Academic literature on the topic 'Monte Carlo Markov Chains (MCMC)'

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Journal articles on the topic "Monte Carlo Markov Chains (MCMC)"

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Siems, Tobias. "Markov Chain Monte Carlo on finite state spaces." Mathematical Gazette 104, no. 560 (2020): 281–87. http://dx.doi.org/10.1017/mag.2020.51.

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We elaborate the idea behind Markov chain Monte Carlo (MCMC) methods in a mathematically coherent, yet simple and understandable way. To this end, we prove a pivotal convergence theorem for finite Markov chains and a minimal version of the Perron-Frobenius theorem. Subsequently, we briefly discuss two fundamental MCMC methods, the Gibbs and Metropolis-Hastings sampler. Only very basic knowledge about matrices, convergence of real sequences and probability theory is required.
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Roy, Vivekananda. "Convergence Diagnostics for Markov Chain Monte Carlo." Annual Review of Statistics and Its Application 7, no. 1 (2020): 387–412. http://dx.doi.org/10.1146/annurev-statistics-031219-041300.

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Markov chain Monte Carlo (MCMC) is one of the most useful approaches to scientific computing because of its flexible construction, ease of use, and generality. Indeed, MCMC is indispensable for performing Bayesian analysis. Two critical questions that MCMC practitioners need to address are where to start and when to stop the simulation. Although a great amount of research has gone into establishing convergence criteria and stopping rules with sound theoretical foundation, in practice, MCMC users often decide convergence by applying empirical diagnostic tools. This review article discusses the
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Koike, Takaaki, and Marius Hofert. "Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations." Risks 8, no. 1 (2020): 6. http://dx.doi.org/10.3390/risks8010006.

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In this paper, we propose a novel framework for estimating systemic risk measures and risk allocations based on Markov Chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the jth conditional marginal loss distribution given the so-called crisis event. By considering a crisis event as an intersection of linear constraints, this class of allocations covers, for example, conditional Value-at-Risk (CoVaR), conditional expected shortfall (CoES), VaR contributions, and range VaR (RVaR) contributions as special cases. For thi
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Stathopoulos, Vassilios, and Mark A. Girolami. "Markov chain Monte Carlo inference for Markov jump processes via the linear noise approximation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1984 (2013): 20110541. http://dx.doi.org/10.1098/rsta.2011.0541.

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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 all
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Chaudhary, A. K. "Bayesian Analysis of Two Parameter Complementary Exponential Power Distribution." NCC Journal 3, no. 1 (2018): 1–23. http://dx.doi.org/10.3126/nccj.v3i1.20244.

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In this paper, the Markov chain Monte Carlo (MCMC) method is used to estimate the parameters of CEP distribution based on a complete sample. A procedure is developed to obtain Bayes estimates of the parameters of the CEP distribution using Markov Chain Monte Carlo (MCMC) simulation method in OpenBUGS, established software for Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. The MCMC methods have been shown to be easier to implement computationally, the estimates always exist and are statistically consistent, and their probability intervals are convenient to construct. The R fun
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Chaudhary, Arun Kumar, and Vijay Kumar. "A Bayesian Estimation and Predictionof Gompertz Extension Distribution Using the MCMC Method." Nepal Journal of Science and Technology 19, no. 1 (2020): 142–60. http://dx.doi.org/10.3126/njst.v19i1.29795.

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In this paper, the Markov chain Monte Carlo (MCMC) method is used to estimate the parameters of the Gompertz extension distribution based on a complete sample. We have developed a procedure to obtain Bayes estimates of the parameters of the Gompertz extension distribution using Markov Chain Monte Carlo (MCMC) simulation method in OpenBUGS, established software for Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. We have obtained the Bayes estimates of the parameters, hazard and reliability functions, and their probability intervals are also presented. We have applied the predic
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Chaudhary, A. K. "A Study of Perks-II Distribution via Bayesian Paradigm." Pravaha 24, no. 1 (2018): 1–17. http://dx.doi.org/10.3126/pravaha.v24i1.20221.

