O comprimento descritivo mínimo na amostragem por transectos lineares

Apresenta·se um breve resumo histórico da evolução da amostragem por transectos lineares e desenvolve·se a sua teoria. Descrevemos a teoria de amostragem por transectos lineares, proposta por Buckland (1992), sendo apresentados os pontos mais relevantes, no que diz respeito à modelação da função de detecção. Apresentamos uma descrição do princípio CDM (Rissanen, 1978) e a sua aplicação à estimação de uma função densidade por um histograma (Kontkanen e Myllymãki, 2006), procedendo à aplicação de um exemplo prático, recorrendo a uma mistura de densidades. Procedemos à sua aplicação ao cálculo do estimador da probabilidade de detecção, no caso dos transectos lineares e desta forma estimar a densidade populacional de animais. Analisamos dois casos práticos, clássicos na amostragem por distâncias, comparando os resultados obtidos. De forma a avaliar a metodologia, simulámos vários conjuntos de observações, tendo como base o exemplo das estacas, recorrendo às funções de detecção semi-normal, taxa de risco, exponencial e uniforme com um cosseno. Os resultados foram obtidos com o programa DISTANCE (Thomas et al., in press) e um algoritmo escrito em linguagem C, cedido pelo Professor Doutor Petri Kontkanen (Departamento de Ciências da Computação, Universidade de Helsínquia). Foram desenvolvidos programas de forma a calcular intervalos de confiança recorrendo à técnica bootstrap (Efron, 1978). São discutidos os resultados finais e apresentadas sugestões de desenvolvimentos futuros. ABSTRACT; We present a brief historical note on the evolution of line transect sampling and its theoretical developments. We describe line transect sampling theory as proposed by Buckland (1992), and present the most relevant issues about modeling the detection function. We present a description of the CDM principle (Rissanen, 1978) and its application to histogram density estimation (Kontkanen and Myllymãki, 2006), with a practical example, using a mixture of densities. We proceed with the application and estimate probability of detection and animal population density in the context of line transect sampling. Two classical examples from the literature are analyzed and compared. ln order to evaluate the proposed methodology, we carry out a simulation study based on a wooden stakes example, and using as detection functions half normal, hazard rate, exponential and uniform with a cosine term. The results were obtained using program DISTANCE (Thomas et al., in press), and an algorithm written in C language, kindly offered by Professor Petri Kontkanen (Department of Computer Science, University of Helsinki). We develop some programs in order to estimate confidence intervals using the bootstrap technique (Efron, 1978). Finally, the results are presented and discussed with suggestions for future developments.

Using zero-norm constraint for sparse probability density function estimation

A new sparse kernel probability density function (pdf) estimator based on zero-norm constraint is constructed using the classical Parzen window (PW) estimate as the target function. The so-called zero-norm of the parameters is used in order to achieve enhanced model sparsity, and it is suggested to minimize an approximate function of the zero-norm. It is shown that under certain condition, the kernel weights of the proposed pdf estimator based on the zero-norm approximation can be updated using the multiplicative nonnegative quadratic programming algorithm. Numerical examples are employed to demonstrate the efficacy of the proposed approach.

Smooth Estimation of a Monotone Density

We investigate the interplay of smoothness and monotonicity assumptions when estimating a density from a sample of observations. The nonparametric maximum likelihood estimator of a decreasing density on the positive half line attains a rate of convergence at a fixed point if the density has a negative derivative. The same rate is obtained by a kernel estimator, but the limit distributions are different. If the density is both differentiable and known to be monotone, then a third estimator is obtained by isotonization of a kernel estimator. We show that this again attains the rate of convergence and compare the limit distributors of the three types of estimators. It is shown that both isotonization and smoothing lead to a more concentrated limit distribution and we study the dependence on the proportionality constant in the bandwidth. We also show that isotonization does not change the limit behavior of a kernel estimator with a larger bandwidth, in the case that the density is known to have more than one derivative.

Large and Moderate Deviations Principles for Recursive Kernel Estimator of a Multivariate Density and its Partial Derivatives

2000 Mathematics Subject Classification: 62G07, 60F10.

Traversability estimation for a planetary rover via experimental kernel learning in a Gaussian process framework

A critical requirement for safe autonomous navigation of a planetary rover is the ability to accurately estimate the traversability of the terrain. This work considers the problem of predicting the attitude and configuration angles of the platform from terrain representations that are often incomplete due to occlusions and sensor limitations. Using Gaussian Processes (GP) and exteroceptive data as training input, we can provide a continuous and complete representation of terrain traversability, with uncertainty in the output estimates. In this paper, we propose a novel method that focuses on exploiting the explicit correlation in vehicle attitude and configuration during operation by learning a kernel function from vehicle experience to perform GP regression. We provide an extensive experimental validation of the proposed method on a planetary rover. We show significant improvement in the accuracy of our estimation compared with results obtained using standard kernels (Squared Exponential and Neural Network), and compared to traversability estimation made over terrain models built using state-of-the-art GP techniques.

