scholarly journals A comparison between Gauss-Newton and Markov-chain Monte Carlo–based methods for inverting spectral induced-polarization data for Cole-Cole parameters

Geophysics ◽  
2008 ◽  
Vol 73 (6) ◽  
pp. F247-F259 ◽  
Author(s):  
Jinsong Chen ◽  
Andreas Kemna ◽  
Susan S. Hubbard
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Optimal Solution ◽  
Stochastic Method ◽  
Objective Functions ◽  
Unknown Parameters ◽  
Deterministic Method ◽  
Initial Values ◽  
Spectral Induced Polarization

We have developed a Bayesian model to invert spectral induced-polarization (SIP) data for Cole-Cole parameters using Markov-chain Monte Carlo (MCMC) sampling methods. We compared the performance of the MCMC-based stochastic method with an iterative Gauss-Newton-based deterministic method for Cole-Cole parameter estimation through inversion of synthetic and laboratory SIP data. The Gauss-Newton-based method can provide an optimal solution for given objective functions under constraints, but the obtained optimal solution generally depends on the choice of initial values and the estimated uncertainty information often is inaccurate or insufficient. In contrast, the MCMC-based inversion method provides extensive globalinformation on unknown parameters, such as the marginal probability distribution functions, from which we can obtain better estimates and tighter uncertainty bounds of the parameters than with the deterministic method. In addition, the results obtained with the MCMC method are independent of the choice of initial values. Because the MCMC-based method does not explicitly offer a single optimal solution for given objective functions, the deterministic and stochastic methods can complement each other. For example, the stochastic method can be used first to obtain the medians of unknown parameters by starting from an arbitrary set of initial values. The deterministic method then can be initiated using the medians as starting values to obtain the optimal estimates of the Cole-Cole parameters.

scholarly journals A Monte Carlo approach for determining cluster evaporation rates from concentration measurements

2016 ◽  
Author(s):  
Oona Kupiainen-Määttä
Keyword(s):  
Experimental Data ◽  
Monte Carlo ◽  
Markov Chain ◽  
Sulfuric Acid ◽  
Markov Chain Monte Carlo ◽  
Mass Spectrometer ◽  
Large Fraction ◽  
Cluster Formation ◽  
Unknown Parameters ◽  
Ammonia Clusters

Abstract. Evaporation rates of small negatively charged sulfuric acid–ammonia clusters are determined by combining detailed cluster formation simulations with cluster distributions measured at CLOUD. The analysis is performed by varying the evaporation rates with Markov chain Monte Carlo (MCMC), running cluster formation simulations with each new set of evaporation rates and comparing the obtained cluster distributions to the measurements. In a second set of simulations, the fragmentation of clusters in the mass spectrometer due to energetic collisions is studied by treating also the fragmentation probabilities as unknown parameters and varying them with MCMC. This second set of simulations results in a better fit to the experimental data, suggesting that a large fraction of the observed HSO4− and HSO4− ⋅ H2SO4 signals may result from fragmentation of larger clusters, most importantly the HSO4− ⋅ (H2SO4)2 trimer.

Parameter Estimation Using Markov Chain Monte Carlo Method in Mechanistic Modeling of Tool Wear During Milling

2015 ◽  
Author(s):  
Farbod Akhavan Niaki ◽  
Durul Ulutan ◽  
Laine Mears
Keyword(s):  
Monte Carlo ◽  
Parameter Estimation ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Tool Wear ◽  
End Milling ◽  
Mechanistic Modeling ◽  
Unknown Parameters ◽  
Workpiece Material ◽  
Machining Parameter

Several models have been proposed to describe the relationship between cutting parameters and machining outputs such as cutting forces and tool wear. However, these models usually cannot be generalized, due to the inherent uncertainties that exist in the process. These uncertainties may originate from machining, workpiece material composition, and measurements. A stochastic approach can be utilized to compensate for the lack of certainty in machining, particularly for tool wear evolution. The Markov Chain Monte Carlo (MCMC) method is a powerful tool for addressing uncertainties in machining parameter estimation. The Hybrid Metropolis-Gibbs algorithm has been chosen in this work to estimate the unknown parameters in a mechanistic tool wear model for end milling of difficult-to-machine alloys. The results show a good potential of the Markov Chain Monte Carlo modeling in prediction of parameters in the presence of uncertainties.

