Weighted Monte Carlo estimators for angular distributions of the solar radiation reflected from a cloud layer

2016 ◽  
Vol 31 (4) ◽  
Author(s):  
Gennady A. Mikhailov ◽  
Sergey M. Prigarin ◽  
Sergey A. Rozhenko
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Solar Radiation ◽  
Model Problem ◽  
Cloud Layer ◽  
Angular Distributions ◽  
Spectral Maximum ◽  
Wide Range ◽  
Scattering Phase ◽  
Scattering Phase Function

AbstractThe paper is focused on development of weighted Monte Carlo methods allowing one to estimate simultaneously the characteristics of the radiation field reflected from the medium based on a single Markov chain and in a sufficiently wide range of wavelengths. Such Markov chain is constructed with the use of a special ‘artificial’ scattering phase function whose choice is approximately optimized according to the criterion of minimum of the spectral maximum of the variance of estimates. The efficiency of the considered weighted method is studied on a model problem related to scattering of solar radiation by a cloud layer. The weighted method developed in the present article is aimed to supercomputer simulation.

Monte Carlo Simulation of Radiative Heat Transfer in Coarse Fibrous Media

2003 ◽  
Vol 125 (4) ◽  
pp. 748-752 ◽  
Author(s):  
Eugen Nisipeanu ◽  
Peter D. Jones
Keyword(s):  
Monte Carlo ◽  
Radiative Heat ◽  
Orientation Angle ◽  
Index Of Refraction ◽  
Radiative Properties ◽  
Fibrous Media ◽  
Polar Orientation ◽  
Scattering Phase ◽  
Scattering Phase Function ◽  
Orientation Bias

Direct Geometric Monte Carlo modeling of a fibrous medium is undertaken. The medium is represented as a monodisperse array, with known solidity, of randomly oriented cylinders of known index of refraction. This technique has the advantage that further radiative properties of the medium (absorption coefficient, scattering albedo, scattering phase function) are not required, and the drawback that its’ Snell- and Fresnel-generated dynamics suggest a limitation to large, smooth fibers. It is found that radiative heat flux results are highly dependent on bias in the polar orientation angle (relative to the boundary planes) of the fibers. Randomly oriented fiber results compare well to both the large (specular radiosity method) and small (radiative transfer equation) limits, while the results of previous experiments lie within the range of simulation results generated using varying degrees of orientation bias.

scholarly journals Efficient stochastic optimisation by unadjusted Langevin Monte Carlo

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Valentin De Bortoli ◽  
Alain Durmus ◽  
Marcelo Pereyra ◽  
Ana F. Vidal
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Stochastic Approximation ◽  
Likelihood Estimation ◽  
Stochastic Optimisation ◽  
Monte Carlo Algorithms ◽  
Wide Range ◽  
Optimisation Methods ◽  
Langevin Monte Carlo

AbstractStochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric empirical Bayesian estimation. Combined with Markov chain Monte Carlo algorithms, these stochastic optimisation methods have been successfully applied to a wide range of problems in science and industry. However, this strategy scales poorly to large problems because of methodological and theoretical difficulties related to using high-dimensional Markov chain Monte Carlo algorithms within a stochastic approximation scheme. This paper proposes to address these difficulties by using unadjusted Langevin algorithms to construct the stochastic approximation. This leads to a highly efficient stochastic optimisation methodology with favourable convergence properties that can be quantified explicitly and easily checked. The proposed methodology is demonstrated with three experiments, including a challenging application to statistical audio analysis and a sparse Bayesian logistic regression with random effects problem.

A Combined P1 and Monte Carlo Model for Radiative Transfer in Multi-Dimensional Anisotropically Scattering Media

2010 ◽  
Author(s):  
Leonid Dombrovsky ◽  
Wojciech Lipin´ski
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Phase Function ◽  
Monte Carlo Model ◽  
Reference Method ◽  
Computational Time ◽  
Scattering Media ◽  
Combined Method ◽  
Scattering Phase ◽  
Scattering Phase Function