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In this paper, the Markov chain Monte Carlo (MCMC) method is used to estimate the parameters of Perks-II distribution based on a complete sample. The procedures are developed to perform full Bayesian analysis of the Perks-II distributions using Markov Chain Monte Carlo (MCMC) simulation method in OpenBUGS, established software for Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. We have obtained the Bayes estimates of the parameters, hazard and reliability functions, and their probability intervals are also presented. We have also discussed the issue of model compatibility for
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Müller, Christian, Fabian Weysser, Thomas Mrziglod, and Andreas Schuppert. "Markov-Chain Monte-Carlo methods and non-identifiabilities." Monte Carlo Methods and Applications 24, no. 3 (2018): 203–14. http://dx.doi.org/10.1515/mcma-2018-0018.

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Abstract We consider the problem of sampling from high-dimensional likelihood functions with large amounts of non-identifiabilities via Markov-Chain Monte-Carlo algorithms. Non-identifiabilities are problematic for commonly used proposal densities, leading to a low effective sample size. To address this problem, we introduce a regularization method using an artificial prior, which restricts non-identifiable parts of the likelihood function. This enables us to sample the posterior using common MCMC methods more efficiently. We demonstrate this with three MCMC methods on a likelihood based on a
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Shadare, A. E., M. N. O. Sadiku, and S. M. Musa. "Markov Chain Monte Carlo Solution of Poisson’s Equation in Axisymmetric Regions." Advanced Electromagnetics 8, no. 5 (2019): 29–36. http://dx.doi.org/10.7716/aem.v8i5.1255.

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The advent of the Monte Carlo methods to the field of EM have seen floating random walk, fixed random walk and Exodus methods deployed to solve Poisson’s equation in rectangular coordinate and axisymmetric solution regions. However, when considering large EM domains, classical Monte Carlo methods could be time-consuming because they calculate potential one point at a time. Thus, Markov Chain Monte Carlo (MCMC) is generally preferred to other Monte Carlo methods when considering whole-field computation. In this paper, MCMC has been applied to solve Poisson’s equation in homogeneous and inhomoge
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Finke, Axel, Arnaud Doucet, and Adam M. Johansen. "Limit theorems for sequential MCMC methods." Advances in Applied Probability 52, no. 2 (2020): 377–403. http://dx.doi.org/10.1017/apr.2020.9.

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AbstractBoth sequential Monte Carlo (SMC) methods (a.k.a. ‘particle filters’) and sequential Markov chain Monte Carlo (sequential MCMC) methods constitute classes of algorithms which can be used to approximate expectations with respect to (a sequence of) probability distributions and their normalising constants. While SMC methods sample particles conditionally independently at each time step, sequential MCMC methods sample particles according to a Markov chain Monte Carlo (MCMC) kernel. Introduced over twenty years ago in [6], sequential MCMC methods have attracted renewed interest recently as
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Dissertations / Theses on the topic "Monte Carlo Markov Chains (MCMC)"

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Lindsten, Fredrik. "Particle filters and Markov chains for learning of dynamical systems." Doctoral thesis, Linköpings universitet, Reglerteknik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-97692.

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Sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) methods provide computational tools for systematic inference and learning in complex dynamical systems, such as nonlinear and non-Gaussian state-space models. This thesis builds upon several methodological advances within these classes of Monte Carlo methods.Particular emphasis is placed on the combination of SMC and MCMC in so called particle MCMC algorithms. These algorithms rely on SMC for generating samples from the often highly autocorrelated state-trajectory. A specific particle MCMC algorithm, referred to as particle Gibbs
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Browne, William J. "Applying MCMC methods to multi-level models." Thesis, University of Bath, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.268210.

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Guha, Subharup. "Benchmark estimation for Markov Chain Monte Carlo samplers." The Ohio State University, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=osu1085594208.

