Related papers: Wavelet-based simulation of random processes from …
Consider a stochastic process $\{X(t)\}$ on a finite state space $ {\sf X}=\{1,\dots, d\}$. It is conditionally Markov, given a real-valued `input process' $\{\zeta(t)\}$. This is assumed to be small, which is modeled through the scaling,…
We use Daubechies' orthonormal compact wavelets as a variational basis for the $XY$ model in two and three dimensions. Assuming that the fluctuations of the wavelet coefficients are Gaussian and uncorrelated, minimization of the free energy…
We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in…
We present a unified view of likelihood based Gaussian progress regression for simulation experiments exhibiting input-dependent noise. Replication plays an important role in that context, however previous methods leveraging replicates have…
The covariance of a stationary process $X$ is diagonalized by a Fourier transform. It does not take into account the complex Fourier phase and defines Gaussian maximum entropy models. We introduce a general family of phase harmonic…
The construction of synthetic complex-valued signals from real-valued observations is an important step in many time series analysis techniques. The most widely used approach is based on the Hilbert transform, which maps the real-valued…
This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multivariate Gaussian processes from the circulant embedding…
Stochastic processes defined on integer valued state spaces are popular within the physical and biological sciences. These models are necessary for capturing the dynamics of small systems where the individual nature of the populations…
Many recent flow-matching and diffusion-style generative models rely on auxiliary stochastic dynamics during training: a richer process is simulated to define conditional targets, but the auxiliary state is either intractable to sample at…
We propose a simple stochastic process for modeling improper or noncircular complex-valued signals. The process is a natural extension of a complex-valued autoregressive process, extended to include a widely linear autoregressive term. This…
We consider the problem of modelling noisy but highly symmetric shapes that can be viewed as hierarchies of whole-part relationships in which higher level objects are composed of transformed collections of lower level objects. To this end,…
A wavelet-based method for compression of three-dimensional simulation data is presented and its software framework is described. It uses wavelet decomposition and subsequent range coding with quantization suitable for floating-point data.…
Many records in environmental sciences exhibit asymmetric trajectories and there is a need for simple and tractable models which can reproduce such features. In this paper we explore an approach based on applying both a time change and a…
We suggest an adaptive sampling rule for obtaining information from noisy signals using wavelet methods. The technique involves increasing the sampling rate when relatively high-frequency terms are incorporated into the wavelet estimator,…
We consider a process $Z$ on the real line composed from a L\'evy process and its exponentially tilted version killed with arbitrary rates and give an expression for the joint law of $Z$ seen from its supremum, the supremum $\overline Z$…
This research presents a new turbulence generation method based on stochastic wavelets and tests its various properties in both homogeneous and inhomogeneous turbulence. Turbulence field can be generated with less basis compared to previous…
Normalizing flows are a class of probabilistic generative models which allow for both fast density computation and efficient sampling and are effective at modelling complex distributions like images. A drawback among current methods is…
Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…
Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the…
We find the class, ${\cal{C}}_k, k \ge 0$, of all zero mean stationary Gaussian processes, $Y(t), ~t \in \reals$ with $k$ derivatives, for which \begin{equation} Z(t) \equiv (Y^{(0)}(t), Y^{(1)}(t), \ldots, Y^{(k)}(t) ), ~ t \ge 0…