tgp: An R Package for Bayesian Nonstationary, Semiparametric Nonlinear Regression and Design by Treed Gaussian Process Models

The tgp package for R is a tool for fully Bayesian nonstationary, semiparametric nonlinear regression and design by treed Gaussian processes with jumps to the limiting linear model. Special cases also implemented include Bayesian linear models, linear CART, stationary separable and isotropic Gaussian processes. In addition to inference and posterior prediction, the package supports the (sequential) design of experiments under these models paired with several objective criteria. 1-d and 2-d plotting, with higher dimension projection and slice capabilities, and tree drawing functions (requiring maptree and combinat packages), are also provided for visualization of tgp objects.

tgp: An R Package for Bayesian Nonstationary, Semiparametric Nonlinear Regression and Design by Treed Gaussian Process Models

The tgp package for R is a tool for fully Bayesian nonstationary, semiparametric nonlinear regression and design by treed Gaussian processes with jumps to the limiting linear model. Special cases also implemented include Bayesian linear models, linear CART, stationary separable and isotropic Gaussian processes. In addition to inference and posterior prediction, the package supports the (sequential) design of experiments under these models paired with several objective criteria. 1-d and 2-d plotting, with higher dimension projection and slice capabilities, and tree drawing functions (requiring maptree and combinat packages), are also provided for visualization of tgp objects

Categorical Inputs, Sensitivity Analysis, Optimization and Importance Tempering with tgp Version 2, an R Package for Treed Gaussian Process Models

This document describes the new features in version 2.x of the tgp package for R, implementing treed Gaussian process (GP) models. The topics covered include methods for dealing with categorical inputs and excluding inputs from the tree or GP part of the model; fully Bayesian sensitivity analysis for inputs/covariates; sequential optimization of black-box functions; and a new Monte Carlo method for inference in multi-modal posterior distributions that combines simulated tempering and importance sampling. These additions extend the functionality of tgp across all models in the hierarchy: from Bayesian linear models, to classification and regression trees (CART), to treed Gaussian processes with jumps to the limiting linear model. It is assumed that the reader is familiar with the baseline functionality of the package, outlined in the first vignette (Gramacy 2007).

Categorical Inputs, Sensitivity Analysis, Optimization and Importance Tempering with tgp Version 2, an R Package for Treed Gaussian Process Models

This document describes the new features in version 2.x of the tgp package for R, implementing treed Gaussian process (GP) models. The topics covered include methods for dealing with categorical inputs and excluding inputs from the tree or GP part of the model; fully Bayesian sensitivity analysis for inputs/covariates; sequential optimization of black-box functions; and a new Monte Carlo method for inference in multi-modal posterior distributions that combines simulated tempering and importance sampling. These additions extend the functionality of tgp across all models in the hierarchy: from Bayesian linear models, to classification and regression trees (CART), to treed Gaussian processes with jumps to the limiting linear model. It is assumed that the reader is familiar with the baseline functionality of the package, outlined in the first vignette (Gramacy 2007)

Performance Evaluation of Unscented Kalman Filter for Gaussian and non-Gaussian Tracking Application

State estimation theory is one of the best mathematical approaches to analyze variants in the states of the system or process. The state of the system is defined by a set of variables that provide a complete representation of the internal condition at any given instant of time. Filtering of Random processes is referred to as Estimation, and is a well defined statistical technique. There are two types of state estimation processes, Linear and Nonlinear. Linear estimation of a system can easily be analyzed by using Kalman Filter (KF) but  is optimal only when the model is linear .But  Most of the state estimation problems are nonlinear, thereby limiting the practical applications of the KF and EKF. Unscented Kalman filter and Particle filter are best known for nonlinear estimates. The approach in this paper is to analyze the algorithm for maneuvering target tracking using   bearing only measurements for both Gaussian /Nongaussian distributions where UKF provides better probability of state estimation.  Montecarlo computer simulations are used to analyse the performance .The simulations results showed that UKF provides better performance for Gaussian distributed models compared to the nongaussian models.DOI:http://dx.doi.org/10.11591/ijece.v3i1.32

On Compound Poisson Processes Arising in Change-Point Type Statistical Models as Limiting Likelihood Ratios

Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these likelihood ratios, which is an exponential functional of a two-sided Poisson process driven by some parameter, can be approximated (for sufficiently small values of the parameter) by another one, which is an exponential functional of a two-sided Brownian motion. In this paper we consider yet another likelihood ratio, which is the exponent of a two-sided compound Poisson process driven by some parameter. We establish, that similarly to the Poisson type one, the compound Poisson type likelihood ratio can be approximated by the Brownian type one for sufficiently small values of the parameter. We equally discuss the asymptotics for large values of the parameter and illustrate the results by numerical simulations

On the Mar\v{c}enko-Pastur law for linear time series

This paper is concerned with extensions of the classical Mar\v{c}enko-Pastur law to time series. Specifically, $p$-dimensional linear processes are considered which are built from innovation vectors with independent, identically distributed (real- or complex-valued) entries possessing zero mean, unit variance and finite fourth moments. The coefficient matrices of the linear process are assumed to be simultaneously diagonalizable. In this setting, the limiting behavior of the empirical spectral distribution of both sample covariance and symmetrized sample autocovariance matrices is determined in the high-dimensional setting $p/n\to c\in (0,\infty)$ for which dimension $p$ and sample size $n$ diverge to infinity at the same rate. The results extend existing contributions available in the literature for the covariance case and are one of the first of their kind for the autocovariance case.Comment: Published at http://dx.doi.org/10.1214/14-AOS1294 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org