Sequentially adaptive Bayesian learning algorithms for inference and optimization

Geweke, John; Durham, Garland

doi:10.1016/j.jeconom.2018.11.002

Cited by 9 publications

(7 citation statements)

References 31 publications

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“…This section provides a brief summary of the method and discusses features that are most pertinent in its application to ARFIMA posterior distributions in this article. For full details see Durham and Geweke (), Geweke () and especially Geweke and Durham ()…”

Section: The Sabl Algorithm For Bayesian Inferencementioning

confidence: 99%

“…It also provides two statistics related to the accuracy of the SABL approximation of the posterior mean: the NSE of the first moment approximation; and the relative numerical efficiency (RNE) of this approximation, which is the ratio of the NSE in a hypothetical random sample from the posterior distribution to the one achieved by SABL. Geweke and Durham () provide more detail on the construction and interpretation of NSE and RNE. For our purposes it is sufficient to note that posterior mean approximations are good to about 3 significant figures.…”

Section: Applicationsmentioning

confidence: 99%

“…All of the other bivariate posterior distributions are non‐Gaussian, due mostly to the relevance of the stationarity condition d < 1/2 and invertibility condition | θ 1 | < 1 in this application. This can be made explicit by overplotting the bivariate ML confidence regions, as in Geweke and Durham (). That has not been done here to maintain the legibility of Figure .…”

Section: Applicationsmentioning

confidence: 99%

“…This article uses sequentially adaptive Bayesian learning (SABL), a generic sequential Monte Carlo method developed recently in Durham and Geweke () and Geweke and Durham (). In most cases, including ARFIMA models, it entails no application‐specific tuning, making it available to applied statisticians who are not specialists in Bayesian posterior sampling methods.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Inference for ARFIMA Models

Durham

Geweke

Porter‐Hudak

et al. 2019

Journal Time Series Analysis

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This article develops practical methods for Bayesian inference in the autoregressive fractionally integrated moving average (ARFIMA) model using the exact likelihood function, any proper prior distribution, and time series that may have thousands of observations. These methods utilize sequentially adaptive Bayesian learning, a sequential Monte Carlo algorithm that can exploit massively parallel desktop computing with graphics processing units (GPUs). The article identifies and solves several problems in the computation of the likelihood function that apparently have not been addressed in the literature. Four applications illustrate the utility of the approach. The most ambitious is an ARFIMA(2,d,2) model for the Campito tree ring time series (length 5405), for which the methods developed in the article provide an essentially uncorrelated sample of size 16,384 from the exact posterior distribution in under four hours. Less ambitious applications take as little as 4 minutes without exploiting GPUs.

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Section: The Sabl Algorithm For Bayesian Inferencementioning

confidence: 99%

Section: Applicationsmentioning

confidence: 99%

Section: Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bayesian Inference for ARFIMA Models

Durham

Geweke

Porter‐Hudak

et al. 2019

Journal Time Series Analysis

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“…The Bayesian scientific approach is widely used to create effective statistical estimates in various fields of activity [1][2][3][4][5][6][7][8][9][10][11][12]. Radio engineering, classification theory, machine learning, the creation of self-learning and self-tuning systems are just some of the areas where the Bayesian approach is effectively used.…”

Section: Introductionmentioning

confidence: 99%

Method for constructing estimates of accuracy of measuring equipment based on Bayesian scientific approach

Khayrullin

2019

E3S Web Conf.

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Before putting new unique samples of technical systems into commercial operation, as well as before introducing new technologies into production, as a rule, all kinds of tests are carried out. Small and very small volume of statistical data during testing is a characteristic feature of unique and small-scale products and technical systems. Therefore, the problem of constructing effective statistical estimates with a limited amount of statistical information is an important practical problem. The article proposes the development of the Bayesian approach to the construction of point and interval estimates of the parameters of the known distribution laws. The joint use of a priori and posterior information in the processing of statistical data of a limited volume can significantly increase the reliability of the result. As an example, we consider two most typical distribution laws that arise when testing new unique samples of measuring devices and equipment: normal distribution with an unknown average value and a known dispersion, as well as with an unknown average value and an unknown dispersion. It is shown that for these cases, the parameters of the distribution laws themselves are random variables and obey the normal law and gamma normal law. Recalculation formulas are obtained to refine the parameters of these laws, taking into account a posteriori information. If these formulas are applied several times successively, the process of self-learning of the system or self-tuning of the system occurs. Thus, the proposed scientific approach can find application in the development of intelligent self-learning and self-turning systems.

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Sequential Bayesian bandwidth selection for multivariate kernel regression with applications

Zhang

2022

Economic Modelling

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Sequentially adaptive Bayesian learning algorithms for inference and optimization

Cited by 9 publications

References 31 publications

Bayesian Inference for ARFIMA Models

Bayesian Inference for ARFIMA Models

Method for constructing estimates of accuracy of measuring equipment based on Bayesian scientific approach

Sequential Bayesian bandwidth selection for multivariate kernel regression with applications

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