Adaptive proposal distribution for random walk Metropolis algorithm

“…Based on Metropolis algorithm, Hastings [38] developed Metropolis-Hastings(M-H) algorithm which is able to make use of any form of transition function, and meet the requirement of detailed balance. Aim at the selection of proposal function, Haario et al [39] developed an adaptive proposal distribution (AP) algorithm, AP is operated by a normal distribution of which the mean and variance are calculated by retained samples. Based on AP algorithm, Haario et al [40] developed an Adaptive Metropolis (AM) algorithm, with respect to AP, AM is superior in updating the mean and covariance of proposal distribution by using previous sampling information based on a regression formula.…”

Section: Uncertainty Analysis Of Groundwater Model Parametersmentioning

confidence: 99%

Review of the uncertainty analysis of groundwater numerical simulation

Zeng

2013

Chin. Sci. Bull.

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Groundwater system is a complex and open system, which is affected by natural conditions and human activities. Natural hydrological processes is conceptualized through relatively simple flow governing equations in groundwater models. Moreover, observation data is always limited in field hydrogeological conditions. Therefore, the predictive results of groundwater simulation often deviate from true values, which is attribute to the uncertainty of groundwater numerical simulation. According to the process of system simulation, the uncertainty sources of groundwater numerical simulation can be divided into model parameters, conceptual model and observation data uncertainties. In addition, the uncertainty stemmed from boundary conditions is sometimes refered as scenario uncertainty. In this paper, the origination and category of groundwater modeling uncertainty are analyzed. The recent progresses on the methods of groundwater modeling uncertainty analysis are reivewed. Furthermore, the researches on the comprehensive analysis of uncertainty sources, and the predictive uncertainty of model outputs are discussed. Finally, several prospects on the deveolpment of groundwater modeling uncetainty analysis are proposed.groundwater modeling, uncertainty analysis, model parameter, conceptual model, observation data Citation:

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“…The most common adaptive single chain methods are the adaptive proposal (AP) (Haario et al, 1999), adaptive Metropolis (AM) (Haario et al, 2001) and delayed rejection adaptive metropolis (DRAM) algorithm (Haario et al, 2006), respectively. These methods work with a single trajectory, and continuously adapt the covariance, S of a Gaussian proposal distribution, q t ðx tÀ1 ; ,Þ ¼ N d ðx tÀ1 ; s d SÞ using the accepted samples of the chain, S ¼ cov(x 0 ,…,x tÀ1 ) þ 4I d .…”

Section: Single-chain Methodsmentioning

confidence: 99%

“…The SCEM-UA method can be made an exact sampler if the multi-chain adaptation of the covariance matrix is restricted to the burn-in period only. In a fashion similar to the AP (Haario et al, 1999) and AM algorithm, the method then derives an efficient Gaussian proposal distribution for the standard Metropolis algorithm. Nevertheless, I do not consider the SCEM-UA algorithm herein.…”

Section: Multi-chain Methods: De-mcmentioning

confidence: 99%