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A representation of Gaussian distributed sparsely sampled longitudinal data in terms of predictive distributions for their functional principal component scores (FPCs) maps available data for each subject to a multivariate Gaussian…
The widespread use of Markov Chain Monte Carlo (MCMC) methods for high-dimensional applications has motivated research into the scalability of these algorithms with respect to the dimension of the problem. Despite this, numerous problems…
Approximate Bayesian Computation (ABC) has become one of the major tools of likelihood-free statistical inference in complex mathematical models. Simultaneously, stochastic differential equations (SDEs) have developed to an established tool…
We study the relaxation dynamics of a coarse-grained polymer chain at different degrees of stretching by both analytical means and numerical simulations. The macromolecule is modelled as a string of beads, connected by anharmonic springs,…
Gaussian process (GP) models that combine both categorical and continuous input variables have found use in analysis of longitudinal data and computer experiments. However, standard inference for these models has the typical cubic scaling,…
Gaussian mixture distributions are commonly employed to represent general probability distributions. Despite the importance of using Gaussian mixtures for uncertainty estimation, the entropy of a Gaussian mixture cannot be calculated…
Discrepancy measures between probability distributions, often termed statistical distances, are ubiquitous in probability theory, statistics and machine learning. To combat the curse of dimensionality when estimating these distances from…
In this paper we propose to numerically assess the performance of standard Gaussian approximations to probe the posterior distribution that arises from Bayesian data assimilation in petroleum reservoirs. In particular we assess the…
We present a theoretical approach to scale the artificially fast dynamics of simulated coarse-grained polymer liquids down to its realistic value. As coarse-graining affects entropy and dissipation, two factors enter the rescaling:…
We study a discrete model of an heterogeneous elastic line with internal disorder, submitted to thermal fluctuations. The monomers are connected through random springs with independent and identically distributed elastic constants drawn…
We develop a systematic theory of spectral decimation for quantum many-body Hamiltonians and show that it provides a quantitative probe of emergent symmetries in statistically mixed spectra. Building on an analytical description of…
Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In…
The statistical distribution of levels of an integrable system is claimed to be a Poisson distribution. In this paper, we numerically generate an ensemble of N dimensional random diagonal matrices as a model for regular systems. We evaluate…
To sensitively test scaling in the 2D XY model quenched from high-temperatures into the ordered phase, we study the difference between measured correlations and the (scaling) results of a Gaussian-closure approximation. We also directly…
In logistic regression, separation occurs when a linear combination of the predictors can perfectly classify part or all of the observations in the sample, and as a result, finite maximum likelihood estimates of the regression coefficients…
Out-of-equilibrium quasistationary states (QSSs) are one of the signatures of a broken ergodicity in long-range interacting systems. For the widely studied Hamiltonian Mean-Field model, the lifetime of some QSSs has been shown to diverge…
In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
Many glass-forming fluids exhibit a remarkable thermodynamic scaling in which dynamic properties, such as the viscosity, the relaxation time, and the diffusion constant, can be described under different thermodynamic conditions in terms of…
Describing the collective dynamics of large neural populations using low-dimensional models for averaged variables has long been an attractive task in theoretical neuroscience. Recently developed reduction methods make it possible to derive…