Differential Evolution Markov Chain Monte Carlo Research Articles

Source term estimation for continuous plume dispersion in Fusion Field Trial-07: Bayesian inference probability adjoint inverse method

In scenarios involving sudden releases of unidentified gases or concealed pollution emergencies, source control emerges as a critical procedure to safeguard residential air quality. Appropriate inverse source tracking methodology depending on diverse measurement data could be utilized to promptly identify pollutant source parameters. In this study, source term estimation (STE) method, i.e., jointly combining probability adjoint method with the Bayesian inference method, has been proposed. General form of the pollutant inverse transport equation was firstly established. Subsequently, the pollution source information, assumed from single continuous point releases during Fusion Field Trials 2007 under an unsteady wind field, was identified using the Bayesian inference probability adjoint inverse method. Metropolis-Hastings Markov Chain Monte Carlo (MH-MCMC) and Differential Evolution Markov Chain Monte Carlo (DE-MCMC) were then compared as sampling methods for Bayesian inference. Results indicated that the DE-MCMC algorithm has superior convergence and could present higher accuracy of pollutant source information than that of MH-MCMC algorithm, particularly for highly nonlinear and multi-modal distribution systems. Furthermore, the integration of Union standard Adjoint Location Probability (UALP) as prior information into the Bayesian inference probability adjoint inverse method effectively narrowed the sampling range, enhancing both the accuracy and robustness of the proposed approach. Finally, the impact of the covariance matrix on the inverse identification accuracy was explored. Overall, this research has provided insights into the future applicability of this Bayesian inference inversion technique for point source identification.

Probabilistic Multi-Objective Inverse Analysis for Damage Identification Using Piezoelectric Impedance Measurement Under Uncertainties

Piezoelectric impedance sensing is promising for highly accurate damage identification because of its high-frequency active interrogative nature and simplicity in data acquisition. To fully unleash the potential, effective inverse analysis is needed in order to pinpoint the damage location and identify the severity. The inverse analysis, however, may be underdetermined since there exists a very large number of unknowns (i.e., locations and severity levels) to be solved in a finite element model but only limited measurements are available in actual practice. To uncover the true damage scenario, an inverse analysis strategy built upon the multi-objective optimization, which aims at matching the multiple sets of measurements with model predictions in the damage parametric space, can be formulated to identify a small set of solutions. This solution set then allows the incorporation of empirical knowledge to facilitate final decision-making. The main disadvantage of the conventional inverse analysis strategy is that it overlooks uncertainties that exist in both baseline structural modeling and actual measurements. To address this, in this research, we formulate a probabilistic multi-objective optimization-based inverse analysis framework, which is fundamentally built upon the differential evolution Markov chain Monte Carlo (DEMC) technique. The new approach can yield the Pareto optimal set (solutions) and the respective Pareto front, which are represented in a probabilistic sense to account for uncertainties. Comprehensive case studies with experimental investigations are conducted to demonstrate the effectiveness of this new approach.

Direct estimation of discrete fluid facies and fluid indicators via a Bayesian Seismic Probabilistic Inversion and a novel exact PP-wave reflection coefficient

Estimation of rock pore-fluid properties in subsurface reservoirs using seismic reflection data is an important topic in exploration geophysics. Prestack seismic inversion is a key approach for reservoir characterization and fluid discrimination. In this study, we propose a simultaneous estimation approach for discrete fluid facies (i.e., gas, oil, water) and continuous fluid indicators via a Bayesian seismic nonlinear inversion and the differential evolution Markov Chain Monte Carlo model. We derived one novel nonlinear exact PP-wave reflection coefficients equation characterized by Gassmann fluid term, shear modulus and density and the equation is more accurate and suitable for large incident angles. Besides, a mixture probability model is utilized as the prior probability density function (PDF) of the model parameters in the Bayesian seismic probabilistic inversion. Furthermore, the differential evolution Markov Chain Monte Carlo (DE-MCMC) model is developed to optimize the mixture posterior PDF in Bayesian seismic inference. The discrete fluid facies is estimated via the posterior weights of each probability component directly, which can reduce the uncertainty and the accumulation errors of seismic fluid discrimination. The main advantage of the DE-MCMC seismic probabilistic inversion is that it can simulate the posterior probability density distributions of the model parameters efficiently based on the simultaneous optimization of multiple Markov chains, which is helpful for the uncertainty assessment of the inversion results and fluid discrimination. Synthetic examples are provided to demonstrate the feasibility and stability of the proposed method. Furthermore, one field case of oil-gas exploration is presented to show the practicability of this method in reservoir fluid discrimination.

