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A Bayesian treatment of deep learning allows for the computation of uncertainties associated with the predictions of deep neural networks. We show how the concept of Errors-in-Variables can be used in Bayesian deep regression to also…

Machine Learning · Computer Science 2023-05-15 Jörg Martin , Clemens Elster

The purpose of this paper is to propose a time-varying vector autoregressive model (TV-VAR) for forecasting multivariate time series. The model is casted into a state-space form that allows flexible description and analysis. The volatility…

Statistical Finance · Quantitative Finance 2008-12-02 K. Triantafyllopoulos

Stochastic variational Bayes algorithms have become very popular in the machine learning literature, particularly in the context of nonparametric Bayesian inference. These algorithms replace the true but intractable posterior distribution…

Methodology · Statistics 2024-10-04 Pedro Regueiro , Abel Rodríguez , Juan Sosa

The availability of multidimensional economic datasets has grown significantly in recent years. An example is bilateral trade values across goods among countries, comprising three dimensions -- importing countries, exporting countries, and…

Econometrics · Economics 2025-11-24 Yaling Qi

In this paper, a new way to integrate volatility information for estimating value at risk (VaR) and conditional value at risk (CVaR) of a portfolio is suggested. The new method is developed from the perspective of Bayesian statistics and it…

Risk Management · Quantitative Finance 2022-05-04 Taras Bodnar , Vilhelm Niklasson , Erik Thorsén

Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a…

Methodology · Statistics 2014-08-13 Wen-Hsi Yang , Scott H. Holan , Christopher K. Wikle

We formulate a discrete-time Bayesian stochastic volatility model for high-frequency stock-market data that directly accounts for microstructure noise, and outline a Markov chain Monte Carlo algorithm for parameter estimation. The methods…

Applications · Statistics 2016-02-02 Georgi Dinolov , Abel Rodriguez , Hongyun Wang

Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived…

Applications · Statistics 2018-11-12 Dennis Becker

Bayesian neural network models (BNN) have re-surged in recent years due to the advancement of scalable computations and its utility in solving complex prediction problems in a wide variety of applications. Despite the popularity and…

Machine Learning · Statistics 2020-11-20 Shrijita Bhattacharya , Zihuan Liu , Tapabrata Maiti

We develop a Bayesian framework for variable selection in linear regression with autocorrelated errors, accommodating lagged covariates and autoregressive structures. This setting occurs in time series applications where responses depend on…

Methodology · Statistics 2025-08-18 Alokesh Manna , Sujit K. Ghosh

Vector autoregressions (VARs) are a widely used tool for modelling multivariate time-series. It is common to assume a VAR is stationary; this can be enforced by imposing the stationarity condition which restricts the parameter space of the…

The nature of available economic data has changed fundamentally in the last decade due to the economy's digitisation. With the prevalence of often black box data-driven machine learning methods, there is a necessity to develop interpretable…

Econometrics · Economics 2021-10-28 Pratha Khandelwal , Philip Nadler , Rossella Arcucci , William Knottenbelt , Yi-Ke Guo

Vector autoregressive (VAR) models are widely used in practical studies, e.g., forecasting, modelling policy transmission mechanism, and measuring connection of economic agents. To better capture the dynamics, this paper introduces a new…

Econometrics · Economics 2021-11-02 Yayi Yan , Jiti Gao , Bin Peng

While seasonality inherent to raw macroeconomic data is commonly removed by seasonal adjustment techniques before it is used for structural inference, this may distort valuable information in the data. As an alternative method to commonly…

Econometrics · Economics 2025-08-12 Daniel Dzikowski , Carsten Jentsch

A novel spatial autoregressive model for panel data is introduced, which incorporates multilayer networks and accounts for time-varying relationships. Moreover, the proposed approach allows the structural variance to evolve smoothly over…

Applications · Statistics 2023-10-27 Michele Costola , Matteo Iacopini , Casper Wichers

Variational Bayes (VB) has been used to facilitate the calculation of the posterior distribution in the context of Bayesian inference of the parameters of nonlinear models from data. Previously an analytical formulation of VB has been…

Signal Processing · Electrical Eng. & Systems 2020-07-06 Michael A. Chappell , Martin S. Craig , Mark W. Woolrich

Modern regression applications can involve hundreds or thousands of variables which motivates the use of variable selection methods. Bayesian variable selection defines a posterior distribution on the possible subsets of the variables…

Methodology · Statistics 2024-10-16 J. E. Griffin

Varying coefficient models are popular for estimating nonlinear regression functions in functional data models. Their Bayesian variants have received limited attention in large data applications, primarily due to prohibitively slow…

Machine Learning · Statistics 2025-06-03 Rajarshi Guhaniyogi , Laura Baracaldo , Sudipto Banerjee

Bayesian methods have proved powerful in many applications for the inference of model parameters from data. These methods are based on Bayes' theorem, which itself is deceptively simple. However, in practice the computations required are…

Methodology · Statistics 2020-07-10 Michael A. Chappell , Mark W. Woolrich

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…

Computation · Statistics 2019-12-02 Darjus Hosszejni , Gregor Kastner