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Angelino, Elaine Lee. "Accelerating Markov chain Monte Carlo via parallel predictive prefetching." Thesis, Harvard University, 2014. http://nrs.harvard.edu/urn-3:HUL.InstRepos:13070022.

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We present a general framework for accelerating a large class of widely used Markov chain Monte Carlo (MCMC) algorithms. This dissertation demonstrates that MCMC inference can be accelerated in a model of parallel computation that uses speculation to predict and complete computational work ahead of when it is known to be useful. By exploiting fast, iterative approximations to the target density, we can speculatively evaluate many potential future steps of the chain in parallel. In Bayesian inference problems, this approach can accelerate sampling from the target distribution, without compromis
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Durmus, Alain. "High dimensional Markov chain Monte Carlo methods : theory, methods and applications." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLT001/document.

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L'objet de cette thèse est l'analyse fine de méthodes de Monte Carlopar chaînes de Markov (MCMC) et la proposition de méthodologies nouvelles pour échantillonner une mesure de probabilité en grande dimension. Nos travaux s'articulent autour de trois grands sujets.Le premier thème que nous abordons est la convergence de chaînes de Markov en distance de Wasserstein. Nous établissons des bornes explicites de convergence géométrique et sous-géométrique. Nous appliquons ensuite ces résultats à l'étude d'algorithmes MCMC. Nous nous intéressons à une variante de l'algorithme de Metropolis-Langevin aj
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Lindahl, John, and Douglas Persson. "Data-driven test case design of automatic test cases using Markov chains and a Markov chain Monte Carlo method." Thesis, Malmö universitet, Fakulteten för teknik och samhälle (TS), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-43498.

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Large and complex software that is frequently changed leads to testing challenges. It is well established that the later a fault is detected in software development, the more it costs to fix. This thesis aims to research and develop a method of generating relevant and non-redundant test cases for a regression test suite, to catch bugs as early in the development process as possible. The research was executed at Axis Communications AB with their products and systems in mind. The approach utilizes user data to dynamically generate a Markov chain model and with a Markov chain Monte Carlo method,
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Harkness, Miles Adam. "Parallel simulation, delayed rejection and reversible jump MCMC for object recognition." Thesis, University of Bristol, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.324266.

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Smith, Corey James. "Exact Markov Chain Monte Carlo with Likelihood Approximations for Functional Linear Models." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1531833318013379.

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Walker, Neil Rawlinson. "A Bayesian approach to the job search model and its application to unemployment durations using MCMC methods." Thesis, University of Newcastle Upon Tyne, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299053.

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Jeon, Juncheol. "Deterioration model for ports in the Republic of Korea using Markov chain Monte Carlo with multiple imputation." Thesis, University of Dundee, 2019. https://discovery.dundee.ac.uk/en/studentTheses/1cc538ea-1468-4d51-bcf8-711f8b9912f9.

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Condition of infrastructure is deteriorated over time as it gets older. It is the deterioration model that predicts how and when facilities will deteriorate over time. In most infrastructure management system, the deterioration model is a crucial element. Using the deterioration model, it is very helpful to estimate when repair will be carried out, how much will be needed for the maintenance of the entire facilities, and what maintenance costs will be required during the life cycle of the facility. However, the study of deterioration model for civil infrastructures of ports is still in its inf
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Books on the topic "Monte Carlo Markov Chains (MCMC)"

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Cowles, Mary Kathryn. Possible biases induced by MCMC convergence diagnostics. University of Toronto, Dept. of Statistics, 1997.

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Brémaud, Pierre. Markov chains: Gibbs fields, Monte Carlo simulation, and queues. Springer, 1999.

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1947-, Gianola Daniel, ed. Likelihood, Bayesian and MCMC methods in quantitative genetics. Springer-Verlag, 2002.

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Nicol, David M. Automated parallelization of discrete state-space generation. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2000.

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Nicol, David M. Automated parallelization of discrete state-space generation. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2000.

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Cheng, Russell. Finite Mixture Models. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0017.