Bayesian Inference for Multidimensional Scaling Representations with Psychologically Interpretable Metrics

Multidimensional scaling (MDS) models represent stimuli as points in a space consisting of a number of psychological dimensions, such that the distance between pairs of points corresponds to the dissimilarity between the stimuli. Two fundamental challenges in inferring MDS representations from data involve inferring the appropriate number of dimensions and the metric structure of the space used to measure distance. We approach both challenges as Bayesian model-selection problems. Treating MDS as a generative model, we define priors needed for model identifiability under metrics corresponding to psychologically separable and psychologically integral stimulus domains. We then apply a differential evolution Markov-chain Monte Carlo (DE-MCMC) method for parameter inference, and a Warp-III method for model selection. We apply these methods to five previous data sets, which collectively test the ability of the methods to infer an appropriate dimensionality and to infer whether stimuli are psychologically separable or integral. We demonstrate that our methods produce sensible results, but note a number of remaining technical challenges that need to be solved before the method can easily and generally be applied. We also note the theoretical promise of the generative modeling perspective, discussing new and extended models of MDS representation that could be developed.

Thermodynamic integration via differential evolution: A method for estimating marginal likelihoods

A typical goal in cognitive psychology is to select the model that provides the best explanation of the observed behavioral data. The Bayes factor provides a principled approach for making these selections, though the integral required to calculate the marginal likelihood for each model is intractable for most cognitive models. In these cases, Monte Carlo techniques must be used to approximate the marginal likelihood, such as thermodynamic integration (TI; Friel & Pettitt, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70(3), 589–607 2008; Lartillot & Philippe, Systematic Biology, 55(2), 195–207 2006), which relies on sampling from the posterior at different powers (called power posteriors). TI can become computationally expensive when using population Markov chain Monte Carlo (MCMC) approaches such as differential evolution MCMC (DE-MCMC; Turner et al., Psychological Methods, 18(3), 368 2013) that require several interacting chains per power posterior. Here, we propose a method called thermodynamic integration via differential evolution (TIDE), which aims to reduce the computational burden associated with TI by using a single chain per power posterior (R code available at https://osf.io/ntmgw/). We show that when applied to non-hierarchical models, TIDE produces an approximation of the marginal likelihood that closely matches TI. When extended to hierarchical models, we find that certain assumptions about the dependence between the individual- and group-level parameters samples (i.e., dependent/independent) have sizable effects on the TI approximated marginal likelihood. We propose two possible extensions of TIDE to hierarchical models, which closely match the marginal likelihoods obtained through TI with dependent/independent sampling in many, but not all, situations. Based on these findings, we believe that TIDE provides a promising method for estimating marginal likelihoods, though future research should focus on a detailed comparison between the methods of estimating marginal likelihoods for cognitive models.

A multiobjective Markov chain Monte Carlo approach for history matching and uncertainty quantification

We present a probabilistic approach for integrating multiple data types into subsurface flow models. Our approach is based on a Bayesian framework whereby we exhaustively sample the multi-dimensional posterior distribution to define a Pareto front which represents the trade-off between multiple objectives during history matching. These objectives can be matching of water-cut, GOR, BHP and time-lapse seismic data. For field applications, these objectives do not necessarily move in tandem because of measurement errors and also interpretative nature of the seismic data.Our proposed method is built on a Differential Evolution Markov Chain Monte Carlo (DEMC) algorithm in which multiple Markov Chains are run in parallel. First, a dominance relationship is established amongst multiple models. This is followed by construction of the posterior distribution based on a hypervolume measure. A unique aspect of our method is in the parameter proposal generation which is based on a random walk on two arbitrarily selected chains. This promotes effective mixing of the chains resulting in improved convergence.We illustrate the algorithm using a nine-spot waterflood model whereby we use water-cut and bottomhole flowing pressure data to calibrate the permeability field. The permeability field is re-parameterized using a previously proposed Grid Connectivity Transform (GCT) which is a model order reduction technique defined based only on the decomposition of the grid Laplacian. The compression power of GCT allows us to reconstruct the permeability field with few parameters, thus significantly improving the computational efficiency of the McMC approach. Next, we applied the method to the Brugge benchmark case involving 10 water injectors and 20 producers. For both cases, the algorithm provides an ensemble of models all constrained to the history data and defines a probabilistic Pareto front in the objective space. Several experimental runs were conducted to compare the effectiveness of the algorithm with Non-Dominated Sorting Genetic Algorithms (NSGA-II). Higher hypervolume was constantly measured using our algorithm which indicates that more optimal solutions were sampled. Our method provides a novel approach for subsurface model calibration and uncertainty quantification using McMC in which the communication between parallel Markov chains enhances adequate mixing. This significantly improves the convergence without loss in sampling quality.

