Related papers: Monte Carlo error analyses of Spearman's rank test
Mutual information is an important measure of the dependence among variables. It has become widely used in statistics, machine learning, biology, etc. However, the standard techniques for estimating it often perform poorly in higher…
It is a well-known rule of thumb that approximations of stochastic partial differential equations have essentially twice the order of weak convergence compared to the corresponding order of strong convergence. This is already known for many…
It is an important inferential problem to test no association between two binary variables based on data. Tests based on the sample odds ratio are commonly used. We bring in a competing test based on the Pearson correlation coefficient. In…
A group of approaches for calculating forensic likelihood ratios first calculates scores which quantify the degree of difference or the degree of similarity between pairs of samples, then converts those scores to likelihood ratios. In order…
The aim of this paper is to describe a new an integrated methodology for project control under uncertainty. This proposal is based on Earned Value Methodology and risk analysis and presents several refinements to previous methodologies.…
Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
Several statistics used by physicists to declare the signal observability over the background are compared. It is shown that the frequentist method of testing a precise hypothesis allows one to estimate the power value of criteria with…
In Monte Carlo integration an accurate and reliable determination of the numerical intregration error is essential. We point out the need for an independent estimate of the error on this error, for which we present an unbiased estimator. In…
We present a practical implementation of a Monte Carlo method to estimate the significance of cross-correlations in unevenly sampled time series of data, whose statistical properties are modeled with a simple power-law power spectral…
Using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance…
Multiple correlation is a fundamental concept with broad applications. The classical multiple correlation coefficient is developed to assess how strongly a dependent variable is associated with a linear combination of independent variables.…
We propose three physical tests to measure correlations in random numbers used in Monte Carlo simulations. The first test uses autocorrelation times of certain physical quantities when the Ising model is simulated with the Wolff algorithm.…
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…
Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation,…
Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over 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…
Observations of gravitational waves emitted by merging compact binaries have provided tantalising hints about stellar astrophysics, cosmology, and fundamental physics. However, the physical parameters describing the systems, (mass, spin,…
Sequential Monte Carlo (SMC) methods are widely used to draw samples from intractable target distributions. Particle degeneracy can hinder the use of SMC when the target distribution is highly constrained or multimodal. As a motivating…
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…