A general and flexible class of latent Gaussian models is proposed in this paper. The latent Gaussian model is adapted to the generalized additive model for location, scale and shape (GAMLSS), that is, the data density function of each data point can depend on more than a single linear predictor of the latent parameters. We refer to this framework as extended latent Gaussian models. The most commonly applied latent Gaussian models (LGMs) are such that a linear predictor is proposed only for the location parameter. Extended LGMs allow proposing linear predictors also for the scale parameter and potentially other parameters. We propose a novel computationally efficient Markov chain Monte Carlo sampling scheme for the extended LGMs which we refer to as the LGM split sampler. It is a two block Gibbs sampling scheme designed to exploit the model structure of the extended LGMs. An extended LGM is constructed for a simulated dataset and the LGM split sampler is implemented for posterior simulations. The results demonstrate the flexibility of the extended LGM framework and the efficiency of the LGM split sampler.
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.
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. A novel extension of the power-law rating curve, referred to as the generalized power-law rating curve, is proposed. 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 powerlaw 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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.