A combined two-step computational method incorporating (1) transport approximation of the scattering phase function, (2) P1 approximation and the finite element method for computing the radiation source function at the first step, and (3) the Monte Carlo method for computing radiative intensity at the second step, is developed. The accuracy of the combined method is examined for model problems involving two multi-dimensional configurations of an anisotropically scattering medium. A detailed analysis is performed for a medium with scattering phase function described by a family of the Henyey–Greenstein functions. The accuracy of the two-step method is assessed by comparing the distribution of the radiative flux leaving the medium to that obtained by a reference complete Monte Carlo method. This study confirms the main results of previous papers on the errors of the two-step solution method. The combined method leads to a significant reduction in computational time as compared to the reference method, by at least 1 order of magnitude. Finally, possible applications of the combined method are briefly discussed.

scholarly journals Automated Graduation using Bayesian Trans-dimensional Models

2011 ◽  
Vol 5 (2) ◽  
pp. 231-251 ◽  
Author(s):  
R.J. Verrall ◽  
S. Haberman
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Approach ◽  
Model Uncertainty ◽  
Weighted Average ◽  
New Method ◽  
Reversible Jump ◽  
Standard Methods ◽  
Wide Range

AbstractThis paper presents a new method of graduation which uses parametric formulae together with Bayesian reversible jump Markov chain Monte Carlo methods. The aim is to provide a method which can be applied to a wide range of data, and which does not require a lot of adjustment or modification. The method also does not require one particular parametric formula to be selected: instead, the graduated values are a weighted average of the values from a range of formulae. In this way, the new method can be seen as an automatic graduation method which we believe can be applied in many cases without any adjustments and provide satisfactory graduated values. An advantage of a Bayesian approach is that it allows for model uncertainty unlike standard methods of graduation.

scholarly journals Self-Adaptive Acceptance Rate-Driven Markov Chain Monte Carlo Method Applied to the Study of Magnetic Nanoparticles

Computation ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 124
Author(s):  
Juan Camilo Zapata ◽  
Johans Restrepo
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Magnetic Nanoparticles ◽  
Monte Carlo Method ◽  
Magnetic Moments ◽  
Acceptance Rate ◽  
Wide Range ◽  
Acceptance Rates ◽  
Self Adaptive

A standard canonical Markov Chain Monte Carlo method implemented with a single-macrospin movement Metropolis dynamics was conducted to study the hysteretic properties of an ensemble of independent and non-interacting magnetic nanoparticles with uniaxial magneto-crystalline anisotropy randomly distributed. In our model, the acceptance-rate algorithm allows accepting new updates at a constant rate by means of a self-adaptive mechanism of the amplitude of Néel rotation of magnetic moments. The influence of this proposal upon the magnetic properties of our system is explored by analyzing the behavior of the magnetization versus field isotherms for a wide range of acceptance rates. Our results allows reproduction of the occurrence of both blocked and superparamagnetic states for high and low acceptance-rate values respectively, from which a link with the measurement time is inferred. Finally, the interplay between acceptance rate with temperature in hysteresis curves and the time evolution of the saturation processes is also presented and discussed.

Diagnosis of blood cancer using Markov chain Monte Carlo trace model

2017 ◽  
Vol 10 (03) ◽  
pp. 1750034
Author(s):  
K. Vaikundamoorthy
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Maximum Probability ◽  
Monte Carlo Simulation Study ◽  
Node Number ◽  
Blood Cancer ◽  
Initial Stage ◽  
Wide Range ◽  
Trace Model

Maximum probability of existence of cancer in human bodies is normally diagnosed very late, so that it is highly cumbersome for physicians to cure. Reliability in predicting cancer at initial stage is always needed, so that curing and medical recovery is possible. In this paper, an investigation was made to diagnose the presence of blood cancer using Markov Chain Monte Carlo (MCMC) trace model, which is most efficient on a wide range of complex Bayesian statistical models. The analysis was carried out using version 18 of SPSS AMOS software. Totally, 19 components were considered from the blood samples of 750 patients. Various factors such as class, age, lymphatics, block of affarc, block of lymph c, block of lymph s, bypass, extravasate, regeneration of, early uptake in, lym nodes dimin, lym nodes enlar, change in lym, defect in node, changes in node, changes in strue special forms, dislocation, exclusion of node, number of nodes in blood cancer are analyzed. The maximum likelihood estimators of the parameters were derived and assessed their performance through a Monte Carlo simulation study. The convergence in prior distribution and posterior distribution takes irregular position in the diagrams and thus blood cancer is diagnosed through this model.

