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Marginal structural models (MSMs) allow for causal analysis of longitudinal data. The MSMs were originally developed as discrete time models. Recently, continuous-time MSMs were presented as a conceptually appealing alternative for survival…
We propose a class of discrete state sampling algorithms based on Nesterov's accelerated gradient method, which extends the classical Metropolis-Hastings (MH) algorithm. The evolution of the discrete states probability distribution governed…
We demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of Markov Chain Monte Carlo (MCMC) algorithms as a function of the target density and proposal density. The bound relies on…
The histogram reweighting technique, widely used to analyze Monte Carlo data, is shown to be applicable to dynamic properties obtained from Molecular Dynamics simulations. The theory presented here is based on the fact that the correlation…
We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach…
We study the performance of a stochastic algorithm based on the power method that adaptively learns the large deviation functions characterizing the fluctuations of additive functionals of Markov processes, used in physics to model…
In this paper, we propose an efficient simulation method based on adaptive importance sampling, which can automatically find the optimal proposal within the Gaussian family based on previous samples, to evaluate the probability of bit error…
We propose a class of strongly efficient rare event simulation estimators for random walks and compound Poisson processes with a regularly varying increment/jump-size distribution in a general large deviations regime. Our estimator is based…
This paper presents the development of an algorithm, termed the Global-Local Hybrid Surrogate (GLHS), designed to efficiently compute the probability of rare failure events in complex systems. The primary goal is to enhance the accuracy of…
We propose a new sampling algorithm combining two quite powerful ideas in the Markov chain Monte Carlo literature -- adaptive Metropolis sampler and two-stage Metropolis-Hastings sampler. The proposed sampling method will be particularly…
Estimating the probability of failure is a critical step in developing safety-critical autonomous systems. Direct estimation methods such as Monte Carlo sampling are often impractical due to the rarity of failures in these systems. Existing…
Adaptive importance sampling is a powerful tool to sample from complicated target densities, but its success depends sensitively on the initial proposal density. An algorithm is presented to automatically perform the initialization using…
This paper studies a non-random-walk Markov Chain Monte Carlo method, namely the Hamiltonian Monte Carlo (HMC) method in the context of Subset Simulation used for structural reliability analysis. The HMC method relies on a deterministic…
Approximate Bayesian computation (ABC) methods permit approximate inference for intractable likelihoods when it is possible to simulate from the model. However they perform poorly for high dimensional data, and in practice must usually be…
Molecular motors and other complex nonequilibrium systems are controlled by large sets of design parameters, and optimizing those parameters requires computing sensitivities -- derivatives of dynamical observables with respect to the…
This work investigates the computational burden of pricing binary options in rare event regimes and introduces an adaptation of the adaptive multilevel splitting (AMS) method for financial derivatives. Standard Monte Carlo becomes…
This paper considers robust modeling of the survival time for cancer patients. Accurate prediction can be helpful for developing therapeutic and care strategies. We propose a unified Expectation-Maximization approach combined with the…
A hybrid censoring scheme is a mixture of Type-I and Type-II censoring schemes. We study the estimation of parameters of weighted exponential distribution based on Type-II hybrid censored data. By applying EM algorithm, maximum likelihood…
The semiparametric accelerated failure time model is not as widely used as the Cox relative risk model mainly due to computational difficulties. Recent developments in least squares estimation and induced smoothing estimating equations…
Failure probability evaluation for complex physical and engineering systems governed by partial differential equations (PDEs) are computationally intensive, especially when high-dimensional random parameters are involved. Since standard…