scholarly journals Parameters Identification for Inverse Option Problems Using Markov Chain Monte Carlo Methods

2019 ◽  
Author(s):  
Yasushi Ota ◽  
Yu Jiang
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Inference ◽  
Financial Markets ◽  
Sampling Strategy ◽  
Measured Data ◽  
Mcmc Algorithm ◽  
Unknown Parameters ◽  
Posterior Probability Density

This paper investigates the inverse option problems (IOP) in the extended Black--Scholes model arising in financial markets. We identify the volatility and the drift coefficient from the measured data in financial markets using a Bayesian inference approach, which is presented as an IOP solution. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by a Markov Chain Monte Carlo (MCMC) algorithm, which exploits the posterior state space. The efficient sampling strategy of the MCMC algorithm enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown trend and volatility coefficients from the measured data.

scholarly journals Markov Chain Monte Carlo Based Energy Use Behaviors Prediction of Office Occupants

Algorithms ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 21
Author(s):  
Qiao Yan ◽  
Xiaoqian Liu ◽  
Xiaoping Deng ◽  
Wei Peng ◽  
Guiqing Zhang
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Energy Use ◽  
Time Series Data ◽  
Optimal Solution ◽  
Working Hours ◽  
Series Data ◽  
Air Conditioner ◽  
Desktop Computer

Prediction of energy use behaviors is a necessary prerequisite for designing personalized and scalable energy efficiency programs. The energy use behaviors of office occupants are different from those of residential occupants and have not yet been studied as intensively as residential occupants. This paper proposes a method based on Markov chain Monte Carlo (MCMC) to predict the energy use behaviors of office occupants. Firstly, an indoor electrical Internet of Things system (IEIoTS) for the office scenario is developed to collect the switching state time series data of selected user electrical equipment (desktop computer, water dispenser, light) and the historical environment parameters. Then, the Metropolis–Hastings (MH) algorithm is used to sample and obtain the optimal solution of the parameters for the office occupants’ behavior function, the model of which includes the energy action model, energy working hours model, and air-conditioner energy use behavior model. Finally, comparative experiments are carried out to evaluate the performance of the proposed method. The experimental results show that while the mean value performs similarly in estimating the energy use model, the proposed method outperforms the Maximum Likelihood Estimation (MLE) method on uncertainty quantification with relatively narrower confidence intervals.

scholarly journals A comparison of approximate versus exact techniques for Bayesian parameter inference in nonlinear ordinary differential equation models

2020 ◽  
Vol 7 (3) ◽  
pp. 191315
Author(s):  
Amani A. Alahmadi ◽  
Jennifer A. Flegg ◽  
Davis G. Cochrane ◽  
Christopher C. Drovandi ◽  
Jonathan M. Keith
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Inference ◽  
Sequential Monte Carlo ◽  
Simulated Data ◽  
Real Data ◽  
Nonlinear Ordinary Differential Equation ◽  
Unknown Parameters ◽  
Acceptance Probability

The behaviour of many processes in science and engineering can be accurately described by dynamical system models consisting of a set of ordinary differential equations (ODEs). Often these models have several unknown parameters that are difficult to estimate from experimental data, in which case Bayesian inference can be a useful tool. In principle, exact Bayesian inference using Markov chain Monte Carlo (MCMC) techniques is possible; however, in practice, such methods may suffer from slow convergence and poor mixing. To address this problem, several approaches based on approximate Bayesian computation (ABC) have been introduced, including Markov chain Monte Carlo ABC (MCMC ABC) and sequential Monte Carlo ABC (SMC ABC). While the system of ODEs describes the underlying process that generates the data, the observed measurements invariably include errors. In this paper, we argue that several popular ABC approaches fail to adequately model these errors because the acceptance probability depends on the choice of the discrepancy function and the tolerance without any consideration of the error term. We observe that the so-called posterior distributions derived from such methods do not accurately reflect the epistemic uncertainties in parameter values. Moreover, we demonstrate that these methods provide minimal computational advantages over exact Bayesian methods when applied to two ODE epidemiological models with simulated data and one with real data concerning malaria transmission in Afghanistan.

