Related papers: Lower deviation probabilities for supercritical Ga…
We investigate the small deviation probabilities of a class of very smooth stationary Gaussian processes playing an important role in Bayesian statistical inference. Our calculations are based on the appropriate modification of the entropy…
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…
We study properties of a $p-$type subcritical branching process in random environment initiated at moment zero by a vector $\mathbf{z}=\left( z_{1},..,z_{p}\right) $\ of particles of different types. Assuming that the process belongs to the…
We study the asymptotic behaviour of the survival probability of a multi-type branching processes in random environment. The class of processes we consider corresponds, in the one-dimensional situation, to the intermediately subcritical…
Lower bounds for persistence probabilities of stationary Gaussian processes in discrete time are obtained under various conditions on the spectral measure of the process. Examples are given to show that the persistence probability can decay…
Excellent variational approximations to Gaussian process posteriors have been developed which avoid the $\mathcal{O}\left(N^3\right)$ scaling with dataset size $N$. They reduce the computational cost to $\mathcal{O}\left(NM^2\right)$, with…
Birth-and-death processes are widely used to model the development of biological populations. Although they are relatively simple models, their parameters can be challenging to estimate, because the likelihood can become numerically…
We consider a special class of Galton-Watson theta-processes in a varying environment fully defined by four parameters, with two of them $(\theta,r)$ being fixed over time $n$, and the other two $(a_n,c_n)$ characterizing the altering…
The Galton-Watson process is a model for population growth which assumes that individuals reproduce independently according to the same offspring distribution. Inference usually focuses on the offspring average as it allows to classify the…
Birth-death processes form a natural class where ideas and results on large deviations can be tested. In this paper, we derive a large deviation principle under the assumption that the rate of a jump down (death) is growing asymptotically…
A controlled branching process (CBP) is a modification of the standard Bienaym\'e-Galton-Watson process in which the number of progenitors in each generation is determined by a random mechanism. We consider a CBP starting from a random…
We calculate analytically the probability of large deviations from its mean of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles. In particular, we show that the…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
A method is introduced for studying large deviations in the context of statistical physics of disordered systems. The approach, based on an extension of the cavity method to atypical realizations of the quenched disorder, allows us to…
Establishing a Large Deviation Principle (LDP) proves to be a powerful result for a vast number of stochastic models in many application areas of probability theory. The key object of an LDP is the large deviations rate function, from which…
Positive and negative dependence are fundamental concepts that characterize the attractive and repulsive behavior of random subsets. Although some probabilistic models are known to exhibit positive or negative dependence, it is challenging…
Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper…
We study survival properties of inhomogeneous Galton-Watson processes. We determine the so-called branching number (which is the reciprocal of the critical value for percolation) for these random trees (conditioned on being infinite), which…
The aim of this note is to announce some results about the probabilistic and deterministic asymptotic properties of linear groups. The first one is the analogue, for norms of random matrix products, of the classical theorem of Cramer on…
We observe the Galton-Watson Branching Processes. Limit properties of transition functions and their convergence to invariant measures are investigated.