scholarly journals Bayesian Estimation of Adsorption and Desorption Parameters for Pore Scale Transport

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1974
Author(s):  
Vasiliy V. Grigoriev ◽  
Petr N. Vabishchevich
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Inverse Problems ◽  
Bayesian Framework ◽  
Pore Scale ◽  
Identification Procedure ◽  
Adsorption And Desorption ◽  
Credible Intervals ◽  
The Impact

Stochastic parameter estimation and inversion have become increasingly popular in recent years. Nowadays, it is computationally reasonable and regular to solve complex inverse problems within the Bayesian framework. Applications of Bayesian inferences for inverse problems require investigation of the posterior distribution, which usually has a complex landscape and is highly dimensional. In these cases, Markov chain Monte Carlo methods (MCMC) are often used. This paper discusses a Bayesian approach for identifying adsorption and desorption rates in combination with a pore-scale reactive flow. Markov chain Monte Carlo sampling is used to estimate adsorption and desorption rates. The reactive transport in porous media is governed by incompressible Stokes equations, coupled with convection–diffusion equation for species’ transport. Adsorption and desorption are accounted via Robin boundary conditions. The Henry isotherm is considered for describing the reaction terms. The measured concentration at the outlet boundary is provided as additional information for the identification procedure. Metropolis–Hastings and Adaptive Metropolis algorithms are implemented. Credible intervals have been plotted from sampled posterior distributions for both algorithms. The impact of the noise in the measurements and influence of several measurements for Bayesian identification procedure is studied. Sample analysis using the autocorrelation function and acceptance rate is performed to estimate mixing of the Markov chain. As result, we conclude that MCMC sampling algorithm within the Bayesian framework is good enough to determine an admissible set of parameters via credible intervals.

scholarly journals Bayesian solution for nonlinear and non-Gaussian inverse problems by Markov chain Monte Carlo method

2001 ◽  
Vol 106 (D13) ◽  
pp. 14377-14390 ◽  
Author(s):  
Johanna Tamminen ◽  
Erkki Kyrölä
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Method ◽  
Inverse Problems ◽  
Non Gaussian

A review of Markov Chain Monte Carlo and information theory tools for inverse problems in subsurface flow

2011 ◽  
Vol 16 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Ángel Yustres ◽  
Laura Asensio ◽  
Juan Alonso ◽  
Vicente Navarro
Keyword(s):  
Information Theory ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Inverse Problems ◽  
Subsurface Flow

scholarly journals Accessing the syndemic of COVID-19 and malaria intervention in Africa

2020 ◽  
Author(s):  
Benyun Shi ◽  
Jinxin Zheng ◽  
Shang Xia ◽  
Shan Lin ◽  
Xinyi Wang ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Malaria Transmission ◽  
Vectorial Capacity ◽  
Insecticide Treated Nets ◽  
Transmission Potential ◽  
The Impact ◽  
Pharmaceutical Interventions ◽  
Epidemiological Parameters

Abstract Background: The pandemic of the coronavirus disease 2019 (COVID-19) has caused substantial disruptions to health services in the low and middle-income countries with a high burden of other diseases, such as malaria in sub-Saharan Africa. The aim of this study is to assess the impact of COVID-19 pandemic on malaria transmission potential in malaria-endemic countries in Africa. Methods: We present a data-driven method to quantify the extent to which the COVID-19 pandemic, as well as various non-pharmaceutical interventions (NPIs), could lead to the change of malaria transmission potential in 2020. First, we adopt a particle Markov Chain Monte Carlo method to estimate epidemiological parameters in each country by fitting the time series of the cumulative number of reported COVID-19 cases. Then, we simulate the epidemic dynamics of COVID-19 under two groups of NPIs: (i) contact restriction and social distancing, and (ii) early identification and isolation of cases. Based on the simulated epidemic curves, we quantify the impact of COVID-19 epidemic and NPIs on the distribution of insecticide-treated nets (ITNs). Finally, by treating the total number of ITNs available in each country in 2020, we evaluate the negative effects of COVID-19 pandemic on malaria transmission potential based on the notion of vectorial capacity. Results: In this paper, we conduct case studies in four malaria-endemic countries, Ethiopia, Nigeria, Tanzania, and Zambia, in Africa. The epidemiological parameters (i.e., the basic reproduction number R_0 and the duration of infection D_I) of COVID-19 in each country are estimated as follows: Ethiopia (R_0=1.57, D_I=5.32), Nigeria (R_0=2.18, D_I=6.58), Tanzania (R_0=2.47, D_I=6.01), and Zambia (R_0=2.12, D_I=6.96). Based on the estimated epidemiological parameters, the epidemic curves simulated under various NPIs indicated that the earlier the interventions are implemented, the better the epidemic is controlled. Moreover, the effect of combined NPIs is better than contact restriction and social distancing only. By treating the total number of ITNs available in each country in 2020 as a baseline, our results show that even with stringent NPIs, malaria transmission potential will remain higher than expected in the second half of 2020. Conclusions: By quantifying the impact of various NPI response to the COVID-19 pandemic on malaria transmission potential, this study provides a way to jointly address the syndemic between COVID-19 and malaria in malaria-endemic countries in Africa. The results suggest that the early intervention of COVID-19 can effectively reduce the scale of the epidemic and mitigate its impact on malaria transmission potential. Keywords : COVID-19 pandemic; Non-pharmaceutical interventions; Particle Markov chain Monte Carlo; Insecticide-treated nets; Vectorial capacity; Malaria transmission potential

