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We consider generalized Bayesian inference on stochastic processes and dynamical systems with potentially long-range dependency. Given a sequence of observations, a class of parametrized model processes with a prior distribution, and a loss…
Dirichlet processes (DP) are widely applied in Bayesian nonparametric modeling. However, in their basic form they do not directly integrate dependency information among data arising from space and time. In this paper, we propose location…
This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we…
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…
Time-varying mixture densities occur in many scenarios, for example, the distributions of keywords that appear in publications may evolve from year to year, video frame features associated with multiple targets may evolve in a sequence. Any…
Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement,…
Consider a Dirichlet process mixture model (DPM) with random precision parameter $\alpha$, inducing $K_n$ clusters over $n$ observations through its latent random partition. Our goal is to specify the prior distribution…
We consider the problem of estimating Shannon's entropy $H$ from discrete data, in cases where the number of possible symbols is unknown or even countably infinite. The Pitman-Yor process, a generalization of Dirichlet process, provides a…
We study the rates of convergence of the posterior distribution for Bayesian density estimation with Dirichlet mixtures of normal distributions as the prior. The true density is assumed to be twice continuously differentiable. The bandwidth…
Flow cytometry is a high-throughput technology used to quantify multiple surface and intracellular markers at the level of a single cell. This enables to identify cell sub-types, and to determine their relative proportions. Improvements of…
Dataset distillation plays a crucial role in creating compact datasets with similar training performance compared with original large-scale ones. This is essential for addressing the challenges of data storage and training costs. Prevalent…
Forecast combination integrates information from various sources by consolidating multiple forecast results from the target time series. Instead of the need to select a single optimal forecasting model, this paper introduces a deep learning…
Many exact Markov chain Monte Carlo algorithms have been developed for posterior inference in Bayesian nonparametric models which involve infinite-dimensional priors. However, these methods are not generic and special methodology must be…
In this article we propose novel Bayesian nonparametric methods using Dirichlet Process Mixture (DPM) models for detecting pairwise dependence between random variables while accounting for uncertainty in the form of the underlying…
Finite mixture models are flexible methods that are commonly used for model-based clustering. A recent focus in the model-based clustering literature is to highlight the difference between the number of components in a mixture model and the…
We propose a method for estimating the posterior distribution of a standard geostatistical model. After choosing the model formulation and specifying a prior, we use normal mixture densities to approximate the posterior distribution. The…
In Bayesian statistics, many problems can be expressed as the evaluation of the expectation of a quantity of interest with respect to the posterior distribution. Standard Monte Carlo method is often not applicable because the encountered…
We give a new integral characterization of the Dirichlet process on a general phase space. To do so we first prove a characterization of the nonsymmetric Beta distribution via size-biased sampling. Two applications are a new…
Doubly intractable problems occur when both the likelihood and the posterior are available only in unnormalised form, with computationally intractable normalisation constants. Bayesian inference then typically requires direct approximation…
We propose a Bayesian nonparametric approach to the problem of jointly modeling multiple related time series. Our approach is based on the discovery of a set of latent, shared dynamical behaviors. Using a beta process prior, the size of the…