Related papers: Probabilistic View of Explosion in an Inelastic Ka…
We introduce a global thermostat on Kac's 1D model for the velocities of particles in a space-homogeneous gas subjected to binary collisions, also interacting with a (local) Maxwellian thermostat. The global thermostat rescales the…
Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…
Little effort has been devoted to studying generalised notions or models of (un)predictability, yet is an important concept throughout physics and plays a central role in quantum information theory, where key results rely on the supposed…
Probabilistic rounding error analysis can yield much sharper bounds than classical worst-case theory, but existing results typically rely on zero-mean rounding errors and often leave the confidence parameter implicit. This work revisits…
A solution to control for nonresponse bias consists of multiplying the design weights of respondents by the inverse of estimated response probabilities to compensate for the nonrespondents. Maximum likelihood and calibration are two…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
We used Bayesian methods to compare the predictions of probabilistic risk assessment -- the theoretical tool used by the nuclear industry to predict the frequency of nuclear accidents -- with empirical data. The existing record of accidents…
Statistical modeling of multivariate and spatial extreme events has attracted broad attention in various areas of science. Max-stable distributions and processes are the natural class of models for this purpose, and many parametric families…
We consider a system of random autonomous ODEs introduced by Cugliandolo et al. [22], which serves as a non-relaxational analog of the gradient flow for the spherical p-spin model. The asymptotics for the expected number of equilibria in…
G. Edelman, O. Sporns, and G. Tononi have introduced the neural complexity of a family of random variables, defining it as a specific average of mutual information over subfamilies. We show that their choice of weights satisfies two natural…
A random neighbor extremal stick-slip model is introduced. In the thermodynamic limit, the distribution of states has a simple analytical form and the mean avalanche size, as a function of the coupling parameter, is exactly calculable. The…
Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…
Graham, Knuth and Patashnik in their book Concrete Mathematics called for development of a general theory of the solutions of recurrences defined by $$\left|{ n\atop k}\right|=(\alpha n+\beta k+\gamma)\left|{n-1\atop k}\right|+(\alpha'…
A mapping of nonextensive statistical mechanics into Gibbs' statistical mechanics exists, which leads to a generalization of Einstein's formula for fluctuations. A unified treatment of stability of relaxed states in nonextensive statistical…
Let $p_n(y)=\sum_k\hat{\alpha}_k\phi(y-k)+\sum_{l=0}^{j_n-1}\sum_k\hat {\beta}_{lk}2^{l/2}\psi(2^ly-k)$ be the linear wavelet density estimator, where $\phi$, $\psi$ are a father and a mother wavelet (with compact support),…
A process-theoretic approach to electrodynamics based on persistent Kac-type stochastic processes is developed. Finite-velocity stochastic propagation is taken as primary, while relativistic wave equations arise as emergent descriptions…
Inspired by reliability issues in electric transmission networks, we use a probabilistic approach to study the occurrence of large failures in a stylized cascading failure model. In this model, lines have random capacities that initially…
Probabilistic principal component analysis (PCA) and its Bayesian variant (BPCA) are widely used for dimension reduction in machine learning and statistics. The main advantage of probabilistic PCA over the traditional formulation is…
In statistics, assuming samples are independent is reasonable. However, this property can fail to hold for the features, a distinction that has led to several lines of work aiming to remove the latter assumption of independence present in…
Basel II and Solvency 2 both use the Value-at-Risk (VaR) as the risk measure to compute the Capital Requirements. In practice, to calibrate the VaR, a normal approximation is often chosen for the unknown distribution of the yearly log…