Sequential Nonparametric Regression

Sequential design for nonparametric inference

Performance of nonparametric function estimates often depends on the choice of design points. Based on the mean integrated squared error criterion, we propose a sequential design procedure that updates model knowledge and optimal design density sequentially. The methodology is developed under a general framework covering a wide range of nonparametric inference problems, such as conditional mean...

Sequential Markov Chain Monte Carlo

Abstract: We propose a sequential Markov chain Monte Carlo (SMCMC) algorithm to sample from a sequence of probability distributions, corresponding to posterior distributions at different times in on-line applications. SMCMC proceeds as in usual MCMC but with the stationary distribution updated appropriately each time new data arrive. SMCMC has advantages over sequential Monte Carlo (SMC) in avo...

Sequential Fixed-width Confidence Bands for Kernel Regression Estimation

We consider a random design model based on independent and identically distributed (iid) pairs of observations (Xi, Yi), where the regression function m(x) is given by m(x) = E(Yi|Xi = x) with one independent variable. In a nonparametric setting the aim is to produce a reasonable approximation to the unknown function m(x) when we have no precise information about the form of the true density, f...

Nonparametric sequential estimation of zeros and extrema of regression functions

Bayesian Nonparametric Models

A Bayesian nonparametric model is a Bayesian model on an infinite-dimensional parameter space. The parameter space is typically chosen as the set of all possible solutions for a given learning problem. For example, in a regression problem the parameter space can be the set of continuous functions, and in a density estimation problem the space can consist of all densities. A Bayesian nonparametr...