Ensemble Metropolis Light Transport

This article proposes a Markov Chain Monte Carlo ( MCMC ) rendering algorithm based on a family of guided transition kernels. The kernels exploit properties of ensembles of light transport paths, which are distributed according to the lighting in the scene, and utilize this information to make informed decisions for guiding local path sampling. Critically, our approach does not require caching distributions in world space, saving time and memory, yet it is able to make guided sampling decisions based on whole paths. We show how this can be implemented efficiently by organizing the paths in each ensemble and designing transition kernels for MCMC rendering based on a carefully chosen subset of paths from the ensemble. This algorithm is easy to parallelize and leads to improvements in variance when rendering a variety of scenes.

Nonreversible Markov Chain Monte Carlo Algorithm for Efficient Generation of Self-Avoiding Walks

We introduce an efficient nonreversible Markov chain Monte Carlo algorithm to generate self-avoiding walks with a variable endpoint. In two dimensions, the new algorithm slightly outperforms the two-move nonreversible Berretti-Sokal algorithm introduced by H. Hu, X. Chen, and Y. Deng, while for three-dimensional walks, it is 3–5 times faster. The new algorithm introduces nonreversible Markov chains that obey global balance and allow for three types of elementary moves on the existing self-avoiding walk: shorten, extend or alter conformation without changing the length of the walk.

Bayesian inference and Markov chain Monte Carlo based estimation of a geoscience model parameter

The critical slip distance in rate and state model for fault friction in the study of potential earthquakes can vary wildly from micrometers to few meters depending on the length scale of the critically stressed fault. This makes it incredibly important to construct an inversion framework that provides good estimates of the critical slip distance purely based on the observed acceleration at the seismogram. The framework is based on Bayesian inference and Markov chain Monte Carlo. The synthetic data is generated by adding noise to the acceleration output of spring-slider-damper idealization of the rate and state model as the forward model.

Temperature and Salinity Inverted for a Mediterranean Eddy Captured With Seismic Data, Using a Spatially Iterative Markov Chain Monte Carlo Approach

Ocean submesoscale dynamics are thought to play a key role in both the climate system and ocean productivity, however, subsurface observations at these scales remain rare. Seismic oceanography, an established acoustic imaging method, provides a unique tool for capturing oceanic structure throughout the water column with spatial resolutions of tens of meters. A drawback to the seismic method is that temperature and salinity are not measured directly, limiting the quantitative interpretation of imaged features. The Markov Chain Monte Carlo (MCMC) inversion approach has been used to invert for temperature and salinity from seismic data, with spatially quantified uncertainties. However, the requisite prior model used in previous studies relied upon highly continuous acoustic reflection horizons rarely present in real oceanic environments due to instabilities and turbulence. Here we adapt the MCMC inversion approach with an iteratively updated prior model based on hydrographic data, sidestepping the necessity of continuous reflection horizons. Furthermore, uncertainties introduced by the starting model thermohaline fields as well as those from the MCMC inversion itself are accounted for. The impact on uncertainties of varying the resolution of hydrographic data used to produce the inversion starting model is also investigated. The inversion is applied to a mid-depth Mediterranean water eddy (or meddy) captured with seismic imaging in the Gulf of Cadiz in 2007. The meddy boundary exhibits regions of disrupted seismic reflectivity and rapid horizontal changes of temperature and salinity. Inverted temperature and salinity values typically have uncertainties of 0.16°C and 0.055 psu, respectively, and agree well with direct measurements. Uncertainties of inverted results are found to be highly dependent on the resolution of the hydrographic data used to produce the prior model, particularly in regions where background temperature and salinity vary rapidly, such as at the edge of the meddy. This further advancement of inversion techniques to extract temperature and salinity from seismic data will help expand the use of ocean acoustics for understanding the mesoscale to finescale structure of the interior ocean.

Uncertainty quantification of geological model parameters in 3D gravity inversion by Hessian informed Markov chain Monte Carlo

Geological modeling has been widely adopted to investigate underground geometries. However, modeling processes inevitably have uncertainties due to scarcity of data, measurement errors, and simplification of modeling methods. Recent developments in geomodeling methods have introduced a Bayesian framework to constrain the model uncertainties by considering additional geophysical data into the modeling procedure. Markov chain Monte Carlo (MCMC) methods are normally used as tools to solve the Bayesian inference problem. To achieve a more efficient posterior exploration, advances inMCMC methods utilize derivative information. Hence, we introduce an approach to efficiently evaluate second-order derivatives in geological modeling and introduce a Hessian-informed MCMC method, the generalized preconditioned Crank-Nicolson (gpCN), as a tool to solve the 3D model-based gravity Bayesian inversion problem. The result is compared with two other widely applied MCMC methods, random walk Metropolis-Hasting and Hamiltonian Monte Carlo, on a synthetic three-layer geological model. Our experiment demonstrates that superior performance is achieved by the gpCN, which has the potential to be generalized to more complex models.

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

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.