scholarly journals Seemingly unrelated regression with measurement error: estimation via Markov Chain Monte Carlo and mean field variational Bayes approximation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Georges Bresson ◽  
Anoop Chaturvedi ◽  
Mohammad Arshad Rahman ◽  
Shalabh
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Measurement Error ◽  
Mean Field ◽  
Variational Bayes ◽  
Seemingly Unrelated Regression ◽  
Estimation Methods ◽  
Unrelated Regression ◽  
The Impact

Abstract Linear regression with measurement error in the covariates is a heavily studied topic, however, the statistics/econometrics literature is almost silent to estimating a multi-equation model with measurement error. This paper considers a seemingly unrelated regression model with measurement error in the covariates and introduces two novel estimation methods: a pure Bayesian algorithm (based on Markov chain Monte Carlo techniques) and its mean field variational Bayes (MFVB) approximation. The MFVB method has the added advantage of being computationally fast and can handle big data. An issue pertinent to measurement error models is parameter identification, and this is resolved by employing a prior distribution on the measurement error variance. The methods are shown to perform well in multiple simulation studies, where we analyze the impact on posterior estimates for different values of reliability ratio or variance of the true unobserved quantity used in the data generating process. The paper further implements the proposed algorithms in an application drawn from the health literature and shows that modeling measurement error in the data can improve model fitting.

scholarly journals Bayesian molecular dating as a “doubly intractable” problem

2017 ◽  
Author(s):  
Stéphane Guindon
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Inference ◽  
Molecular Dating ◽  
Death Process ◽  
Divergence Times ◽  
Calibration Data ◽  
Fossil Data ◽  
The Impact

1AbstractThis study focuses on a conceptual issue with Bayesian inference of divergence times using Markov chain Monte Carlo. The influence of fossil data on the probabilistic distribution of trees is the crux of the matter considered here. More specifically, among all the phylogenies that a tree model (e.g., the birth-death process) generates, only a fraction of them “agree” with the fossil data at hands. Bayesian inference of divergence times using Markov Chain Monte Carlo requires taking this fraction into account. Yet, doing so is challenging and most Bayesian samplers have simply overlooked this hurdle so far, thereby providing approximate estimates of divergence times and tree process parameters. A generic solution to this issue is presented here. This solution relies on an original technique, the so-called exchange algorithm, dedicated to drawing samples from “doubly intractable” distributions. A small example illustrates the problem of interest and the impact of the approximation aforementioned on tree parameter estimates. The analysis of land plant sequences and multiple fossils further illustrates the importance of proper mathematical handling of calibration data in order to derive accurate estimates of node age.

scholarly journals A Bayesian space–time model for clustering areal units based on their disease trends

Biostatistics ◽  
2018 ◽  
Vol 20 (4) ◽  
pp. 681-697 ◽  
Author(s):  
Gary Napier ◽  
Duncan Lee ◽  
Chris Robertson ◽  
Andrew Lawson
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Disease Risk ◽  
Population Level ◽  
Research Literature ◽  
Time Model ◽  
Bayesian Hierarchical ◽  
Increased Risk ◽  
The Impact

Summary Population-level disease risk across a set of non-overlapping areal units varies in space and time, and a large research literature has developed methodology for identifying clusters of areal units exhibiting elevated risks. However, almost no research has extended the clustering paradigm to identify groups of areal units exhibiting similar temporal disease trends. We present a novel Bayesian hierarchical mixture model for achieving this goal, with inference based on a Metropolis-coupled Markov chain Monte Carlo ((MC)$^3$) algorithm. The effectiveness of the (MC)$^3$ algorithm compared to a standard Markov chain Monte Carlo implementation is demonstrated in a simulation study, and the methodology is motivated by two important case studies in the United Kingdom. The first concerns the impact on measles susceptibility of the discredited paper linking the measles, mumps, and rubella vaccination to an increased risk of Autism and investigates whether all areas in the Scotland were equally affected. The second concerns respiratory hospitalizations and investigates over a 10 year period which parts of Glasgow have shown increased, decreased, and no change in risk.

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