We present some nonparametric methods for graphical modeling. In the discrete case, where the data are binary or drawn from a finite alphabet, Markov random fields are already essentially nonparametric, since the cliques can take only a finite number of values. Continuous data are different. The Gaussian graphical model is the standard parametric model for continuous data, but it makes distribu...

Functional mapping is a useful tool for mapping quantitative trait loci (QTL) that control dynamic traits. It incorporates mathematical aspects of biological processes into the mixture model-based likelihood setting for QTL mapping, thus increasing the power of QTL detection and the precision of parameter estimation. However, in many situations there is no obvious functional form and, in such c...

Normalized random measures with independent increments are a general, tractable class of nonparametric prior. This paper describes sequential Monte Carlo methods for both conjugate and non-conjugate nonparametric mixture models with these priors. A simulation study is used to compare the efficiency of the different algorithms for density estimation. The methods are further illustrated by applic...

This paper develops methods of inference for nonparametric and semiparametric parameters de…ned by conditional moment inequalities and/or equalities. The parameters need not be identi…ed. Con…dence sets and tests are introduced. The correct uniform asymptotic size of these procedures is established. The false coverage probabilities and power of the CS’s and tests are established for …xed altern...

This paper presents a comparative study of the hybrid models, neural networks and nonparametric regression models in time series forecasting. The components of these hybrid models are consisting of the nonparametric regression and artificial neural networks models. Smoothing spline, regression spline and additive regression models are considered as the nonparametric regression components. Furth...

This paper is concerned with a semiparametric partially linear regression model with unknown regression coefficients, an unknown nonparametric function for the non-linear component, and unobservable Gaussian distributed random errors. We present a wavelet thresholding based estimation procedure to estimate the components of the partial linear model by establishing a connection between an l1-pen...

Nonhomogeneous Poisson processes (NHPPs) are frequently used in stochastic simulations to model nonstationary point processes. These NHPP models are often constructed by estimating the rate function from one or more observed realizations of the process. Both parametric and nonparametric models have been developed for the NHPP rate function. The current parametric models require prior knowledge ...

A convenient way of modelling complex interactions is by employing graphs or networks which correspond to conditional independence structures in an underlying statistical model. One main class of models in this regard are Bayesian networks, which have the drawback of making parametric assumptions. Bayesian nonparametric mixture models offer a possibility to overcome this limitation, but have ha...