Performance analysis using equivariant kernel density estimator in nonlinear mixture

This paper investigates the performance analysis of separation of mutually independent sources in nonlinear models. The nonlinear mapping constituted by an unsupervised linear mixture is followed by an unknown and invertible nonlinear distortion, are found in many signal processing cases. Generally, blind separation of sources from their nonlinear mixtures is rather difficult. We propose using a kernel density estimator incorporated with equivariant gradient analysis to separate the sources with nonlinear distortion. The kernel density estimator parameters of which are iteratively updated to minimize the output independence expressed as a mutual information criterion. The equivariant gradient algorithm has the form of nonlinear decorrelation to perform the convergence analysis. Experiments are proposed to illustrate these results.

Malliavin calculus in finance

This article is an introduction to Malliavin Calculus for practitioners.We treat one specific application to the calculation of greeks in Finance.We consider also the kernel density method to compute greeks and anextension of the Vega index called the local vega index.

A Novel Nonparametric Density Estimator

We present a novel nonparametric density estimator and a new data-driven bandwidth selection method with excellent properties. The approach is in- spired by the principles of the generalized cross entropy method. The pro- posed density estimation procedure has numerous advantages over the tra- ditional kernel density estimator methods. Firstly, for the first time in the nonparametric literature, the proposed estimator allows for a genuine incor- poration of prior information in the density estimation procedure. Secondly, the approach provides the first data-driven bandwidth selection method that is guaranteed to provide a unique bandwidth for any data. Lastly, simulation examples suggest the proposed approach outperforms the current state of the art in nonparametric density estimation in terms of accuracy and reliability.

Method to estimate soil macroporosity and microporosity based on sand content and bulk density

Macroporosity is often used in the determination of soil compaction. Reduced macroporosity can lead to poor drainage, low root aeration and soil degradation. The aim of this study was to develop and test different models to estimate macro and microporosity efficiently, using multiple regression. Ten soils were selected within a large range of textures: sand (Sa) 0.07-0.84; silt 0.03-0.24; clay 0.13-0.78 kg kg-1 and subjected to three compaction levels (three bulk densities, BD). Two models with similar accuracy were selected, with a mean error of about 0.02 m³ m-3 (2 %). The model y = a + b.BD + c.Sa, named model 2, was selected for its simplicity to estimate Macro (Ma), Micro (Mi) or total porosity (TP): Ma = 0.693 - 0.465 BD + 0.212 Sa; Mi = 0.337 + 0.120 BD - 0.294 Sa; TP = 1.030 - 0.345 BD 0.082 Sa; porosity values were expressed in m³ m-3; BD in kg dm-3; and Sa in kg kg-1. The model was tested with 76 datum set of several other authors. An error of about 0.04 m³ m-3 (4 %) was observed. Simulations of variations in BD as a function of Sa are presented for Ma = 0 and Ma = 0.10 (10 %). The macroporosity equation was remodeled to obtain other compaction indexes: a) to simulate maximum bulk density (MBD) as a function of Sa (Equation 11), in agreement with literature data; b) to simulate relative bulk density (RBD) as a function of BD and Sa (Equation 13); c) another model to simulate RBD as a function of Ma and Sa (Equation 16), confirming the independence of this variable in relation to Sa for a fixed value of macroporosity and, also, proving the hypothesis of Hakansson & Lipiec that RBD = 0.87 corresponds approximately to 10 % macroporosity (Ma = 0.10 m³ m-3).

Probability density function estimation using orthogonal forward regression

Using the classical Parzen window estimate as the target function, the kernel density estimation is formulated as a regression problem and the orthogonal forward regression technique is adopted to construct sparse kernel density estimates. The proposed algorithm incrementally minimises a leave-one-out test error score to select a sparse kernel model, and a local regularisation method is incorporated into the density construction process to further enforce sparsity. The kernel weights are finally updated using the multiplicative nonnegative quadratic programming algorithm, which has the ability to reduce the model size further. Except for the kernel width, the proposed algorithm has no other parameters that need tuning, and the user is not required to specify any additional criterion to terminate the density construction procedure. Two examples are used to demonstrate the ability of this regression-based approach to effectively construct a sparse kernel density estimate with comparable accuracy to that of the full-sample optimised Parzen window density estimate.

