Statistical Inference and Prediction in Climatology: A Bayesian Approach

Epstein, Edward S.

doi:10.1007/978-1-935704-27-0

Cited by 51 publications

(56 citation statements)

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“…Assuming reasonable prior distributions for these parameters, the posterior is determined through the application of Bayes' rule: 44,45 PðXjT i Þ / LðT i jXÞPðXÞ;…”

Section: B Bayesian Inferencementioning

confidence: 99%

Development of a reduced model of formation reactions in Zr-Al nanolaminates

Vohra

Winokur

Overdeep

et al. 2014

Journal of Applied Physics

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A computational model of anaerobic reactions in metallic multilayered systems with an equimolar composition of zirconium and aluminum is developed. The reduced reaction formalism of M. Salloum and O. M. Knio, Combust. Flame 157(2): 288–295 (2010) is adopted. Attention is focused on quantifying intermixing rates based on experimental measurements of uniform ignition as well as measurements of self-propagating front velocities. Estimates of atomic diffusivity are first obtained based on a regression analysis. A more elaborate Bayesian inference formalism is then applied in order to assess the impact of uncertainties in the measurements, potential discrepancies between predictions and observations, as well as the sensitivity of predictions to inferred parameters. Intermixing rates are correlated in terms of a composite Arrhenius law, which exhibits a discontinuity around the Al melting temperature. Analysis of the predictions indicates that Arrhenius parameters inferred for the low-temperature branch lie within a tight range, whereas the parameters of the high-temperature branch are characterized by higher uncertainty. The latter is affected by scatter in the experimental measurements, and the limited range of bilayers where observations are available. For both branches, the predictions exhibit higher sensitivity to the activation energy than the pre-exponent, whose posteriors are highly correlated.

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“…Assuming reasonable prior distributions for these parameters, the posterior is determined through the application of Bayes' rule: 44,45 PðXjT i Þ / LðT i jXÞPðXÞ;…”

Section: B Bayesian Inferencementioning

confidence: 99%

Development of a reduced model of formation reactions in Zr-Al nanolaminates

Vohra

Winokur

Overdeep

et al. 2014

Journal of Applied Physics

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“…Other examples associated with data assimilation are discussed by Lorenc (1986) and Evensen and Van Leeuwen (2000). A general review of Bayesian analysis intended for geophysical audiences is given by Wikle and Berliner (2006); see also Epstein (1985) and Tarantola (1987). Nevertheless, the full power of the methodology has only recently been making progress in geophysics (e.g.…”

Section: Hierarchical Bayesian Analysismentioning

confidence: 99%

Modeling dynamic controls on ice streams: a Bayesian statistical approach

Berliner¹,

Jezek

Cressie³

et al. 2008

J. Glaciol.

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ABSTRACT. Our main goal is to exemplify the study of ice-stream dynamics via Bayesian statistical analysis incorporating physical, though imperfectly known, models using data that are both incomplete and noisy. The physical-statistical models we propose account for these uncertainties in a coherent, hierarchical manner. The initial modeling assumption estimates basal shear stress as equal to driving stress, but subsequently includes a random corrector process to account for model error. The resulting stochastic equation is incorporated into a simple model for surface velocities. Use of Bayes' theorem allows us to make inferences on all unknowns given basal elevation, surface elevation and surface velocity. The result is a posterior distribution of possible values that can be summarized in a number of ways. For example, the posterior mean of the stress field indicates average behavior at any location in the field, and the posterior standard deviations describe associated uncertainties. We analyze data from the 'Northeast Greenland Ice Stream' and illustrate how scientific conclusions may be drawn from our Bayesian analysis.

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“…First, the basic steps in the Bayesian statistical paradigm are briefly reviewed (for an introduction to the use of Bayesian statistics in climatology, see Epstein 1985): (1) Elicit the joint 'prior probability' distribution for the parameters of the statistical model under consideration (the prior is formulated before 'seeing' the data, and could be 'diffuse' or non-informative). (2) For the statistical model, obtain an expression for the joint conditional distribution of the observations as a function of the parameters (termed the 'likelihood function' in classical statistics).…”

Section: Bayesian Statistical Paradigmmentioning

confidence: 99%

Techniques for estimating uncertainty in climate change scenarios and impact studies

2002

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Methodology for quantifying uncertainty in global climate change studies is reviewed. The focus is on recent developments in statistics, such as hierarchical modeling and Markov chain Monte Carlo simulation techniques, that could enable more full-fledged uncertainty analyses to be performed as part of integrated assessments of climate change and its impacts. First an overview of uncertainty analysis, including its sources and how it propagates, is provided. Presently employed techniques in climate change assessments, such as sensitivity, scenario, and Monte Carlo simulation analyses, are then surveyed. Next alternative approaches, based on more formal statistical theory (especially the Bayesian statistical paradigm), are described. Finally, some tentative recommendations on strategies for achieving the goal of more reliably quantifying uncertainty in global climate change are made.

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Statistical Inference and Prediction in Climatology: A Bayesian Approach

Cited by 51 publications

References 0 publications

Development of a reduced model of formation reactions in Zr-Al nanolaminates

Development of a reduced model of formation reactions in Zr-Al nanolaminates

Modeling dynamic controls on ice streams: a Bayesian statistical approach

Techniques for estimating uncertainty in climate change scenarios and impact studies

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