Related papers: A note on "Bayesian nonparametric estimators deriv…
We explore the construction of nonsubjective prior distributions in Bayesian statistics via a posterior predictive relative entropy regret criterion. We carry out a minimax analysis based on a derived asymptotic predictive loss function and…
We introduce semiparametric Bayesian networks that combine parametric and nonparametric conditional probability distributions. Their aim is to incorporate the advantages of both components: the bounded complexity of parametric models and…
By Poissonization of Jacobi structures on real three-dimensional Lie groups $\mathbf{G}$ and using the realizations of their Lie algebras, we obtain integrable bi-Hamiltonian systems on $\mathbf{G}\otimes \mathbb{R}$.
Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the volatility…
We develop a method to perform model averaging in two-stage linear regression systems subject to endogeneity. Our method extends an existing Gibbs sampler for instrumental variables to incorporate a component of model uncertainty. Direct…
The PAC-Bayesian approach is a powerful set of techniques to derive non- asymptotic risk bounds for random estimators. The corresponding optimal distribution of estimators, usually called the Gibbs posterior, is unfortunately intractable.…
The problem of extracting as much information as possible from a sequence of observations of a stationary stochastic process $X_0,X_1,...X_n$ has been considered by many authors from different points of view. It has long been known through…
The problem of nonparametric estimation of the conditional density of a response, given a vector of explanatory variables, is classical and of prominent importance in many prediction problems since the conditional density provides a more…
This paper concerns the robust regression model when the number of predictors and the number of observations grow in a similar rate. Theory for M-estimators in this regime has been recently developed by several authors [El Karoui et al.,…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying…
This is a supplement to the article "Markov Chain Monte Carlo Based on Deterministic Transformations" available at http://arxiv.org/abs/1106.5850
In this paper, we study the trade-offs of different inference approaches for Bayesian matrix factorisation methods, which are commonly used for predicting missing values, and for finding patterns in the data. In particular, we consider…
The results of this paper have been subsumed by the paper "A geometric invariant theory construction of spaces of stable maps," Elizabeth Baldwin and David Swinarski, arXiv:0706.1381
We present a general framework for Bayesian estimation of incompletely observed multivariate diffusion processes. Observations are assumed to be discrete in time, noisy and incomplete. We assume the drift and diffusion coefficient depend on…
A large amount of observational data has been accumulated in various fields in recent times, and there is a growing need to estimate the generating processes of these data. A linear non-Gaussian acyclic model (LiNGAM) based on the…
A nonparametric and locally adaptive Bayesian estimator is proposed for estimating a binary regression. Flexibility is obtained by modeling the binary regression as a mixture of probit regressions with the argument of each probit regression…
The Bayesian lasso is well-known as a Bayesian alternative for Lasso. Although the advantage of the Bayesian lasso is capable of full probabilistic uncertain quantification for parameters, the corresponding posterior distribution can be…
Estimating mutual information (MI) from samples is a fundamental problem in statistics, machine learning, and data analysis. Recently it was shown that a popular class of non-parametric MI estimators perform very poorly for strongly…
A symbolic method is discussed which can be used to obtain the asymptotic bias and variance to order $O(1/n)$ for estimators in stationary time series. Using this method the bias to $O(1/n)$ of the Burg estimator in AR(1) and AR(2) models…