Monte Carlo Method for Reconstruction of Densities

2000 Mathematics Subject Classification: 65C05

Spatial analysis of avoidable hospitalizations due to tuberculosis in Ribeirao Preto, SP, Brazil (2006-2012)

ABSTRACT OBJECTIVE To describe the spatial distribution of avoidable hospitalizations due to tuberculosis in the municipality of Ribeirao Preto, SP, Brazil, and to identify spatial and space-time clusters for the risk of occurrence of these events. METHODS This is a descriptive, ecological study that considered the hospitalizations records of the Hospital Information System of residents of Ribeirao Preto, SP, Southeastern Brazil, from 2006 to 2012. Only the cases with recorded addresses were considered for the spatial analyses, and they were also geocoded. We resorted to Kernel density estimation to identify the densest areas, local empirical Bayes rate as the method for smoothing the incidence rates of hospital admissions, and scan statistic for identifying clusters of risk. Softwares ArcGis 10.2, TerraView 4.2.2, and SaTScanTM were used in the analysis. RESULTS We identified 169 hospitalizations due to tuberculosis. Most were of men (n = 134; 79.2%), averagely aged 48 years (SD = 16.2). The predominant clinical form was the pulmonary one, which was confirmed through a microscopic examination of expectorated sputum (n = 66; 39.0%). We geocoded 159 cases (94.0%). We observed a non-random spatial distribution of avoidable hospitalizations due to tuberculosis concentrated in the northern and western regions of the municipality. Through the scan statistic, three spatial clusters for risk of hospitalizations due to tuberculosis were identified, one of them in the northern region of the municipality (relative risk [RR] = 3.4; 95%CI 2.7–4,4); the second in the central region, where there is a prison unit (RR = 28.6; 95%CI 22.4–36.6); and the last one in the southern region, and area of protection for hospitalizations (RR = 0.2; 95%CI 0.2–0.3). We did not identify any space-time clusters. CONCLUSIONS The investigation showed priority areas for the control and surveillance of tuberculosis, as well as the profile of the affected population, which shows important aspects to be considered in terms of management and organization of health care services targeting effectiveness in primary health care.

An Introduction to parametric and non-parametric models for bivariate positive insurance claim severity distributions

We present a real data set of claims amounts where costs related to damage are recorded separately from those related to medical expenses. Only claims with positive costs are considered here. Two approaches to density estimation are presented: a classical parametric and a semi-parametric method, based on transformation kernel density estimation. We explore the data set with standard univariate methods. We also propose ways to select the bandwidth and transformation parameters in the univariate case based on Bayesian methods. We indicate how to compare the results of alternative methods both looking at the shape of the overall density domain and exploring the density estimates in the right tail.

The spatiotemporal trajectory of a dengue epidemic in a medium-sized city

Understanding the transmission dynamics of infectious diseases is important to allow for improvements of control measures. To investigate the spatiotemporal pattern of an epidemic dengue occurred at a medium-sized city in the Northeast Region of Brazil in 2009, we conducted an ecological study of the notified dengue cases georeferenced according to epidemiological week (EW) and home address. Kernel density estimation and space-time interaction were analysed using the Knox method. The evolution of the epidemic was analysed using an animated projection technique. The dengue incidence was 6.918.7/100,000 inhabitants; the peak of the epidemic occurred from 8 February-1 March, EWs 6-9 (828.7/100,000 inhabitants). There were cases throughout the city and was identified space-time interaction. Three epicenters were responsible for spreading the disease in an expansion and relocation diffusion pattern. If the health services could detect in real time the epicenters and apply nimbly control measures, may possibly reduce the magnitude of dengue epidemics.