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Fitting a finite mixture model when the number of components, k, is unknown can be carried out using the maximum likelihood (ML) method though it is non-standard. Two well-known Bayesian Markov chain Monte Carlo (MCMC) methods are reviewed and compared with ML: the reversible jump method and one using an approximating Dirichlet process. Another Bayesian method, to be called MAPIS, is examined that first obtains point estimates for the component parameters by the maximum a posteriori method for different k and then estimates posterior distributions, including that for k, using importance sampli
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Martin, Andrew D. Bayesian Analysis. Edited by Janet M. Box-Steffensmeier, Henry E. Brady, and David Collier. Oxford University Press, 2009. http://dx.doi.org/10.1093/oxfordhb/9780199286546.003.0021.

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This article surveys modern Bayesian methods of estimating statistical models. It first provides an introduction to the Bayesian approach for statistical inference, contrasting it with more conventional approaches. It then explains the Monte Carlo principle and reviews commonly used Markov Chain Monte Carlo (MCMC) methods. This is followed by a practical justification for the use of Bayesian methods in the social sciences, and a number of examples from the literature where Bayesian methods have proven useful are shown. The article finally provides a review of modern software for Bayesian infer
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Coolen, A. C. C., A. Annibale, and E. S. Roberts. Graphs with hard constraints: further applications and extensions. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0007.

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This chapter looks at further topics pertaining to the effective use of Markov Chain Monte Carlo to sample from hard- and soft-constrained exponential random graph models. The chapter considers the question of how moves can be sampled efficiently without introducing unintended bias. It is shown mathematically and numerically that apparently very similar methods of picking out moves can give rise to significant differences in the average topology of the networks generated by the MCMC process. The general discussion in complemented with pseudocode in the relevant section of the Algorithms chapte
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Henderson, Daniel A., R. J. Boys, Carole J. Proctor, and Darren J. Wilkinson. Linking systems biology models to data: A stochastic kinetic model of p53 oscillations. Edited by Anthony O'Hagan and Mike West. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198703174.013.7.

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This article discusses the use of a stochastic kinetic model to study protein level oscillations in single living cancer cells, using the p53 and Mdm2 proteins as examples. It describes the refinement of a dynamic stochastic process model of the cellular response to DNA damage and compares this model to time course data on the levels of p53 and Mdm2. The article first provides a biological background on p53 and Mdm2 before explaining how the stochastic kinetic model is constructed. It then introduces the stochastic kinetic model and links it to the data and goes on to apply sophisticated MCMC
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Quintana, José Mario, Carlos Carvalho, James Scott, and Thomas Costigliola. Extracting S&P500 and NASDAQ Volatility: The Credit Crisis of 2007–2008. Edited by Anthony O'Hagan and Mike West. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198703174.013.13.

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This article demonstrates the utility of Bayesian modelling and inference in financial market volatility analysis, using the 2007-2008 credit crisis as a case study. It first describes the applied problem and goal of the Bayesian analysis before introducing the sequential estimation models. It then discusses the simulation-based methodology for inference, including Markov chain Monte Carlo (MCMC) and particle filtering methods for filtering and parameter learning. In the study, Bayesian sequential model choice techniques are used to estimate volatility and volatility dynamics for daily data fo
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Book chapters on the topic "Monte Carlo Markov Chains (MCMC)"

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Robert, Christian P., and Sylvia Richardson. "Markov Chain Monte Carlo Methods." In Discretization and MCMC Convergence Assessment. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1716-9_1.

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Zhang, Yan. "Markov Chain Monte Carlo (MCMC) Simulations." In Encyclopedia of Systems Biology. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_403.

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Bhattacharya, Rabi, Lizhen Lin, and Victor Patrangenaru. "Markov Chain Monte Carlo (MCMC) Simulation and Bayes Theory." In Springer Texts in Statistics. Springer New York, 2016. http://dx.doi.org/10.1007/978-1-4939-4032-5_14.