RUN DMC: AN EFFICIENT, PARALLEL CODE FOR ANALYZING RADIAL VELOCITY OBSERVATIONS USING N -BODY INTEGRATIONS AND DIFFERENTIAL EVOLUTION MARKOV CHAIN MONTE CARLO

In the 20+ years of Doppler observations of stars, scientists have uncovered a diverse population of extrasolar multi-planet systems. A common technique for characterizing the orbital elements of these planets is Markov chain Monte Carlo (MCMC), using a Keplerian model with random walk proposals and paired with the Metropolis-Hastings algorithm. For approximately a couple of dozen planetary systems with Doppler observations, there are strong planet-planet interactions due to the system being in or near a mean-motion resonance (MMR). An N-body model is often required to accurately describe these systems. Further computational difficulties arise from exploring a high-dimensional parameter space ($\sim$7 x number of planets) that can have complex parameter correlations. To surmount these challenges, we introduce a differential evolution MCMC (DEMCMC) applied to radial velocity data while incorporating self-consistent N-body integrations. Our Radial velocity Using N-body DEMCMC (RUN DMC) algorithm improves upon the random walk proposal distribution of the traditional MCMC by using an ensemble of Markov chains to adaptively improve the proposal distribution. We describe the methodology behind the algorithm, along with results of tests for accuracy and performance. We find that most algorithm parameters have a modest effect on the rate of convergence. However, the size of the ensemble can have a strong effect on performance. We show that the optimal choice depends on the number of planets in a system, as well as the computer architecture used and the resulting extent of parallelization. While the exact choices of optimal algorithm parameters will inevitably vary due to the details of individual planetary systems, we offer recommendations for choosing the DEMCMC algorithm's algorithmic parameters that result in excellent performance for a wide variety of planetary systems.

A method for efficiently sampling from distributions with correlated dimensions.

Bayesian estimation has played a pivotal role in the understanding of individual differences. However, for many models in psychology, Bayesian estimation of model parameters can be difficult. One reason for this difficulty is that conventional sampling algorithms, such as Markov chain Monte Carlo (MCMC), can be inefficient and impractical when little is known about the target distribution--particularly the target distribution's covariance structure. In this article, we highlight some reasons for this inefficiency and advocate the use of a population MCMC algorithm, called differential evolution Markov chain Monte Carlo (DE-MCMC), as a means of efficient proposal generation. We demonstrate in a simulation study that the performance of the DE-MCMC algorithm is unaffected by the correlation of the target distribution, whereas conventional MCMC performs substantially worse as the correlation increases. We then show that the DE-MCMC algorithm can be used to efficiently fit a hierarchical version of the linear ballistic accumulator model to response time data, which has proven to be a difficult task when conventional MCMC is used.

Bayesian exoplanet tests of a new method for MCMC sampling in highly correlated model parameter spaces

The Markov chain Monte Carlo (MCMC) method is a powerful technique for facilitating Bayesian non-linear model fitting. In many cases, the MCMC exploration of the parameter space is very inefficient, because the model parameters are highly correlated. Differential evolution MCMC is one technique that addresses this problem by employing multiple parallel chains. We present a new method that automatically achieves efficient MCMC sampling in highly correlated parameter spaces, which does not require additional chains to accomplish this. It was designed to work with an existing hybrid MCMC (HMCMC) algorithm, which incorporates parallel tempering, simulated annealing and genetic cross-over operations. These features, together with the new correlated parameter sampler, greatly facilitate the detection of a global minimum in χ 2 . The new HMCMC algorithm is very general in scope. Two tests of the algorithm are described employing (a) exoplanet precision radial velocity (RV) data and (b) simulated space astrometry data. The latter test explores the accuracy of parameter estimates obtained with the Bayesian HMCMC algorithm on the assumed astrometric noise.