Variable Kernel estimates: On the impossibility of tuning the parameters

For the standard kernel density estimate, it is known that one can tune the bandwidth such that the expected L1 error is within a constant factor of the optimal L1 error (obtained when one is allowed to choose the bandwidth with knowledge of the density). In this paper, we pose the same problem for variable bandwidth kernel estimates where the bandwidths are allowed to depend upon the location. We show in particular that for positive kernels on the real line, for any data-based bandwidth, there exists a densityfor which the ratio of expected L1 error over optimal L1 error tends to infinity. Thus, the problem of tuning the variable bandwidth in an optimal manner is ``too hard''. Moreover, from the class of counterexamples exhibited in the paper, it appears thatplacing conditions on the densities (monotonicity, convexity, smoothness) does not help.

Measuring ecological niche overlap from occurrence and spatial environmental data

1. Aim - Concerns over how global change will influence species distributions, in conjunction with increased emphasis on understanding niche dynamics in evolutionary and community contexts, highlight the growing need for robust methods to quantify niche differences between or within taxa. We propose a statistical framework to describe and compare environmental niches from occurrence and spatial environmental data.¦2. Location - Europe, North America, South America¦3. Methods - The framework applies kernel smoothers to densities of species occurrence in gridded environmental space to calculate metrics of niche overlap and test hypotheses regarding niche conservatism. We use this framework and simulated species with predefined distributions and amounts of niche overlap to evaluate several ordination and species distribution modeling techniques for quantifying niche overlap. We illustrate the approach with data on two well-studied invasive species.¦4. Results - We show that niche overlap can be accurately detected with the framework when variables driving the distributions are known. The method is robust to known and previously undocumented biases related to the dependence of species occurrences on the frequency of environmental conditions that occur across geographic space. The use of a kernel smoother makes the process of moving from geographical space to multivariate environmental space independent of both sampling effort and arbitrary choice of resolution in environmental space. However, the use of ordination and species distribution model techniques for selecting, combining and weighting variables on which niche overlap is calculated provide contrasting results.¦5. Main conclusions - The framework meets the increasing need for robust methods to quantify niche differences. It is appropriate to study niche differences between species, subspecies or intraspecific lineages that differ in their geographical distributions. Alternatively, it can be used to measure the degree to which the environmental niche of a species or intraspecific lineage has changed over time.

Interactive local bandwidth choice

A tool for user choice of the local bandwidth function for a kernel density estimate is developed using KDE, a graphical object-oriented package for interactive kernel density estimation written in LISP-STAT. The bandwidth function is a cubic spline, whose knots are manipulated by the user in one window, while the resulting estimate appears in another window. A real data illustration of this method raises concerns, because an extremely large family of estimates is available.

Integration of local-scale hydrological and regional-scale geophysical based on a nonlinear Bayesian sequential simulation approach

Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale. However, extending the corresponding approaches to the regional scale represents a major, and as-of-yet largely unresolved, challenge. To address this problem, we have developed a downscaling procedure based on a non-linear Bayesian sequential simulation approach. The basic objective of this algorithm is to estimate the value of the sparsely sampled hydraulic conductivity at non-sampled locations based on its relation to the electrical conductivity, which is available throughout the model space. The in situ relationship between the hydraulic and electrical conductivities is described through a non-parametric multivariate kernel density function. This method is then applied to the stochastic integration of low-resolution, re- gional-scale electrical resistivity tomography (ERT) data in combination with high-resolution, local-scale downhole measurements of the hydraulic and electrical conductivities. Finally, the overall viability of this downscaling approach is tested and verified by performing and comparing flow and transport simulation through the original and the downscaled hydraulic conductivity fields. Our results indicate that the proposed procedure does indeed allow for obtaining remarkably faithful estimates of the regional-scale hydraulic conductivity structure and correspondingly reliable predictions of the transport characteristics over relatively long distances.

Active regions for colour texture segmentation integrating region and boundary information

In this paper a colour texture segmentation method, which unifies region and boundary information, is proposed. The algorithm uses a coarse detection of the perceptual (colour and texture) edges of the image to adequately place and initialise a set of active regions. Colour texture of regions is modelled by the conjunction of non-parametric techniques of kernel density estimation (which allow to estimate the colour behaviour) and classical co-occurrence matrix based texture features. Therefore, region information is defined and accurate boundary information can be extracted to guide the segmentation process. Regions concurrently compete for the image pixels in order to segment the whole image taking both information sources into account. Furthermore, experimental results are shown which prove the performance of the proposed method