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Walgama Wellalage, N. K., Tieling Zhang, Richard Dwight, and Khaled El-Akruti. "Bridge Deterioration Modeling by Markov Chain Monte Carlo (MCMC) Simulation Method." In Lecture Notes in Mechanical Engineering. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09507-3_47.

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Lundén, Daniel, Johannes Borgström, and David Broman. "Correctness of Sequential Monte Carlo Inference for Probabilistic Programming Languages." In Programming Languages and Systems. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72019-3_15.

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AbstractProbabilistic programming is an approach to reasoning under uncertainty by encoding inference problems as programs. In order to solve these inference problems, probabilistic programming languages (PPLs) employ different inference algorithms, such as sequential Monte Carlo (SMC), Markov chain Monte Carlo (MCMC), or variational methods. Existing research on such algorithms mainly concerns their implementation and efficiency, rather than the correctness of the algorithms themselves when applied in the context of expressive PPLs. To remedy this, we give a correctness proof for SMC methods in the context of an expressive PPL calculus, representative of popular PPLs such as WebPPL, Anglican, and Birch. Previous work have studied correctness of MCMC using an operational semantics, and correctness of SMC and MCMC in a denotational setting without term recursion. However, for SMC inference—one of the most commonly used algorithms in PPLs as of today—no formal correctness proof exists in an operational setting. In particular, an open question is if the resample locations in a probabilistic program affects the correctness of SMC. We solve this fundamental problem, and make four novel contributions: (i) we extend an untyped PPL lambda calculus and operational semantics to include explicit resample terms, expressing synchronization points in SMC inference; (ii) we prove, for the first time, that subject to mild restrictions, any placement of the explicit resample terms is valid for a generic form of SMC inference; (iii) as a result of (ii), our calculus benefits from classic results from the SMC literature: a law of large numbers and an unbiased estimate of the model evidence; and (iv) we formalize the bootstrap particle filter for the calculus and discuss how our results can be further extended to other SMC algorithms.
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Amiri, Esmail. "Bayesian Automatic Parameter Estimation of Threshold Autoregressive (TAR) Models using Markov Chain Monte Carlo (MCMC)." In Compstat. Physica-Verlag HD, 2002. http://dx.doi.org/10.1007/978-3-642-57489-4_24.

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Shiao, Michael, Tzi-Kang Chen, and Zhu Mao. "Probabilistic Maintenance-Free Operating Period via Bayesian Filter with Markov Chain Monte Carlo (MCMC) Simulations and Subset Simulation." In Model Validation and Uncertainty Quantification, Volume 3. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74793-4_27.

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Bonamente, Massimiliano. "Monte Carlo Markov Chains." In Statistics and Analysis of Scientific Data. Springer New York, 2016. http://dx.doi.org/10.1007/978-1-4939-6572-4_16.

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Brémaud, Pierre. "Monte Carlo Markov Chains." In Texts in Applied Mathematics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45982-6_11.

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Bonamente, Massimiliano. "Markov Chains and Monte Carlo Markov Chains." In Statistics and Analysis of Scientific Data. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7984-0_10.

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Conference papers on the topic "Monte Carlo Markov Chains (MCMC)"

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Vaiciulyte, Ingrida. "Adaptive Monte-Carlo Markov chain for multivariate statistical estimation." In International Workshop of "Stochastic Programming for Implementation and Advanced Applications". The Association of Lithuanian Serials, 2012. http://dx.doi.org/10.5200/stoprog.2012.21.

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The estimation of the multivariate skew t-distribution by the Monte-Carlo Markov Chain (MCMC) method is considered in the paper. Thus, the MCMC procedure is constructed for recurrent estimation of skew t-distribution, following the maximum likelihood method, where the Monte-Carlo sample size is regulated to ensure the convergence and to decrease the total amount of Monte-Carlo trials, required for estimation. The confidence intervals of Monte-Carlo estimators are introduced because of their asymptotic normality. The termination rule is also implemented by testing statistical hypotheses on an i
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Auvinen, Harri, Tuomo Raitio, Samuli Siltanen, and Paavo Alku. "Utilizing Markov chain Monte Carlo (MCMC) method for improved glottal inverse filtering." In Interspeech 2012. ISCA, 2012. http://dx.doi.org/10.21437/interspeech.2012-450.

