Related papers: Markov Stick-breaking Processes
We introduce and study branching interval partition diffusions in their natural generality. We let interval widths evolve independently according to a general real-valued diffusion subject only to conditions that ensure finite lifetimes of…
Piecewise-deterministic Markov processes form a general class of non-diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In this paper, we state a new characterization of the jump rate…
The Pitman-Yor process is a random probability distribution, that can be used as a prior distribution in a nonparametric Bayesian analysis. The process is of species sampling type and generates discrete distributions, which yield of the…
We propose a Bayesian nonparametric model based on Markov Chain Monte Carlo (MCMC) methods for the joint reconstruction and prediction of discrete time stochastic dynamical systems, based on $m$-multiple time-series data, perturbed by…
We propose a Bayesian nonparametric mixture model for the reconstruction and prediction from observed time series data, of discretized stochastic dynamical systems, based on Markov Chain Monte Carlo methods (MCMC). Our results can be used…
We consider the connections among `clumped' residual allocation models (RAMs), a general class of stick-breaking processes including Dirichlet processes, and the occupation laws of certain discrete space time-inhomogeneous Markov chains…
In order for clinicians to manage disease progression and make effective decisions about drug dosage, treatment regimens or scheduling follow up appointments, it is necessary to be able to identify both short and long-term trends in…
In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations.…
The Pitman-Yor process is a random discrete measure. The random weights or masses follow the two-parameter Poisson-Dirichlet distribution with parameters $0<\alpha<1, \theta>-\alpha$. The parameters $\alpha$ and $\theta$ correspond to the…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
Splitting probabilities quantify the likelihood of particular outcomes out of a set of mutually-exclusive possibilities for stochastic processes and play a central role in first-passage problems. For two-dimensional Markov processes…
Nonparametric mixture models based on the Pitman-Yor process represent a flexible tool for density estimation and clustering. Natural generalization of the popular class of Dirichlet process mixture models, they allow for more robust…
When analyzing data from multiple sources, it is often convenient to strike a careful balance between two goals: capturing the heterogeneity of the samples and sharing information across them. We introduce a novel framework to model a…
Markov models are often used to capture the temporal patterns of sequential data for statistical learning applications. While the Hidden Markov modeling-based learning mechanisms are well studied in literature, we analyze a…
In this work we introduce the discrete-space broken line process (with discrete and continues parameter values) and derive some of its properties. We explore polygonal Markov fields techniques developed by Arak-Surgailis. The discrete…
A piecewise-deterministic Markov process is a stochastic process whose behavior is governed by an ordinary differential equation punctuated by random jumps occurring at random times. We focus on the nonparametric estimation problem of the…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
Diffusion models are typically trained using score matching, a learning objective agnostic to the underlying noising process that guides the model. This paper argues that Markov noising processes enjoy an advantage over alternatives, as the…
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 propose a general modeling framework for marked Poisson processes observed over time or space. The modeling approach exploits the connection of the nonhomogeneous Poisson process intensity with a density function. Nonparametric Dirichlet…