Related papers: Analytic Posteriors for Pearson's Correlation Coef…
A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…
Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only…
Specifying a Bayesian prior is notoriously difficult for complex models such as neural networks. Reasoning about parameters is made challenging by the high-dimensionality and over-parameterization of the space. Priors that seem benign and…
We explore the applicability of the causal analysis based on temporally shifted (lagged) Pearson correlation applied to diverse time series of different natures in context of the problem of financial market prediction. Theoretical…
Commonalities and differences in correlation analysis in terms of phase space, conditioning and uncorrelatedness are discussed. The Poisson process is not generally appropriate as reference distribution for normalisation and cumulants, so…
We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric…
A Poisson autoregressive (PAR) model accounting for discreteness and autocorrelation of count time series data is typically estimated in the state-space modelling framework through extended Kalman filter. However, because of the complex…
Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…
We propose a novel class of prior distributions for sequences of orthogonal functions, which are frequently required in various statistical models such as functional principal component analysis (FPCA). Our approach constructs priors…
Measuring the correlation (association) between two random variables is one of the important goals in statistical applications. In the literature, the covariance between two random variables is a widely used criterion in measuring the…
A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…
Prior elicitation methods for Bayesian analyses transfigure prior information into quantifiable prior distributions. Recently, methods that leverage copulas have been proposed to accommodate more flexible dependence structures when…
We consider the scenario where the parameters of a probabilistic model are expected to vary over time. We construct a novel prior distribution that promotes sparsity and adapts the strength of correlation between parameters at successive…
The Jaccard similarity index has often been employed in science and technology as a means to quantify the similarity between two sets. When modified to operate on real-valued values, the Jaccard similarity index can be applied to compare…
Nonparametric and nonlinear measures of statistical dependence between pairs of random variables are important tools in modern data analysis. In particular the emergence of large data sets can now support the relaxation of linearity…
Objective priors for sequential experiments are considered. Common priors, such as the Jeffreys prior and the reference prior, will typically depend on the stopping rule used for the sequential experiment. New expressions for reference…
The Pearson correlation coefficient is commonly used for quantifying the global level of degree-degree association in complex networks. Here, we use a probabilistic representation of the underlying network structure for assessing the…
Physics has been transforming our view of nature for centuries. While combining physical knowledge with computational approaches has enabled detailed modeling of physical systems' evolution, understanding the emergence of patterns and…
The covariance of two random variables measures the average joint deviations from their respective means. We generalise this well-known measure by replacing the means with other statistical functionals such as quantiles, expectiles, or…
This paper introduces a causation coefficient which is defined in terms of probabilistic causal models. This coefficient is suggested as the natural causal analogue of the Pearson correlation coefficient and permits comparing causation and…