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Garcia, Edwin M., Alexander Aguila, Idi Isaac, Jorge W. Gonzalez, and Gabriel Lopez. "Analysis of voltage profile to determine energy demand using Monte Carlo algorithms and Markov Chains (MCMC)." In 2016 51st International Universities Power Engineering Conference (UPEC). IEEE, 2016. http://dx.doi.org/10.1109/upec.2016.8114092.

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Emery, A. F., and E. Valenti. "Estimating Parameters of a Packed Bed by Least Squares and Markov Chain Monte Carlo." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-82086.

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Most parameter estimation is based upon the assumption of normally distributed errors using least squares and the confidence intervals are computed from the sensitivities and the statistics of the residuals. For nonlinear problems, the assumption of a normal distribution of the parameters may not be valid. Determining the probability density distribution can be difficult, particularly when there is more than one parameter to be estimated or there is uncertainty about other parameters. An alternative approach is Bayesian inference, but the numerical computations can be expensive. Markov Chain M
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ur Rehman, M. Javvad, Sarat Chandra Dass, and Vijanth Sagayan Asirvadam. "Markov chain Monte Carlo (MCMC) method for parameter estimation of nonlinear dynamical systems." In 2015 IEEE International Conference on Signal and Image Processing Applications (ICSIPA). IEEE, 2015. http://dx.doi.org/10.1109/icsipa.2015.7412154.

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Hassan, Badreldin G. H., Isameldin A. Atiem, and Ping Feng. "Rainfall Frequency Analysis of Sudan by Using Bayesian Markov chain Monte Carlo (MCMC) methods." In 2013 International Conference on Information Science and Technology Applications. Atlantis Press, 2013. http://dx.doi.org/10.2991/icista.2013.21.

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Niaki, Farbod Akhavan, Durul Ulutan, and Laine Mears. "Parameter Estimation Using Markov Chain Monte Carlo Method in Mechanistic Modeling of Tool Wear During Milling." In ASME 2015 International Manufacturing Science and Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/msec2015-9357.

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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 pa
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Agdas, Duzgun, Michael T. Davidson, and Ralph D. Ellis. "Efficiency Comparison of Markov Chain Monte Carlo Simulation with Subset Simulation (MCMC/ss) to Standard Monte Carlo Simulation (sMC) for Extreme Event Scenarios." In First International Symposium on Uncertainty Modeling and Analysis and Management (ICVRAM 2011); and Fifth International Symposium on Uncertainty Modeling and Anaylsis (ISUMA). American Society of Civil Engineers, 2011. http://dx.doi.org/10.1061/41170(400)11.

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Park, Jae Phil, Subhasish Mohanty, and Chi Bum Bahn. "Time-Series Fatigue Damage States Forecasting and Probabilistic Environmental Fatigue Life Prediction Using Markov-Chain-Monte-Carlo Techniques." In ASME 2019 Pressure Vessels & Piping Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/pvp2019-93955.

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Abstract In general, probabilistic fatigue life estimation were performed using Weibull analysis and end-of-life fatigue data. This is basically using traditional strain/stress ∼ life (S∼N) data. Although it is always better to estimate the reliability of a component based on probabilistic evaluation of end-of-life data, it may not be always possible to conduct hundreds of costly and time-consuming fatigue experiments for each and every different loading case. The strain/stress ∼ life data are mostly related to push-pull type symmetric (R = −1) loading cases and the traditional Weibull probabi
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He, Xin, Brian S. Caffo, and Eric C. Frey. "Markov chain Monte Carlo (MCMC) based ideal observer estimation using a parameterized phantom and a pre-calculated dataset." In Medical Imaging, edited by Yulei Jiang and Berkman Sahiner. SPIE, 2007. http://dx.doi.org/10.1117/12.710173.

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