Bayesian prediction of monthly precipitation on a fine grid using covariates based on a regional meteorological model

Sigurðarson, Atli Norðmann; Hrafnkelsson, Birgir

doi:10.1002/env.2372

Cited by 11 publications

(6 citation statements)

References 12 publications

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“…The variance of Model 0 varies with water elevation. The smoothly varying variance function in Model 0 and Model 1 has not been introduced for rating curve models before, however, examples of smoothly varying variance with respect to some variable of interest, for example, geographical coordinates, can be found in Sigurdarson and Hrafnkelsson (2016); Yarger et al (2020).…”

Section: F I G U R Ementioning

confidence: 99%

Generalization of the power‐law rating curve using hydrodynamic theory and Bayesian hierarchical modeling

Hrafnkelsson

Sigurdarson²,

Rögnvaldsson

et al. 2021

Environmetrics

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The power-law rating curve has been used extensively in hydraulic practice and hydrology. It is given by Q(h) = a(h − c) b , where Q is discharge, h is water elevation, a, b, and c are unknown parameters. We propose a novel extension of the power-law rating curve, referred to as the generalized power-law rating curve. It is constructed by linking the physics of open channel flow to a model of the form h) . The function f (h) is referred to as the power-law exponent and it depends on the water elevation. The proposed model and the power-law model are fitted within the framework of Bayesian hierarchical models. By exploring the properties of the proposed rating curve and its power-law exponent, we find that cross-sectional shapes that are likely to be found in nature are such that the power-law exponent f (h) will usually be in the interval [1.0, 2.67].This fact is utilized for the construction of prior densities for the model parameters. An efficient Markov chain Monte Carlo sampling scheme, that utilizes the lognormal distributional assumption at the data level and Gaussian assumption at the latent level, is proposed for the two models. The two statistical models were applied to four datasets. In the case of three datasets the generalized power-law rating curve gave a better fit than the power-law rating curve while in the fourth case the two models fitted equally well and the generalized power-law rating curve mimicked the power-law rating curve. We developed an R package, bdrc, for fitting the power-law and generalized power-law rating curve models. It is available on CRAN.

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Section: F I G U R Ementioning

confidence: 99%

Generalization of the power‐law rating curve using hydrodynamic theory and Bayesian hierarchical modeling

Hrafnkelsson

Sigurdarson²,

Rögnvaldsson

et al. 2021

Environmetrics

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“…In this paper we focus on latent Gaussian models (LGMs), which form a general and very flexible class of models that has proven to be useful in a wide range of concrete applications (see, e.g., Gelfand et al, 2007;Cooley et al, 2007;Rue et al, 2009;Margeirsson et al, 2010;Sigurdarson and Hrafnkelsson, 2016;Zinszer et al, 2017;Opitz et al, 2018;Lombardo et al, 2018Lombardo et al, , 2019. We here introduce Max-and-Smooth, a novel approximate Bayesian inference procedure for LGMs with independent data replicates that is both accurate and fast, providing significant speedups in high dimensions.…”

Section: Introductionmentioning

confidence: 99%

Max-and-Smooth: A Two-Step Approach for Approximate Bayesian Inference in Latent Gaussian Models

et al. 2021

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With modern high-dimensional data, complex statistical models are necessary, requiring computationally feasible inference schemes. We introduce Max-and-Smooth, an approximate Bayesian inference scheme for a flexible class of latent Gaussian models (LGMs) where one or more of the likelihood parameters are modeled by latent additive Gaussian processes. Our proposed inference scheme is a two-step approach. In the first step (Max), the likelihood function is approximated by a Gaussian density with mean and covariance equal to either (a) the maximum likelihood estimate and the inverse observed information, respectively, or (b) the mean and covariance of the normalized likelihood function. In the second step (Smooth), the latent parameters and hyperparameters are inferred and smoothed with the approximated likelihood function. The proposed method ensures that the uncertainty from the first step is correctly propagated to the second step. Because the prior density for the latent parameters is assumed to be Gaussian and the approximated likelihood function is Gaussian, the approximate posterior density of the latent parameters (conditional on the hyperparameters) is also Gaussian, thus facilitating efficient posterior inference in high dimensions. Furthermore, the approximate marginal posterior distribution of the hyperparameters is tractable, and as a result, the hyperparameters can be sampled independently of the latent parameters. We show that the computational cost of Max-and-Smooth is close to being insensitive to the number of independent data replicates, and that it scales well with increased dimension of the latent parameter vector provided that its Gaussian prior density is specified with a sparse precision matrix. In the case of a large number of independent data replicates, sparse precision matrices, and high-dimensional latent vectors, the speedup is substantial in comparison to an MCMC scheme that infers the posterior density from the exact likelihood function. The accuracy of the Gaussian approximation to the likelihood function increases with the number of data replicates per latent model parameter. The proposed inference scheme is demonstrated on one spatially referenced real dataset and on simulated data mimicking spatial, temporal, and spatio-temporal inference problems. Our results show that Max-and-Smooth is accurate and fast.

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“…Both numerical error and model uncertainty can be incorporated at the process level, while measurement errors can be modeled at the data level. This approach has been applied in a variety of scientific contexts, including the study of ozone concentrations (Berrocal et al, 2014), sediment loads at the Great Barrier Reef (Pagendam et al, 2014), precipitation in Iceland (Sigurdarson and Hrafnkelsson, 2016), Antarctic contributions to sea level rise (Zammit-Mangion et al, 2014), and tropical ocean surface winds (Wikle et al, 2001) (among many others). In Gopalan et al (2018), the motivating example for the work in this paper, a Bayesian hierarchical model for shallow glaciers based on the shallow ice approximation (SIA) PDE was developed and evaluated.…”

Section: Introductionmentioning

confidence: 99%

A Hierarchical Spatiotemporal Statistical Model Motivated by Glaciology

Gopalan

Hrafnkelsson

Wikle

et al. 2019

JABES

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In this paper, we extend and analyze a Bayesian hierarchical spatio-temporal model for physical systems. A novelty is to model the discrepancy between the output of a computer simulator for a physical process and the actual process values with a multivariate random walk. For computational efficiency, linear algebra for bandwidth limited matrices is utilized, and first-order emulator inference allows for the fast emulation of a numerical partial differential equation (PDE) solver. A test scenario from a physical system motivated by glaciology is used to examine the speed and accuracy of the computational methods used, in addition to the viability of modeling assumptions. We conclude by discussing how the model and associated methodology can be applied in other physical contexts besides glaciology.

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Bayesian prediction of monthly precipitation on a fine grid using covariates based on a regional meteorological model

Cited by 11 publications

References 12 publications

Generalization of the power‐law rating curve using hydrodynamic theory and Bayesian hierarchical modeling

Generalization of the power‐law rating curve using hydrodynamic theory and Bayesian hierarchical modeling

Max-and-Smooth: A Two-Step Approach for Approximate Bayesian Inference in Latent Gaussian Models

A Hierarchical Spatiotemporal Statistical Model Motivated by Glaciology

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