Multivariate Granger causality: an estimation framework based on factorization of the spectral density matrix

Granger causality is increasingly being applied to multi-electrode neurophysiological and functional imaging data to characterize directional interactions between neurons and brain regions. For a multivariate dataset, one might be interested in different subsets of the recorded neurons or brain regions. According to the current estimation framework, for each subset, one conducts a separate autoregressive model fitting process, introducing the potential for unwanted variability and uncertainty. In this paper, we propose a multivariate framework for estimating Granger causality. It is based on spectral density matrix factorization and offers the advantage that the estimation of such a matrix needs to be done only once for the entire multivariate dataset. For any subset of recorded data, Granger causality can be calculated through factorizing the appropriate submatrix of the overall spectral density matrix.

Spatially Adaptive Kernel Regression Using Risk Estimation

An important question in kernel regression is one of estimating the order and bandwidth parameters from available noisy data. We propose to solve the problem within a risk estimation framework. Considering an independent and identically distributed (i.i.d.) Gaussian observations model, we use Stein's unbiased risk estimator (SURE) to estimate a weighted mean-square error (MSE) risk, and optimize it with respect to the order and bandwidth parameters. The two parameters are thus spatially adapted in such a manner that noise smoothing and fine structure preservation are simultaneously achieved. On the application side, we consider the problem of image restoration from uniform/non-uniform data, and show that the SURE approach to spatially adaptive kernel regression results in better quality estimation compared with its spatially non-adaptive counterparts. The denoising results obtained are comparable to those obtained using other state-of-the-art techniques, and in some scenarios, superior.

Quantitative estimation of density variation in high-speed flows through inversion of the measured wavefront distortion

A simple method employing an optical probe is presented to measure density variations in a hypersonic flow obstructed by a test model in a typical shock tunnel. The probe has a plane light wave trans-illuminating the flow and casting a shadow of a random dot pattern. Local slopes of the distorted wavefront are obtained from shifts of the dots in the pattern. Local shifts in the dots are accurately measured by cross-correlating local shifted shadows with the corresponding unshifted originals. The measured slopes are suitably unwrapped by using a discrete cosine transform based phase unwrapping procedure and also through iterative procedures. The unwrapped phase information is used in an iterative scheme for a full quantitative recovery of density distribution in the shock around the model through refraction tomographic inversion. Hypersonic flow field parameters around a missile shaped body at a free-stream Mach number of 5.8 measured using this technique are compared with the numerically estimated values. (C) 2014 Society of Photo-Optical Instrumentation Engineers (SPIE)

Kernel conditional quantile estimation via reduction revisited

Quantile regression refers to the process of estimating the quantiles of a conditional distribution and has many important applications within econometrics and data mining, among other domains. In this paper, we show how to estimate these conditional quantile functions within a Bayes risk minimization framework using a Gaussian process prior. The resulting non-parametric probabilistic model is easy to implement and allows non-crossing quantile functions to be enforced. Moreover, it can directly be used in combination with tools and extensions of standard Gaussian Processes such as principled hyperparameter estimation, sparsification, and quantile regression with input-dependent noise rates. No existing approach enjoys all of these desirable properties. Experiments on benchmark datasets show that our method is competitive with state-of-the-art approaches. © 2009 IEEE.

Macroscopic limit of time-dependent density-functional theory for adiabatic local approximations of the exchange-correlation kernel

Time-dependent density-functional theory is a rather accurate and efficient way to compute electronic excitations for finite systems. However, in the macroscopic limit (systems of increasing size), for the usual adiabatic random-phase, local-density, or generalized-gradient approximations, one recovers the Kohn-Sham independent-particle picture, and thus the incorrect band gap. To clarify this trend, we investigate the macroscopic limit of the exchange-correlation kernel in such approximations by means of an algebraical analysis complemented with numerical studies of a one-dimensional tight-binding model. We link the failure to shift the Kohn-Sham spectrum of these approximate kernels to the fact that the corresponding operators in the transition space act only on a finite subspace.

Kernel-based local order estimation of nonlinear nonparametric systems

We consider the local order estimation of nonlinear autoregressive systems with exogenous inputs (NARX), which may have different local dimensions at different points. By minimizing the kernel-based local information criterion introduced in this paper, the strongly consistent estimates for the local orders of the NARX system at points of interest are obtained. The modification of the criterion and a simple procedure of searching the minimum of the criterion, are also discussed. The theoretical results derived here are tested by simulation examples.