Related papers: Clustering of discretely observed diffusion proces…
The data mining technique of time series clustering is well established in many fields. However, as an unsupervised learning method, it requires making choices that are nontrivially influenced by the nature of the data involved. The aim of…
Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
This article considers a model for alternative processes for securities prices and compares this model with actual return data of several securities. The distributions of returns that appear in the model can be Gaussian as well as…
Estimation of parameters of a diffusion based on discrete time observations poses a difficult problem due to the lack of a closed form expression for the likelihood. From a Bayesian computational perspective it can be casted as a missing…
There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes. However existing algorithms can only be used if the target distribution of interest is differentiable…
We describe an inference task in which a set of timestamped event observations must be clustered into an unknown number of temporal sequences with independent and varying rates of observations. Various existing approaches to multi-object…
In computational system biology, the mesoscopic model of reaction-diffusion kinetics is described by a continuous time, discrete space Markov process. To simulate diffusion stochastically, the jump coefficients are obtained by a…
This note outlines a method for clustering time series based on a statistical model in which volatility shifts at unobserved change-points. The model accommodates some classical stylized features of returns and its relation to GARCH is…
A diffusion taking value in probability measures on a graph with a vertex set $V$, $\sum_{i\in V}x_i\delta_i$, is studied. The masses on each vertices satisfy the stochastic differential equation of the form $dx_i=\sum_{j\in…
The fluctuation-dissipation theorem is a central result in statistical mechanics and is usually formulated for systems described by diffusion processes. In this paper, we propose a generalization for a wider class of stochastic processes,…
In the context of nonparametric Bayesian estimation a Markov chain Monte Carlo algorithm is devised and implemented to sample from the posterior distribution of the drift function of a continuously or discretely observed one-dimensional…
For one-dimensional Jump-Drift and Jump-Diffusion processes converging towards some steady state, the large deviations of a long dynamical trajectory are described from two perspectives. Firstly, the joint probability of the empirical…
In this paper, a modification of the conventional approximations to the quasi-maximum likelihood method is introduced for the parameter estimation of diffusion processes from discrete observations. This is based on a convergent…
Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…
This study aims to alleviate the trade-off between utility and privacy of differentially private clustering. Existing works focus on simple methods, which show poor performance for non-convex clusters. To fit complex cluster distributions,…
This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…
We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast…
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…