Related papers: Error estimation and reduction with cross correlat…
Thermal or finite-size scaling analyses of importance sampling Monte Carlo time series in the vicinity of phase transition points often combine different estimates for the same quantity, such as a critical exponent, with the intent to…
We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is…
The efficiency of a Markov chain Monte Carlo algorithm might be measured by the cost of generating one independent sample, or equivalently, the total cost divided by the effective sample size, defined in terms of the integrated…
Monte Carlo experiments produce samples in order to estimate features of a given distribution. However, simultaneous estimation of means and quantiles has received little attention, despite being common practice. In this setting we…
Markov Chain Monte Carlo (MCMC) methods for sampling probability density functions (combined with abundant computational resources) have transformed the sciences, especially in performing probabilistic inferences, or fitting models to data.…
Empirical relationships are derived for the expected sampling error of quantile estimations using Monte Carlo experiments for two frequency distributions frequently encountered in climate sciences. The relationships found are expressed as a…
Covariance matrix estimation, a classical statistical topic, poses significant challenges when the sample size is comparable to or smaller than the number of features. In this paper, we frame covariance matrix estimation as a compound…
Bias correction can often improve the finite sample performance of estimators. We show that the choice of bias correction method has no effect on the higher-order variance of semiparametrically efficient parametric estimators, so long as…
A general jackknife estimator for the asymptotic covariance of moment estimators is considered in the case when the sample is taken from a mixture with varying concentrations of components. Consistency of the estimator is demonstrated. A…
An increasing body of research focuses on using neural networks to model time series. A common assumption in training neural networks via maximum likelihood estimation on time series is that the errors across time steps are uncorrelated.…
Using the Ehrenfest urn model we illustrate the subtleties of error estimation in Monte Carlo simulations. We discuss how the smooth results of correlated sampling in Markov chains can fool one's perception of the accuracy of the data, and…
We employ the jackknife algorithm to analyze the propagation of the statistical quantum Monte Carlo error through the Bethe--Salpeter equation. This allows us to estimate the error of dynamical mean-field theory calculations of the…
Quasi-Monte Carlo sampling can attain far better accuracy than plain Monte Carlo sampling. However, with plain Monte Carlo sampling it is much easier to estimate the attained accuracy. This article describes methods old and new to quantify…
In Markov Chain Monte Carlo (MCMC) simulations, the thermal equilibria quantities are estimated by ensemble average over a sample set containing a large number of correlated samples. These samples are selected in accordance with the…
We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Further, we investigate techniques to estimate the associated…
Markov chain Monte Carlo algorithms are used to simulate from complex statistical distributions by way of a local exploration of these distributions. This local feature avoids heavy requests on understanding the nature of the target, but it…
When dealing with difficult inverse problems such as inverse rendering, using Monte Carlo estimated gradients to optimise parameters can slow down convergence due to variance. Averaging many gradient samples in each iteration reduces this…
Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…
There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…
We present correction terms that allow delete-one Jackknife and Bootstrap methods to be used to recover unbiased estimates of the data covariance matrix of the two-point correlation function $\xi\left(\mathbf{r}\right)$. We demonstrate the…