相关论文: Log Gaussian Cox processes on the sphere

This paper proposes a physically consistent Gaussian Process (GP) enabling the identification of uncertain Lagrangian systems. The function space is tailored according to the energy components of the Lagrangian and the differential equation…

Two types of Gaussian processes, namely the Gaussian field with generalized Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic…

Inhomogeneities in real-world data, e.g., due to changes in the observation noise level or variations in the structural complexity of the source function, pose a unique set of challenges for statistical inference. Accounting for them can…

Heteroscedastic regression considering the varying noises among observations has many applications in the fields like machine learning and statistics. Here we focus on the heteroscedastic Gaussian process (HGP) regression which integrates…

Bayesian deep Gaussian processes (DGPs) outperform ordinary GPs as surrogate models of complex computer experiments when response surface dynamics are non-stationary, which is especially prevalent in aerospace simulations. Yet DGP…

We define a copula process which describes the dependencies between arbitrarily many random variables independently of their marginal distributions. As an example, we develop a stochastic volatility model, Gaussian Copula Process Volatility…

A critical bottleneck for scientific progress is the costly nature of computer simulations for complex systems. Surrogate models provide an appealing solution: such models are trained on simulator evaluations, then used to emulate and…

It is known that the limiting behavior of the contact process strongly depends upon the geometry of the graph on which particles evolve: while the contact process on the regular lattice exhibits only two phases, the process on homogeneous…

This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…

Consider that the coordinates of $N$ points are randomly generated along the edges of a $d$-dimensional hypercube (random point problem). The probability that an arbitrary point is the $m$th nearest neighbor to its own $n$th nearest…

In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…

Decoders built on Gaussian processes (GPs) are enticing due to the marginalisation over the non-linear function space. Such models (also known as GP-LVMs) are often expensive and notoriously difficult to train in practice, but can be scaled…

Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…

In the first part of my thesis I am concerned with the phenomenology of DGLAP equations, and in particular I propose an algorithm to solve them numerically and discuss its implementation in a computer program. I also illustrate some…

In this paper, we consider a cluster model of weighted Euclidean random balls generated by a shot-noise Cox process. It is an example of cluster point process. We perform a scaling on the model by shrinking the radii of the balls and…

We analyze nonequilibrium fluctuations of the averaging process on $\mathbb T_\varepsilon^d$, a continuous degenerate Gibbs sampler running over the edges of the discrete $d$-dimensional torus. We show that, if we start from a smooth…

Recent research has shown the potential utility of Deep Gaussian Processes. These deep structures are probability distributions, designed through hierarchical construction, which are conditionally Gaussian. In this paper, the current…

The existence of a discontinuity in the inverse dielectric constant of the two-dimensional Coulomb gas is demonstrated on purely numerical grounds. This is done by expanding the free energy in an applied twist and performing a finite-size…

Rich new marked point process data allow researchers to consider disparate problems such as the factors affecting the location and type of police use of force incidents, and the characteristics that impact the location and size of forest…

A Gaussian process is proposed as a model for the posterior distribution of the local predictive ability of a model or expert, conditional on a vector of covariates, from historical predictions in the form of log predictive scores. Assuming…