Related papers: Conditional Sampling for Max-Stable Processes with…
We study stationary max-stable processes $\{\eta(t)\colon t\in\mathbb R\}$ admitting a representation of the form $\eta(t)=\max_{i\in\mathbb N}(U_i+ Y_i(t))$, where $\sum_{i=1}^{\infty} \delta_{U_i}$ is a Poisson point process on $\mathbb…
We study maximum likelihood estimation for spatial generalized linear mixed models with Gaussian process approximations using a stochastic Newton-Raphson algorithm. We consider two Gaussian Process approximations in this context: spectral…
The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…
Many processes in chemistry and physics take place on timescales that cannot be explored using standard molecular dynamics simulations. This renders the use of enhanced sampling mandatory. Here we introduce an enhanced sampling method that…
Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. For statistical inference it is often assumed that…
Consider the max-stable process $\eta(t) = \max_{i\in\mathbb N} U_i \rm{e}^{\langle X_i, t\rangle - \kappa(t)}$, $t\in\mathbb{R}^d$, where $\{U_i, i\in\mathbb{N}\}$ are points of the Poisson process with intensity $u^{-2}\rm{d} u$ on…
In simulations of multiscale dynamical systems, not all relevant processes can be resolved explicitly. Taking the effect of the unresolved processes into account is important, which introduces the need for paramerizations. We present a…
We study maximum likelihood estimation in log-linear models under conditional Poisson sampling schemes. We derive necessary and sufficient conditions for existence of the maximum likelihood estimator (MLE) of the model parameters and…
In this paper, we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for…
We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative…
In recent years, parametric models for max-stable processes have become a popular choice for modeling spatial extremes because they arise as the asymptotic limit of rescaled maxima of independent and identically distributed random…
This paper develops the first class of algorithms that enable unbiased estimation of steady-state expectations for multidimensional reflected Brownian motion. In order to explain our ideas, we first consider the case of compound Poisson…
Sampling the stationary points of a complicated potential energy landscape is a challenging problem. Here we introduce a sampling method based on relaxation from stationary points of the highest index of the Hessian matrix. We illustrate…
Under a complex technical condition, similar to such used in extreme value theory, we find the rate q(\epsilon)^{-1} at which a stochastic process with stationary increments \xi should be sampled, for the sampled process \xi(\lfloor\cdot…
Many specific problems ranging from theoretical probability to applications in statistical physics, combinatorial optimization and communications can be formulated as an optimal tuning of local parameters in large systems of interacting…
Point pattern data often exhibit features such as abrupt changes, hotspots and spatially varying dependence in local intensity. Under a Poisson process framework, these correspond to discontinuities and nonstationarity in the underlying…
A class of random non-stationary signals termed timbre x dynamics is introduced and studied. These signals are obtained by non-linear transformations of sta-tionary random gaussian signals, in such a way that the transformation can be…
Due to complex physical phenomena, the distribution of heavy rainfall events is difficult to model spatially. Physically based numerical models can often provide physically coherent spatial patterns, but may miss some important…
This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…
While max-stable processes are typically written as pointwise maxima over an infinite number of stochastic processes, in this paper, we consider a family of representations based on $\ell^p$ norms. This family includes both the construction…