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This article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the…

It is proposed in the literature that in some complicated problems maximum likelihood estimates (MLE) are not suitable or even do not exist. An alternative to MLE for estimation of the parameters is the Bayesian method. The Markov chain…

Particle Markov Chain Monte Carlo methods are used to carry out inference in non-linear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Current approaches usually perform…

Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…

Markov chain Monte Carlo (MCMC) algorithms are ubiquitous in Bayesian computations. However, they need to access the full data set in order to evaluate the posterior density at every step of the algorithm. This results in a great…

We propose a sequential Markov chain Monte Carlo (SMCMC) algorithm to sample from a sequence of probability distributions, corresponding to posterior distributions at different times in on-line applications. SMCMC proceeds as in usual MCMC…

A number of optimal decision problems with uncertainty can be formulated into a stochastic optimal control framework. The Least-Squares Monte Carlo (LSMC) algorithm is a popular numerical method to approach solutions of such stochastic…

Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across individual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from…

The examination of uncertainty in the predictions of machine learning (ML) models is receiving increasing attention. One uncertainty modeling technique used for this purpose is Monte-Carlo (MC)-Dropout, where repeated predictions are…

Markov Chain Monte Carlo (MCMC) methods have revolutionised Bayesian data analysis over the years by making the direct computation of posterior probability densities feasible on modern workstations. However, the calculation of the prior…

We present a data augmentation scheme to perform Markov chain Monte Carlo inference for models where data generation involves a rejection sampling algorithm. Our idea, which seems to be missing in the literature, is a simple scheme to…

A novel procedure is described for accelerating the convergence of Markov chain Monte Carlo computations. The algorithm uses an adaptive bootstrap technique to generate candidate steps in the Markov Chain. It is efficient for symmetric,…

The stochastic volatility model is a popular tool for modeling the volatility of assets. The model is a nonlinear and non-Gaussian state space model, and consequently is difficult to fit. Many approaches, both classical and Bayesian, have…

We propose a Bayesian tensor-on-tensor regression approach to predict a multidimensional array (tensor) of arbitrary dimensions from another tensor of arbitrary dimensions, building upon the Tucker decomposition of the regression…

Mixture models are becoming a popular tool for the clustering and classification of high-dimensional data. In such high dimensional applications, model selection is problematic. The Bayesian information criterion, which is popular in lower…

In many modern applications, there is interest in analyzing enormous data sets that cannot be easily moved across computers or loaded into memory on a single computer. In such settings, it is very common to be interested in clustering.…

The hybrid Monte Carlo (HMC) algorithm is used for Bayesian analysis of the generalized autoregressive conditional heteroscedasticity (GARCH) model. The HMC algorithm is one of Markov chain Monte Carlo (MCMC) algorithms and it updates all…

Dynamic Bayesian predictive synthesis is a formal approach to coherently synthesizing multiple predictive distributions into a single distribution. In sequential analysis, the computation of the synthesized predictive distribution has…

We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…

The past decades have seen enormous improvements in computational inference based on statistical models, with continual enhancement in a wide range of computational tools, in competition. In Bayesian inference, first and foremost, MCMC…