Abstract We propose a Bayesian nonparametric procedure for density estimation, data in closed, bounded interval, say [0,1]. To this aim, we use prior based on Bemstein polynomials. This corresponds to expressing the of as mixture given beta densities, with random weights and number components. The estimate is then obtained corresponding predictive function. Comparison classical kernel estimates provided. proposed illustrated an example; MCMC algorithm approximating also discussed.

Random Bernstein polynomials which are also probability distribution functions on the closed unit interval studied. The law of a polynomial so defined provides novel prior space [0, 1] has full support and can easily select absolutely continuous with smooth derivative. In particular, approximates Dirichlet process is This may be interest in Bayesian non‐parametric inference. second part paper, we study posterior from “Bernstein–Dirichlet” suggest hybrid Monte Carlo approximation it. proposed...

Summary A Bernstein prior is a probability measure on the space of all distribution functions [0, 1]. Under very general assumptions, it selects absolutely continuous functions, whose densities are mixtures known beta densities. The interest in Bayesian nonparametric inference with data. We study consistency posterior from prior. first show that, under mild weakly consistent for any function P0 1] and bounded Lebesgue density. With slightly stronger assumptions prior, also Hellinger...

Summary In functional data analysis, curves or surfaces are observed, up to measurement error, at a finite set of locations, for, say, sample n individuals. Often, the homogeneous, except perhaps for individual-specific regions that provide heterogeneous behaviour (e.g. ‘damaged’ areas irregular shape on an otherwise smooth surface). Motivated by applications with this nature, we propose Bayesian mixture model, aim dimension reduction, representing through smaller canonical curves. We novel...

Journal Article Bayes and empirical Bayes: do they merge? Get access S. Petrone, Petrone Department of Decision Sciences, Bocconi University, Via G. Röntgen 1, 20136 Milano, Italy, sonia.petrone@unibocconi.it Search for other works by this author on: Oxford Academic Google Scholar J. Rousseau, Rousseau CREST-ENSAE, 3, Avenue P. Larousse, 92240 Malakoff, France, rousseau@ceremade.dauphine.fr C. Scricciolo catia.scricciolo@unibocconi.it Biometrika, Volume 101, Issue 2, June 2014, Pages...

Abstract Bayesian non‐parametrics has evolved into a broad area encompassing flexible methods for inference, combinatorial structures, tools complex data reduction, and more. Discrete prior laws play an important role in these developments, various choices are available nowadays. However, many existing priors, such as the Dirichlet process, have limitations if require nested clustering structures. Thus, we introduce discrete non‐parametric prior, termed enriched Pitman–Yor which offers...

We give an overview of some the software tools available in R, either as built- functions or contributed packages, for analysis state space models. Several illustrative examples are included, covering constant and time-varying models both univariate multivariate time series. Maximum likelihood Bayesian methods to obtain parameter estimates considered.

The precision parameter $\alpha$ plays an important role in the Dirichlet Pro- cess. When assigning a Process prior to set of probability measures on $\mathbb{R}^k, k \gt 1$, this can be restrictive sense that variability is determined by single parameter. aim paper construct enrichment foof more flexible with respect yet still conjugate, starting from notion enriched conjugate priors, which have been proposed address analogous lack flexibility standard priors parametric setting. resulting...

The characterization of models and priors through a predictive approach is fundamental problem in Bayesian statistics. In the last decades, it has received renewed interest, as basis important developments nonparametrics machine learning. this paper, we review classical recent work based on these areas. Our focus construction for nonparametric inference, exchangeable partially sequences. Some results are revisited to shed light theoretical connections among them.

The precision parameter $\alpha$ plays an important role in the Dirichlet Pro- cess. When assigning a Process prior to set of probability measures on $\mathbb{R}^k, k \gt 1$, this can be restrictive sense that variability is determined by single parameter. aim paper construct enrichment foof more flexible with respect yet still conjugate, starting from notion enriched conjugate priors, which have been proposed address analogous lack flexibility standard priors parametric setting. resulting...

Abstract This paper examines the use of Dirichlet process mixtures for curve fitting. An important modelling aspect in this setting is choice between constant and covariate‐dependent weights. By examining problem fitting from a predictive perspective, we show advantages using These are result incorporation covariate proximity latent partition. However, closer examination partition yields further complications, which arise vast number total partitions. To overcome this, propose to modify...

Summary Bayesian methods are often optimal, yet increasing pressure for fast computations, especially with streaming data, brings renewed interest in faster, possibly suboptimal, solutions. The extent to which these algorithms approximate solutions is a question of interest, but unanswered. We propose methodology address this predictive settings, when the algorithm can be reinterpreted as probabilistic rule. specifically develop proposed recursive procedure on-line learning non-parametric...

Abstract Non-Gaussian state-space models arise in several applications, and within this framework the binary time series setting provides a relevant example. However, unlike for Gaussian — where filtering, predictive smoothing distributions are available closed form require approximations or sequential Monte Carlo strategies inference prediction. This is due to apparent absence of conjugacy between states likelihood induced by observation equation data. In article we prove that dynamic...