English
Related papers

Related papers: Bayesian Analysis of AR(1) Model

200 papers

We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit…

Statistics Theory · Mathematics 2009-09-29 Aad van der Vaart , Harry van Zanten

We introduce and explore a new class of stationary time series models for variance matrices based on a constructive definition exploiting inverse Wishart distribution theory. The main class of models explored is a novel class of stationary,…

Methodology · Statistics 2011-07-27 Emily B. Fox , Mike West

The choice of the prior distribution is a key aspect of Bayesian analysis. For the spatial regression setting a subjective prior choice for the parameters may not be trivial, from this perspective, using the objective Bayesian analysis…

Statistics Theory · Mathematics 2020-04-10 Jose A. Ordoñez , Marcos O. Prates , Larissa A. Matos , Victor H. Lachos

Conjugate priors allow for fast inference in large dimensional vector autoregressive (VAR) models but, at the same time, introduce the restriction that each equation features the same set of explanatory variables. This paper proposes a…

Econometrics · Economics 2020-08-27 Niko Hauzenberger , Florian Huber , Luca Onorante

Empirical Bayes methods have been around for a long time and have a wide range of applications. These methods provide a way in which historical data can be aggregated to provide estimates of the posterior mean. This thesis revisits some of…

Methodology · Statistics 2021-08-17 Xiuwen Duan

An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density \gamma,…

Statistics Theory · Mathematics 2007-06-13 Iain M. Johnstone , Bernard W. Silverman

In Bayesian statistics, horseshoe prior has attracted increasing attention as an approach to the sparse estimation. The estimation accuracy of compressed sensing with the horseshoe prior is evaluated by statistical mechanical method. It is…

Disordered Systems and Neural Networks · Physics 2023-03-29 Yasushi Nagano , Koji Hukushima

Sparse modeling for signal processing and machine learning has been at the focus of scientific research for over two decades. Among others, supervised sparsity-aware learning comprises two major paths paved by: a) discriminative methods and…

Machine Learning · Statistics 2022-11-23 Lei Cheng , Feng Yin , Sergios Theodoridis , Sotirios Chatzis , Tsung-Hui Chang

We investigate the frequentist properties of Bayesian procedures for estimation based on the horseshoe prior in the sparse multivariate normal means model. Previous theoretical results assumed that the sparsity level, that is, the number of…

Statistics Theory · Mathematics 2017-02-14 Stéphanie van der Pas , Botond Szabó , Aad van der Vaart

A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…

Methodology · Statistics 2015-09-29 Tiep Mai , Simon Wilson

Approximate Bayesian computation (ABC) methods, which are applicable when the likelihood is difficult or impossible to calculate, are an active topic of current research. Most current ABC algorithms directly approximate the posterior…

Computation · Statistics 2012-12-10 Y. Fan , D. J. Nott , S. A. Sisson

A general asymptotic theory is given for the panel data AR(1) model with time series independent in different cross sections. The theory covers the cases of stationary process, nearly non-stationary process, unit root process, mildly…

Applications · Statistics 2016-11-15 Jianfei Shen , Tianxiao Pang

In this paper, we consider objective Bayesian inference of the generalized exponential distribution using the independence Jeffreys prior and validate the propriety of the posterior distribution under a family of structured priors. We…

Methodology · Statistics 2023-09-26 Aojun Li , Keying Ye , Min Wang

We introduce a simulation-based, amortised Bayesian inference scheme to infer the parameters of random walks. Our approach learns the posterior distribution of the walks' parameters with a likelihood-free method. In the first step a graph…

Machine Learning · Computer Science 2022-12-07 Hippolyte Verdier , François Laurent , Alhassan Cassé , Christian Vestergaard , Jean-Baptiste Masson

We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in…

Machine Learning · Computer Science 2023-05-16 Rafael Orozco , Ali Siahkoohi , Mathias Louboutin , Felix J. Herrmann

We introduce a new method for learning Bayesian neural networks, treating them as a stack of multivariate Bayesian linear regression models. The main idea is to infer the layerwise posterior exactly if we know the target outputs of each…

Machine Learning · Computer Science 2024-11-20 Richard Kurle , Alexej Klushyn , Ralf Herbrich

Bayesian models provide recursive inference naturally because they can formally reconcile new data and existing scientific information. However, popular use of Bayesian methods often avoids priors that are based on exact posterior…

Methodology · Statistics 2019-04-29 Mevin B. Hooten , Devin S. Johnson , Brian M. Brost

Prior distributions elicited for modelling the natural fluctuations or the uncertainty on parameters of Bayesian fishery population models, can be chosen among a vast range of statistical laws. Since the statistical framework is defined by…

Statistics Theory · Mathematics 2010-10-12 Nicolas Bousquet

For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…

Applications · Statistics 2022-08-08 Taylor R. Brown

Standard Bayesian analyses can be difficult to perform when the full likelihood, and consequently the full posterior distribution, is too complex and difficult to specify or if robustness with respect to data or to model misspecifications…

Methodology · Statistics 2019-01-08 Federica Giummolè , Valentina Mameli , Erlis Ruli , Laura Ventura
‹ Prev 1 4 5 6 7 8 10 Next ›