Multilevel Estimation of Rare Events

Application of spherical subset simulation method and auxiliary domain method on a benchmark reliability study

To study the mechanisms for local evolutionary changes in DNA sequences involving slippage-type insertions and deletions, an alignment approach is explored that can consider the posterior probabilities of alignment models. Various patterns of insertion and deletion that can link the ancestor and descendant sequences are proposed and evaluated by simulation and compared by the Markov chain Monte Carlo (MCMC) method. Analyses of pseudogenes reveal that the introduction of the parameters that control the probability of slippage-type events markedly augments the probability of the observed sequence evolution, arguing that a cryptic involvement of slippage occurrences is manifested as insertions and deletions of short nucleotide segments. Strikingly, approximately 80% of insertions in human pseudogenes and approximately 50% of insertions in murids pseudogenes are likely to be caused by the slippage-mediated process, as represented by BC in ABCD --> ABCBCD. We suggest that, in both human and murids, even very short repetitive motifs, such as CAGCAG, CACACA, and CCCC, have approximately 10- to 15-fold susceptibility to insertions and deletions, compared to nonrepetitive sequences. Our protocol, namely, indel-MCMC, thus seems to be a reasonable approach for statistical analyses of the early phase of microsatellite evolution.

Computation of failure probability via hierarchical clustering

An introduction of Markov chain Monte Carlo method to geochemical inverse problems: Reading melting parameters from REE abundances in abyssal peridotites

Markov Chain Monte Carlo simulation has received considerable attention within the past decade as reportedly one of the most powerful techniques for the first passage probability estimation of dynamic systems. A very popular method in this direction capable of estimating probability of rare events with low computation cost is the subset simulation (SS). The idea of the method is to break a rare event into a sequence of more probable events which are easy to be estimated based on the conditional simulation techniques. Recently, two algorithms have been proposed in order to increase the efficiency of the method by modifying the conditional sampler. In this paper, applicability of the original SS is compared to the recently introduced modifications of the method on a wind turbine model. The model incorporates a PID pitch controller which aims at keeping the rotational speed of the wind turbine rotor equal to its nominal value. Finally Monte Carlo simulations are performed which allow assessment of the accuracy of the first passage probability estimation by the SS methods.

Since the physical structure and mathematical models are more complex, reliability analysis in practical engineering can be expensive and difficult. A two-level multifidelity metamodel method for reliability analysis is introduced. Following the surrogate model in most of the relevant works, low-fidelity data and high-fidelity data are integrated by co-Kriging model. Besides, the co-Kriging model also provide an approximation for initial performance function. Bayesian method is adopted in model solution and a hybrid Markov chain Monte Carlo (MCMC) sampling algorithm is proposed. High-fidelity response of reliability performance function is estimated by the conditional distribution derivation based on Bayesian theory. Failure domain is identified by indicator function in sampling space that consists of samples derived from MCMC. Accordingly, failure probability estimations are obtained using Monte Carlo simulation (MCS). It is demonstrated through an illustrative example that the proposed method is valid and accurate.

This paper presents a new methodology for reliability-based inspection planning focusing on robust and accurate computational strategies for fatigue-reliability updating using inspection results. The core of the proposed strategy is a conditioned sampling-based method, implemented by a Fast Probability Analyzer (FPA) software where efficiency is achieved by using the importance sampling principal. For a single component or limit state, FPA first generates Markov-Chain Monte Carlo (MCMC) samples in the failure domain, then applies an adaptive stratified importance sampling (ASIS) method to compute probability of failure (PoF) with error control. Once the MCMC samples have been created, solving a reliability updating problem is fairly straightforward and computationally robust relative to the conventional system reliability methods that rely on linearization of the limit states. The new approach is demonstrated using examples including stiffened panels of a ship-shaped vessel where reliability is updated using inspection results from 100 panel connections.

We describe parallel Markov chain Monte Carlo methods that propagate a collective ensemble of paths, with local covariance information calculated from neighbouring replicas. The use of collective dynamics eliminates multiplicative noise and stabilizes the dynamics, thus providing a practical approach to difficult anisotropic sampling problems in high dimensions. Numerical experiments with model problems demonstrate that dramatic potential speedups, compared to various alternative schemes, are attainable.

The aim of the research is to implement Markov Chain Monte Carlo (MCMC) simulation method to price the futures contract of cocoa commodities. The result shows that MCMC is more flexible than Standard Monte Carlo (SMC) simulation method because MCMC method uses hit-and-run sampler algorithm to generate proposal movements that are subsequently accepted or rejected with a probability that depends on the distribution of the target that we want to be achieved. This research shows that MCMC method is suitable to be used to simulate the model of cocoa commodity price movement. The result of this research is a simulation of future contract prices for the next three months and future contract prices that must be paid at the time the contract expires. Pricing future contract by using MCMC method will produce the cheaper contract price if it compares to Standard Monte Carlo simulation.

