Related papers: An efficient estimation of nested expectations wit…
We present a new unbiased algorithm that estimates the expected value of f(U) via Monte Carlo simulation, where U is a vector of d independent random variables, and f is a function of d variables. We assume that f does not depend equally on…
Probabilistic prediction of sequences from images and other high-dimensional data is a key challenge, particularly in risk-sensitive applications. In these settings, it is often desirable to quantify the uncertainty associated with the…
Constructing unbiased estimators from Markov chain Monte Carlo (MCMC) outputs is a difficult problem that has recently received a lot of attention in the statistics and machine learning communities. However, the current unbiased MCMC…
Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…
Nested simulation encompasses the estimation of functionals linked to conditional expectations through simulation techniques. In this paper, we treat conditional expectation as a function of the multidimensional conditioning variable and…
In the nano era in integrated circuit fabrication technologies, the performance variability due to statistical process and circuit parameter variations is becoming more and more significant. Considerable effort has been expended in the EDA…
Nested Sampling is a method for computing the Bayesian evidence, also called the marginal likelihood, which is the integral of the likelihood with respect to the prior. More generally, it is a numerical probabilistic quadrature rule. The…
To increase statistical efficiency in a randomized experiment, researchers often use stratification (i.e., blocking) in the design stage. However, conventional practices of stratification fail to exploit valuable information about the…
We propose a novel method for estimating nonseparable selection models. We show that, for a given selection function, the potential outcome distributions are nonparametrically identified from the selected outcome distributions and can be…
Sobol' sensitivity index estimators for stochastic models are functions of nested Monte Carlo estimators, which are estimators built from two nested Monte Carlo loops. The outer loop explores the input space and, for each of the…
Most solved dynamic structural macrofinance models are non-linear and/or non-Gaussian state-space models with high-dimensional and complex structures. We propose an annealed controlled sequential Monte Carlo method that delivers numerically…
In this paper we develop a methodology that we call split sampling methods to estimate high dimensional expectations and rare event probabilities. Split sampling uses an auxiliary variable MCMC simulation and expresses the expectation of…
In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential…
Model performance evaluation is a critical and expensive task in machine learning and computer vision. Without clear guidelines, practitioners often estimate model accuracy using a one-time completely random selection of the data. However,…
For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed…
The order of convergence of the Monte Carlo method is 1/2 which means that we need quadruple samples to decrease the error in half in the numerical simulation. Multilevel Monte Carlo methods reach the same order of error by spending less…
Conditional Monte Carlo refers to sampling from the conditional distribution of a random vector X given the value T(X) = t for a function T(X). Classical conditional Monte Carlo methods were designed for estimating conditional expectations…
Although a few methods have been developed recently for building confidence intervals after model selection, how to construct confidence sets for joint post-selection inference is still an open question. In this paper, we develop a new…
Tempering is a popular tool in Bayesian computation, being used to transform a posterior distribution $p_1$ into a reference distribution $p_0$ that is more easily approximated. Several algorithms exist that start by approximating $p_0$ and…
We introduce a class of Monte Carlo estimators that aim to overcome the rapid growth of variance with dimension often observed for standard estimators by exploiting the target's independence structure. We identify the most basic…