idea of ancillarity-sufficiency interweaving (ASIS), we combine the resulting samplers in order to guarantee stable sampling efficiency irrespective of the baseline parameterization.We carry out an extensive comparison to already existing sampling methods for this model using simulated as well as real world data.

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arXiv2019

Dealing with Stochastic Volatility in Time Series Using the R Package stochvol

The R package stochvol provides a fully Bayesian implementation of heteroskedasticity modeling within the framework of stochastic volatility. It utilizes Markov chain Monte Carlo (MCMC) samplers to conduct inference by obtaining draws from the posterior distribution of parameters and latent variables which can then be used for predicting future volatilities. The package can straightforwardly be employed as a stand-alone tool; moreover, it allows for easy incorporation into other MCMC samplers. The main focus of this paper is to show the functionality of stochvol. In addition, it provides a brief mathematical description of the model, an overview of the sampling schemes used, and several illustrative examples using exchange rate data.

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arXiv2018

Should I stay or should I go? A latent threshold approach to large-scale mixture innovation models

This paper proposes a straightforward algorithm to carry out inference in large time-varying parameter vector autoregressions (TVP-VARs) with mixture innovation components for each coefficient in the system. We significantly decrease the computational burden by approximating the latent indicators that drive the time-variation in the coefficients with a latent threshold process that depends on the absolute size of the shocks. The merits of our approach are illustrated with two applications. First, we forecast the US term structure of interest rates and demonstrate forecast gains of the proposed mixture innovation model relative to other benchmark models. Second, we apply our approach to US macroeconomic data and find significant evidence for time-varying effects of a monetary policy tightening.

stat.ME↗

arXiv2018

Introducing shrinkage in heavy-tailed state space models to predict equity excess returns

We forecast S&P 500 excess returns using a flexible Bayesian econometric state space model with non-Gaussian features at several levels. More precisely, we control for overparameterization via novel global-local shrinkage priors on the state innovation variances as well as the time-invariant part of the state space model. The shrinkage priors are complemented by heavy tailed state innovations that cater for potential large breaks in the latent states. Moreover, we allow for leptokurtic stochastic volatility in the observation equation. The empirical findings indicate that several variants of the proposed approach outperform typical competitors frequently used in the literature, both in terms of point and density forecasts.

econ.EM↗

arXiv2017

Sparse Bayesian time-varying covariance estimation in many dimensions

We address the curse of dimensionality in dynamic covariance estimation by modeling the underlying co-volatility dynamics of a time series vector through latent time-varying stochastic factors. The use of a global-local shrinkage prior for the elements of the factor loadings matrix pulls loadings on superfluous factors towards zero. To demonstrate the merits of the proposed framework, the model is applied to simulated data as well as to daily log-returns of 300 S&P 500 members. Our approach yields precise correlation estimates, strong implied minimum variance portfolio performance and superior forecasting accuracy in terms of log predictive scores when compared to typical benchmarks.

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arXiv2017

Sophisticated and small versus simple and sizeable: When does it pay off to introduce drifting coefficients in Bayesian VARs?

We assess the relationship between model size and complexity in the time-varying parameter VAR framework via thorough predictive exercises for the Euro Area, the United Kingdom and the United States. It turns out that sophisticated dynamics through drifting coefficients are important in small data sets, while simpler models tend to perform better in sizeable data sets. To combine the best of both worlds, novel shrinkage priors help to mitigate the curse of dimensionality, resulting in competitive forecasts for all scenarios considered. Furthermore, we discuss dynamic model selection to improve upon the best performing individual model for each point in time.

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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.

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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.

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