scholarly journals Semi-Analytic Monte Carlo Model for Oceanographic Lidar Systems: Lookup Table Method Used for Randomly Choosing Scattering Angles

2018 ◽  
Vol 9 (1) ◽  
pp. 48 ◽  
Author(s):  
Peng Chen ◽  
Delu Pan ◽  
Zhihua Mao ◽  
Hang Liu
Keyword(s):  
Monte Carlo ◽  
Radiative Transfer ◽  
Phase Function ◽  
Geometric Model ◽  
Airborne Lidar ◽  
Cumulative Distribution ◽  
Lookup Table ◽  
Transfer Model ◽  
Scattering Phase ◽  
Scattering Phase Function

Monte Carlo (MC) is a significant technique for finding the radiative transfer equation (RTE) solution. Nowadays, the Henyey-Greenstein (HG) scattering phase function (spf) has been widely used in most studies during the core procedure of randomly choosing scattering angles in oceanographic lidar MC simulations. However, the HG phase function does not work well at small or large scattering angles. Other spfs work well, e.g., Fournier-Forand phase function (FF); however, solving the cumulative distribution function (cdf) of the scattering phase function (even if possible) would result in a complicated formula. To avoid the above-mentioned problems, we present a semi-analytic MC radiative transfer model in this paper, which uses the cdf equation to build up a lookup table (LUT) of ψ vs. P Ψ ( ψ ) to determine scattering angles for various spfs (e.g., FF, Petzold measured particle phase function, and so on). Moreover, a lidar geometric model for analytically estimating the probability of photon scatter back to a remote receiver was developed; in particular, inhomogeneous layers are divided into voxels with different optical properties; therefore, it is useful for inhomogeneous water. First, the simulations between the inverse function method for HG cdf and the LUT method for FF cdf were compared. Then, multiple scattering and wind-driven sea surface condition effects were studied. Finally, we compared our simulation results with measurements of airborne lidar. The mean relative errors between simulation and measurements in inhomogeneous water are within 14% for the LUT method and within 22% for the inverse cdf (ICDF) method. The results suggest feasibility and effectiveness of our simulation model.

scholarly journals Efficient Markov Chain Monte Carlo Methods for Decoding Neural Spike Trains

2011 ◽  
Vol 23 (1) ◽  
pp. 46-96 ◽  
Author(s):  
Yashar Ahmadian ◽  
Jonathan W. Pillow ◽  
Liam Paninski
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Mutual Information ◽  
Posterior Distribution ◽  
Spike Trains ◽  
Mcmc Methods ◽  
Average Error ◽  
Model Parameters ◽  
Wide Range

Stimulus reconstruction or decoding methods provide an important tool for understanding how sensory and motor information is represented in neural activity. We discuss Bayesian decoding methods based on an encoding generalized linear model (GLM) that accurately describes how stimuli are transformed into the spike trains of a group of neurons. The form of the GLM likelihood ensures that the posterior distribution over the stimuli that caused an observed set of spike trains is log concave so long as the prior is. This allows the maximum a posteriori (MAP) stimulus estimate to be obtained using efficient optimization algorithms. Unfortunately, the MAP estimate can have a relatively large average error when the posterior is highly nongaussian. Here we compare several Markov chain Monte Carlo (MCMC) algorithms that allow for the calculation of general Bayesian estimators involving posterior expectations (conditional on model parameters). An efficient version of the hybrid Monte Carlo (HMC) algorithm was significantly superior to other MCMC methods for gaussian priors. When the prior distribution has sharp edges and corners, on the other hand, the “hit-and-run” algorithm performed better than other MCMC methods. Using these algorithms, we show that for this latter class of priors, the posterior mean estimate can have a considerably lower average error than MAP, whereas for gaussian priors, the two estimators have roughly equal efficiency. We also address the application of MCMC methods for extracting nonmarginal properties of the posterior distribution. For example, by using MCMC to calculate the mutual information between the stimulus and response, we verify the validity of a computationally efficient Laplace approximation to this quantity for gaussian priors in a wide range of model parameters; this makes direct model-based computation of the mutual information tractable even in the case of large observed neural populations, where methods based on binning the spike train fail. Finally, we consider the effect of uncertainty in the GLM parameters on the posterior estimators.

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