scholarly journals Anytime Monte Carlo

2021 ◽  
Vol 2 ◽  
Author(s):  
Lawrence M. Murray ◽  
Sumeetpal S. Singh ◽  
Anthony Lee
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Real Time ◽  
Graphics Processing Units ◽  
Large Scale ◽  
Sequential Monte Carlo ◽  
Time Budget ◽  
Mcmc Algorithm ◽  
Length Bias ◽  
Markov Jump

Abstract Monte Carlo algorithms simulates some prescribed number of samples, taking some random real time to complete the computations necessary. This work considers the converse: to impose a real-time budget on the computation, which results in the number of samples simulated being random. To complicate matters, the real time taken for each simulation may depend on the sample produced, so that the samples themselves are not independent of their number, and a length bias with respect to compute time is apparent. This is especially problematic when a Markov chain Monte Carlo (MCMC) algorithm is used and the final state of the Markov chain—rather than an average over all states—is required, which is the case in parallel tempering implementations of MCMC. The length bias does not diminish with the compute budget in this case. It also occurs in sequential Monte Carlo (SMC) algorithms, which is the focus of this paper. We propose an anytime framework to address the concern, using a continuous-time Markov jump process to study the progress of the computation in real time. We first show that for any MCMC algorithm, the length bias of the final state’s distribution due to the imposed real-time computing budget can be eliminated by using a multiple chain construction. The utility of this construction is then demonstrated on a large-scale SMC $ {}^2 $ implementation, using four billion particles distributed across a cluster of 128 graphics processing units on the Amazon EC2 service. The anytime framework imposes a real-time budget on the MCMC move steps within the SMC $ {}^2 $ algorithm, ensuring that all processors are simultaneously ready for the resampling step, demonstrably reducing idleness to due waiting times and providing substantial control over the total compute budget.

scholarly journals Prevention of Mountain Disasters and Maintenance of Residential Area through Real-Time Terrain Rendering

2021 ◽  
Vol 13 (5) ◽  
pp. 2950
Author(s):  
Su-Kyung Sung ◽  
Eun-Seok Lee ◽  
Byeong-Seok Shin
Keyword(s):  
Real Time ◽  
Graphics Processing Units ◽  
High Speed ◽  
Large Scale ◽  
Civil Engineering ◽  
Three Dimensional ◽  
Sampled Data ◽  
Residential Areas ◽  
Terrain Rendering ◽  
Mountain Disasters

Climate change increases the frequency of localized heavy rains and typhoons. As a result, mountain disasters, such as landslides and earthworks, continue to occur, causing damage to roads and residential areas downstream. Moreover, large-scale civil engineering works, including dam construction, cause rapid changes in the terrain, which harm the stability of residential areas. Disasters, such as landslides and earthenware, occur extensively, and there are limitations in the field of investigation; thus, there are many studies being conducted to model terrain geometrically and to observe changes in terrain according to external factors. However, conventional topography methods are expressed in a way that can only be interpreted by people with specialized knowledge. Therefore, there is a lack of consideration for three-dimensional visualization that helps non-experts understand. We need a way to express changes in terrain in real time and to make it intuitive for non-experts to understand. In conventional height-based terrain modeling and simulation, there is a problem in which some of the sampled data are irregularly distorted and do not show the exact terrain shape. The proposed method utilizes a hierarchical vertex cohesion map to correct inaccurately modeled terrain caused by uniform height sampling, and to compensate for geometric errors using Hausdorff distances, while not considering only the elevation difference of the terrain. The mesh reconstruction, which triangulates the three-vertex placed at each location and makes it the smallest unit of 3D model data, can be done at high speed on graphics processing units (GPUs). Our experiments confirm that it is possible to express changes in terrain accurately and quickly compared with existing methods. These functions can improve the sustainability of residential spaces by predicting the damage caused by mountainous disasters or civil engineering works around the city and make it easy for non-experts to understand.

scholarly journals A sequential Bayesian approach for the estimation of the age–depth relationship of Dome Fuji ice core

2015 ◽  
Vol 2 (3) ◽  
pp. 939-968
Author(s):  
S. Nakano ◽  
K. Suzuki ◽  
K. Kawamura ◽  
F. Parrenin ◽  
T. Higuchi
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Sequential Monte Carlo ◽  
Ice Core ◽  
Posterior Distributions ◽  
Metropolis Method ◽  
Depth Relationship ◽  
Relationship Of ◽  
Thinning Process

Abstract. A technique for estimating the age–depth relationship in an ice core and evaluating its uncertainty is presented. The age–depth relationship is mainly determined by the accumulation of snow at the site of the ice core and the thinning process due to the horizontal stretching and vertical compression of ice layers. However, since neither the accumulation process nor the thinning process are fully understood, it is essential to incorporate observational information into a model that describes the accumulation and thinning processes. In the proposed technique, the age as a function of depth is estimated from age markers and δ18O data. The estimation is achieved using the particle Markov chain Monte Carlo (PMCMC) method, in which the sequential Monte Carlo (SMC) method is combined with the Markov chain Monte Carlo method. In this hybrid method, the posterior distributions for the parameters in the models for the accumulation and thinning processes are computed using the Metropolis method, in which the likelihood is obtained with the SMC method. Meanwhile, the posterior distribution for the age as a function of depth is obtained by collecting the samples generated by the SMC method with Metropolis iterations. The use of this PMCMC method enables us to estimate the age–depth relationship without assuming either linearity or Gaussianity. The performance of the proposed technique is demonstrated by applying it to ice core data from Dome Fuji in Antarctica.

Markov Chain Monte Carlo

2015 ◽  
Author(s):  
N. Thompson Hobbs ◽  
Mevin B. Hooten
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Analysis ◽  
Posterior Distribution ◽  
Mcmc Algorithm ◽  
Bayesian Analyses ◽  
Seminal Paper ◽  
Formal Treatment ◽  
High Level

This chapter explains how to implement Bayesian analyses using the Markov chain Monte Carlo (MCMC) algorithm, a set of methods for Bayesian analysis made popular by the seminal paper of Gelfand and Smith (1990). It begins with an explanation of MCMC with a heuristic, high-level treatment of the algorithm, describing its operation in simple terms with a minimum of formalism. In this first part, the chapter explains the algorithm so that all readers can gain an intuitive understanding of how to find the posterior distribution by sampling from it. Next, the chapter offers a somewhat more formal treatment of how MCMC is implemented mathematically. Finally, this chapter discusses implementation of Bayesian models via two routes—by using software and by writing one's own algorithm.

scholarly journals Markov chain Monte Carlo inference for Markov jump processes via the linear noise approximation

2013 ◽  
Vol 371 (1984) ◽  
pp. 20110541 ◽  
Author(s):  
Vassilios Stathopoulos ◽  
Mark A. Girolami
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Jump Processes ◽  
Mcmc Methods ◽  
Computationally Efficient ◽  
Markov Jump ◽  
Riemann Manifold ◽  
Exact Inference ◽  
Markov Jump Processes

Bayesian analysis for Markov jump processes (MJPs) is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding, thus its applicability is limited to a small class of problems. In this paper, we describe the application of Riemann manifold Markov chain Monte Carlo (MCMC) methods using an approximation to the likelihood of the MJP that is valid when the system modelled is near its thermodynamic limit. The proposed approach is both statistically and computationally efficient whereas the convergence rate and mixing of the chains allow for fast MCMC inference. The methodology is evaluated using numerical simulations on two problems from chemical kinetics and one from systems biology.

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