scholarly journals Markov Chain Investigation of Discretization Schemes and Computational Cost Reduction in Modeling Photon Multiple Scattering

2018 ◽  
Vol 8 (11) ◽  
pp. 2288 ◽  
Author(s):  
Shangze Yang ◽  
Di Xiao ◽  
Xuesong Li ◽  
Zhen Ma
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Multiple Scattering ◽  
Cost Reduction ◽  
Computational Cost ◽  
Detailed Comparison ◽  
Iterative Approach ◽  
Computational Costs ◽  
Markov Chain Method ◽  
Discretization Schemes

Establishing fast and reversible photon multiple scattering algorithms remains a modeling challenge for optical diagnostics and noise reduction purposes, especially when the scattering happens within the intermediate scattering regime. Previous work has proposed and verified a Markov chain approach for modeling photon multiple scattering phenomena through turbid slabs. The fidelity of the Markov chain method has been verified through detailed comparison with Monte Carlo models. However, further improvement to the Markov chain method is still required to improve its performance in studying multiple scattering. The present research discussed the efficacy of non-uniform discretization schemes and analyzed errors induced by different schemes. The current work also proposed an iterative approach as an alternative to directly carrying out matrix inversion manipulations, which would significantly reduce the computational costs. The benefits of utilizing non-uniform discretization schemes and the iterative approach were confirmed and verified by comparing the results to a Monte Carlo simulation.

Sparse Code Multiple Access Decoding Based on a Monte Carlo Markov Chain Method

2016 ◽  
Vol 23 (5) ◽  
pp. 639-643 ◽  
Author(s):  
Jienan Chen ◽  
Zhenbing Zhang ◽  
Shuaining He ◽  
Jianhao Hu ◽  
Gerald E. Sobelman
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Multiple Access ◽  
Monte Carlo Markov Chain ◽  
Sparse Code ◽  
Markov Chain Method

A Bayesian Monte Carlo Markov Chain Method for Loss Models and Risk Measure Assessments

2009 ◽  
Vol 12 (03) ◽  
pp. 529-543
Author(s):  
Ling Hu ◽  
Yating Yang
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Normal Distribution ◽  
Risk Measure ◽  
Markov Chain Method ◽  
Flood Loss ◽  
Bayesian Monte Carlo ◽  
Loss Models ◽  
Log Normal ◽  
Log Normal Distribution

Natural disasters are also known as catastrophes with low frequency but high damages. Typhoons and floods are the major catastrophes which lead to gargantuan losses in Asia. Once a disaster occurs, a broad region will be affected and this will result in huge social loss. If issuers or governments use the wrong loss models or risk measure indexes to price the related insurance products, they will get an inaccurate price and thus be insolvent to the claims. Previous researches often use a Log-Normal distribution to model a catastrophic loss. This is not appropriate since the characteristics of a loss distribution have some empirical facts, including the positive skewness and the heavy-tailed properties. Recently, some studies (McNeil and Frey, 2000; Rootzen and Tajvidi, 2000; Thuring et al., 2008) also point out that using Log-Normal distribution to model a characteristic loss is not suitable. Therefore, we build a typhoon and flood loss model with higher order moments and estimate the parameters through a Bayesian Monte Carlo Markov Chain method. According to the Kolmogorov-Smirnov test, we find that the Pareto distribution is more adaptive for modeling the loss of typhoon and flood. Further, we evaluate different kinds of risk measure indexes through simulating and numerical analysis. It gives the beacon to issuers or governments when they want to issue the insurance products about typhoon and flood loss.

scholarly journals Basis-constrained Bayesian Markov-chain Monte Carlo difference inversion for geoelectrical monitoring of hydrogeologic processes

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. A37-A42 ◽  
Author(s):  
Erasmus Kofi Oware ◽  
James Irving ◽  
Thomas Hermans
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Computational Cost ◽  
Model Space ◽  
Time Lapse ◽  
Tracer Experiment ◽  
Hydrologic Process ◽  
Spatially Distributed ◽  
Geophysical Imaging

Bayesian Markov-chain Monte Carlo (McMC) techniques are increasingly being used in geophysical estimation of hydrogeologic processes due to their ability to produce multiple estimates that enable comprehensive assessment of uncertainty. Standard McMC sampling methods can, however, become computationally intractable for spatially distributed, high-dimensional problems. We have developed a novel basis-constrained Bayesian McMC difference inversion framework for time-lapse geophysical imaging. The strategy parameterizes the Bayesian inversion model space in terms of sparse, hydrologic-process-tuned bases, leading to dimensionality reduction while accounting for the physics of the target hydrologic process. We evaluate the algorithm on cross-borehole electrical resistivity tomography (ERT) field data acquired during a heat-tracer experiment. We validate the ERT-estimated temperatures with direct temperature measurements at two locations on the ERT plane. We also perform the inversions using the conventional smoothness-constrained inversion (SCI). Our approach estimates the heat plumes without excessive smoothing in contrast with the SCI thermograms. We capture most of the validation temperatures within the 90% confidence interval of the mean. Accounting for the physics of the target process allows the detection of small temperature changes that are undetectable by the SCI. Performing the inversion in the reduced-dimensional model space results in significant gains in computational cost.

scholarly journals Numerical Study of Turbid Slab Optical Properties Reconstruction from Multiple Scattering Signals Using Time-Based Markov Chain Model

2021 ◽  
Vol 11 (2) ◽  
pp. 588
Author(s):  
Hujie Pan ◽  
Qinglin Xu ◽  
Xuesong Li ◽  
Shangning Wang ◽  
Min Xu
Keyword(s):  
Optical Properties ◽  
Markov Chain ◽  
Multiple Scattering ◽  
Transition Matrix ◽  
Numerical Study ◽  
Markov Chain Model ◽  
Chain Model ◽  
Layer By Layer ◽  
Reconstruction Process ◽  
Computational Costs

The reconstruction of optical properties for opaque mediums is highly desired for medical, atmosphere and aerosol applications. However, the modeling and reconstruction process is highly related with multiple scattering phenomena, which elevates both the complexity and computational costs for such efforts. This work introduces a time-based Markov chain method, which uses a sparse transition matrix to represent the likelihood for a photon to transit in the turbid media. The accuracy of the time-based Markov chain model was verified against the forwarding calculations of the scattering-based Markov chain model and Monte Carlo simulations. Then, reconstruction was performed with backscattered photon angular distributions. Based on the characteristics of the sparse transition matrix, the optical properties (droplet diameters) could be obtained layer by layer with transmitted photon distributions at different time durations. It is shown that the time-based Markov chain model can reconstruct the optical properties of a turbid slab with satisfactory accuracy and lower computational costs.

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