Related papers: Adaptive Importance Sampling via Stochastic Convex…
We analyze the optimized adaptive importance sampler (OAIS) for performing Monte Carlo integration with general proposals. We leverage a classical result which shows that the bias and the mean-squared error (MSE) of the importance sampling…
In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…
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 consider the problem of unconstrained minimization of a smooth objective function in $\R^n$ in a setting where only function evaluations are possible. While importance sampling is one of the most popular techniques used by machine…
Monte Carlo methods can provide accurate p-value estimates of word counting test statistics and are easy to implement. They are especially attractive when an asymptotic theory is absent or when either the search sequence or the word pattern…
Importance sampling (IS) is a powerful Monte Carlo methodology for the approximation of intractable integrals, very often involving a target probability density function. The performance of IS heavily depends on the appropriate selection of…
Recent research has developed several Monte Carlo methods for estimating the normalization constant (partition function) based on the idea of annealing. This means sampling successively from a path of distributions that interpolate between…
This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the…
Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution whose multivariate nature has so far been ignored in the MCMC…
Model fitting is possibly the most extended problem in science. Classical approaches include the use of least-squares fitting procedures and maximum likelihood methods to estimate the value of the parameters in the model. However, in recent…
Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics…
Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…
Random sampling is an essential tool in the processing and transmission of data. It is used to summarize data too large to store or manipulate and meet resource constraints on bandwidth or battery power. Estimators that are applied to the…
We consider the problem of choosing design parameters to minimize the probability of an undesired rare event that is described through the average of $n$ iid random variables. Since the probability of interest for near optimal design…
Importance sampling of target probability distributions belonging to a given convex class is considered. Motivated by previous results, the cost of importance sampling is quantified using the relative entropy of the target with respect to…
Model comparison for the purposes of selection, averaging and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of models within a…
We present two Monte Carlo sampling algorithms for probabilistic inference that guarantee polynomial-time convergence for a larger class of network than current sampling algorithms provide. These new methods are variants of the known…
The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…
We introduce new quantile estimators with adaptive importance sampling. The adaptive estimators are based on weighted samples that are neither independent nor identically distributed. Using a new law of iterated logarithm for martingales,…
We motive and calculate Newton--Cotes quadrature integration variance and compare it directly with Monte Carlo (MC) integration variance. We find an equivalence between deterministic quadrature sampling and random MC sampling by noting that…