scholarly journals A Monte Carlo approach for determining cluster evaporation rates from concentration measurements

2016 ◽  
Vol 16 (22) ◽  
pp. 14585-14598 ◽  
Author(s):  
Oona Kupiainen-Määttä
Keyword(s):  
Experimental Data ◽  
Monte Carlo ◽  
Markov Chain ◽  
Sulfuric Acid ◽  
Markov Chain Monte Carlo ◽  
Mass Spectrometer ◽  
Large Fraction ◽  
Cluster Formation ◽  
Unknown Parameters ◽  
Ammonia Clusters

Abstract. Evaporation rates of small negatively charged sulfuric acid–ammonia clusters are determined by combining detailed cluster formation simulations with cluster distributions measured in the CLOUD experiment at CERN. The analysis is performed by varying the evaporation rates with Markov chain Monte Carlo (MCMC), running cluster formation simulations with each new set of evaporation rates and comparing the obtained cluster distributions to the measurements. In a second set of simulations, the fragmentation of clusters in the mass spectrometer due to energetic collisions is studied by treating also the fragmentation probabilities as unknown parameters and varying them with MCMC. This second set of simulations results in a better fit to the experimental data, suggesting that a large fraction of the observed HSO4− and HSO4− ⋅ H2SO4 signals may result from fragmentation of larger clusters, most importantly the HSO4− ⋅ (H2SO4)2 trimer.

Markov-chain Monte Carlo estimation of distributed Debye relaxations in spectral induced polarization

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. E159-E170 ◽  
Author(s):  
John Keery ◽  
Andrew Binley ◽  
Ahmed Elshenawy ◽  
Jeremy Clifford
Keyword(s):  
Porous Media ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Physical Properties ◽  
Relaxation Times ◽  
Synthetic Data ◽  
Induced Polarization ◽  
Posterior Distributions ◽  
Spectral Induced Polarization

There is growing interest in the link between electrical polarization and physical properties of geologic porous media. In particular, spectral characteristics may be controlled by the same pore geometric properties that influence fluid permeability of such media. Various models have been proposed to describe the spectral-induced-polarization (SIP) response of permeable rocks, and the links between these models and hydraulic properties have been explored, albeit empirically. Computation of the uncertainties in the parameters of such electrical models is essential for effective use of these relationships. The formulation of an electrical dispersion model in terms of a distribution of relaxation times and associated chargeabilities has been demonstrated to be an effective generalized approach; however, thus far, such an approach has only been considered in a deterministic framework. Here, we formulate a spectral model based on a distribution of polarizations. By using a simple polynomial descriptor of such a distribution, we are able to cast the model in a stochastic manner and solve it using a Markov-chain Monte Carlo (McMC) sampler, thus allowing the computation of model-parameter uncertainties. We apply the model to synthetic data and demonstrate that the stochastic method can provide posterior distributions of model parameters with narrow bounds around the true values when little or no noise is added to the synthetic data, with posterior distributions that broaden with increasing noise. We also apply our model to experimental measurements of six sandstone samples and compare physical properties of a number of samples of porous media with stochastic estimates of characteristic relaxation times. We demonstrate the utility of our method on electrical spectra with different response characteristics and show that a single metric of relaxation time for the SIP response is not sufficient to provide clear insight into the physical characteristics of a sample.

scholarly journals RJMCMC based Text Placement to Optimize Label Placement and Quantity

2018 ◽  
Vol 1 ◽  
pp. 1-3
Author(s):  
Guillaume Touya ◽  
Thibaud Chassin
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Optimization Technique ◽  
Optimal Solution ◽  
Reversible Jump ◽  
Optimal Position ◽  
Label Placement ◽  
Map Design ◽  
First Results

Label placement is a tedious task in map design, and its automation has long been a goal for researchers in cartography, but also in computational geometry. Methods that search for an optimal or nearly optimal solution that satisfies a set of constraints, such as label overlapping, have been proposed in the literature. Most of these methods mainly focus on finding the optimal position for a given set of labels, but rarely allow the removal of labels as part of the optimization. This paper proposes to apply an optimization technique called Reversible-Jump Markov Chain Monte Carlo that enables to easily model the removal or addition during the optimization iterations. The method, quite preliminary for now, is tested on a real dataset, and the first results are encouraging.

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