A Markov Chain Monte Carlo technique for parameter estimation and inference in pesticide fate and transport modeling

Tunnels, drifts, drives, and other types of underground excavation are very common in mining as well as in the construction of roads, railways, dams, and other civil engineering projects. Planning is essential to the success of tunnel excavation, and construction time is one of the most important factors to be taken into account. This paper proposes a simulation algorithm based on a stochastic numerical method, the Markov chain Monte Carlo method, that can provide the best estimate of the opening excavation times for the classic method of drilling and blasting. Taking account of technical considerations that affect the tunnel excavation cycle, the simulation is developed through a computational algorithm. Using the Markov chain Monte Carlo method, the unit operations involved in the underground excavation cycle are identified and assigned probability distributions that, with random number input, make it possible to simulate the total excavation time. The results obtained with this method are compared with a real case of tunneling excavation. By incorporating variability in the planning, it is possible to determine with greater certainty the ranges over which the execution times of the unit operations fluctuate. In addition, the financial risks associated with planning errors can be reduced and the exploitation of resources maximized.

This article reviews the Bayesian inference with the Monte Carlo Markov Chain (MCMC) and the Hamiltonian Monte Carlo (HMC) samplers as a competitor of the classical likelihood statistical inference for pharmacometricians. The MCMC and the HMC samplers have greatly contributed to realization of the Bayesian methods with minimal requirement of mathematical theory. They do not require any closed form of the posterior density nor linear approximation of complex nonlinear models in high dimension even with non-conjugate priors. The HMC even weakens the dependency of the chain and improves computational efficiency. Pharmacometrics is one of great beneficiaries since they use complex multivariate multilevel nonlinear mixed effects models based on the restricted maximum likelihood estimation. Comprehension of the Bayesian approach will help pharmacometricians to access the data analysis more conveniently.

A new method is proposed based on the finite difference method (FDM), differential evolution algorithm and Markov Chain Monte Carlo (MCMC) simulation to identify water quality model parameters of an open channel in a long distance water transfer project. Firstly, this parameter identification problem is considered as a Bayesian estimation problem and the forward numerical model is solved by FDM, and the posterior probability density function of the parameters is deduced. Then these parameters are estimated using a sampling method with differential evolution algorithm and MCMC simulation. Finally this proposed method is compared with FDM-MCMC by a twin experiment. The results show that the proposed method can be used to identify water quality model parameters of an open channel in a long distance water transfer project under different scenarios better with fewer iterations, higher reliability and anti-noise capability compared with FDM-MCMC. Therefore, it provides a new idea and method to solve the traceability problem in sudden water pollution accidents.

Passive systems, which completely depend on natural phenomena such as gravity, conduction and convection to accomplish the safety functions, are increasingly being used in new generation nuclear reactor designs. However, since the driving forces of passive systems are weak, they are more vulnerable to associated uncertainties and there may be a non-zero probability for the system to deviate from the intended behavior and leads to functional failure. Methods for quantification of the functional failure include Monte-Carlo simulation of the system uncertainties using a validated mechanistic code. Generally, the mechanistic codes used for complex system modeling are computationally expensive and Monte- Carlo simulation for estimating small failure probabilities requires more time and often become prohibitive. In this respect, recently, functional reliability methodologies including advanced simulation techniques such as subset simulation, Markov chain Monte-Carlo, importance sampling, and response conditioning method are reported in open literature. Unlike in the case of direct Monte Carlo simulation, for the probability estimates obtained using these advanced simulations, analytical formulas are not available to estimate standard error and confidence interval. In this paper, the estimation of standard error and confidence interval of functional reliability estimates using computationally efficient re-sampling methods based on bootstrap technique are described. Numerical application of these methods, to quantify the variability of functional reliability estimates, is also explained.

The launch of Roll Back Malaria (RBM) initiative in the early 2000s marked the first serious international efforts to control, prevent and treat malaria in endemic countries of sub-Sahara Africa unparalleled since the demise of the global malaria eradication campaign in the 1960s. These efforts have led to accelerated scale-up of highly proven malaria interventions, that is, insecticide-treated nets, indoor residual spraying, and case management with artemisinin-based combination therapies. This has been followed by a decline of malaria morbidity and mortality in high endemic countries including Uganda which is ranked in the top six high-burden countries. Despite these achievements, malaria remains a major global public health problem and a leading cause of hospitalization and death in Uganda. The RBM support in Uganda has been extended to malaria surveillance specifically to strengthen the national Health Management Information System (HMIS), and periodical implementation of nationally representative household surveys such as Malaria Indicator Survey (MIS) and Demographic Health Surveys (DHS), and facility assessment surveys. The availability of these large datasets notwithstanding, their utilization remains low and the information extracted is limited to national averages that neither take into account subnational heterogeneities and disparities nor evaluate the effects of interventions and other important confounders on malaria burden changes in space and time. In this thesis, we developed Bayesian hierarchical geostatistical and spatio-temporal models for malaria surveillance data collected in Uganda during 2009-2017 to estimate malaria burden, assess interventions and health system-related effects on its changes, and forecast malaria cases to support early warning systems. These models fitted via Markov Chain Monte Carlo (MCMC) simulations offer the flexibility to incorporate correlation of malaria in space and time and can easily be extended to capture complex relationships.