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Topic: Density estimation

	Illustration of density estimation - Wikipedia, the free encyclopedia
		In this example, we will construct three density estimates for "glu" (plasma glucose concentration), one conditional on the presence of diabetes, the second conditional on the absence of diabetes, and the third not conditional on diabetes.
		The density estimates are kernel density estimates using a Gaussian kernel.
		That is, a Gaussian density function is placed at each data point, and the sum of the density functions is computed over the range of the data.
	en.wikipedia.org /wiki/Illustration_of_density_estimation (504 words)

	Density estimation - Wikipedia, the free encyclopedia
		In probability and statistics, density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function.
		The unobservable density function is thought of as the density according to which a large population is distributed; the data are usually thought of as a random sample from that population.
		A variety of approaches to density estimation are used, including Parzen windows and a range of data clustering techniques.
	en.wikipedia.org /wiki/Density_estimation (99 words)

	Adding Density Estimates (Site not responding. Last check: 2007-10-21)
		Density estimation is the construction of an estimate of the density function from the observed data.
		Density curves are sometimes preferred because they do not contain the discontinuous steps present in histograms.
		In parametric estimation, the data are assumed to be from a known parametric family of distributions.
	www.uni.edu /sasdoc/insight/chap12/sect5.htm (150 words)

	Density Estimation
		The density estimate at a point is computed by dividing the number of observations within a sphere centered at the point by the product of the sample size and the volume of the sphere.
		Cascaded density estimates are obtained by computing initial kernel density estimates and then, at each observation, taking the arithmetic mean, harmonic mean, or sum of the initial density estimates of the observations within the neighborhood.
		Cascaded estimates, especially using sums, may be more sensitive to the local covariance structure of the distribution than are the uncascaded kernel estimates.
	www.asu.edu /sas/sasdoc/sashtml/stat/chap42/sect10.htm (821 words)

	Log-density estimation in linear inverse problems, Ja-Yong Koo, Han-Yeong Chung
		We estimate a probability density function p which is related by a linear operator K to a density function q in sequences of regular exponential families based on a random sample from q.
		Bounds on the Kullback-Leibler distance between the true density and the estimators are obtained and rates of convergence are established for log-density functions having a measure of smoothness.
		The density estimator converges to the unknown density in the Kullback-Leibler sense and in the $L_2$-sense at a rate determined not only by the order of smoothness of the log-density and the dimension of data but also by the decay rate of the singular values of the operator.
	projecteuclid.org /Dienst/UI/1.0/Display/euclid.aos/1030563989 (891 words)

	Kernel Density Estimation (Site not responding. Last check: 2007-10-21)
		Statistical density estimation involves approximating a hypothesized probability density function from observed data.
		Kernel density estimation is a nonparametric technique for density estimation in which a known density function (the kernel) is averaged across the observed data points to create a smooth approximation.
		PROC KDE uses a Gaussian density as the kernel, and its assumed variance determines the smoothness of the resulting estimate.
	www.nysaes.cornell.edu /cc/stat/STAT-HTML/CHAP13/SECT13.HTM (128 words)

	Nonparametric density estimation via wavelets
		It transfers a density estimation problem into a regression problem by binning the observations, and then treating the square root of the observation counts as the new data for regression.
		Because of the automatic adaptivity of wavelet methods, this density estimation method achieves the optimal convergence rate and is computationally efficient.
		In this setting the density estimator is used to describe the arrival rate of phone calls as a function of covariates such as time-of-day and day of the week.
	repository.upenn.edu /dissertations/AAI3043983 (160 words)

	Density Estimation (Site not responding. Last check: 2007-10-21)
		Provided a set of data, the procedure will compute a kernel density estimate (see Silverman (1986) or other references for details) at a specified number of points, and plot the resulting estimate.
		The user can choose from among several kernels, and specify both a bandwidth value and the number of points at which the estimate is computed.
		Silverman, B. Density Estimation for Statistics and Data Analysis.
	www.stat.sc.edu /rsrch/gasp/density (111 words)

	Density Estimation
		Density, ratio of the mass of a substance to its volume, expressed, for example, in units of grams per cubic centimeter or pounds per cubic foot.
		The density of a pure substance varies little from sample to sample and is often considered a characteristic property of the substance.
		The density of a gas is often converted mathematically to what it would be at a standard temperature and pressure (STP).
	www.pirika.com /chem/TCPEE/Den/ourDen.htm (178 words)

	Chong's Research
		The data are plotted as the finely-binned histogram in dotted lines, the estimate is in solid line, and the true density is in dashed line.
		Below is a simulated example of density estimation using length-biased data on [0,1].
		Estimated joint density is contoured in the triangle, data are superimposed as circles, and the corresponding marginals are plotted in the blank space.
	www.stat.purdue.edu /~chong/resch.html (510 words)

	Kernel Density Estimation from (Site not responding. Last check: 2007-10-21)
		We extend the kernel density estimation method to accept uncertain observations modeled by likelihood functions of the unobserved samples.
		The estimation of probability density functions form random samples is a basic problem in several domains of applied sciences, machine learning among them.
		Kernel method is the non-parametric technique used in our approach to density estimation, but conveniently adapted to cope with uncertainty in the observations.
	learn98.tsc.uc3m.es /~learn98/papers/abstracts/paper001/abstract.html (1271 words)

	Conditional Density Estimation
		with the j superscript to indicate that it is obtained from the previous estimate of the joint density.
		The Bayesian integration estimate of the conditional density appears to be different and inferior from the conditional Bayesian integration estimate of the unconditional density.
		From this example we note that (regardless of the degree of sophistication of the inference) direct conditional density estimation is different and superior to conditioned joint density estimation.
	vismod.media.mit.edu /tech-reports/TR-507/node36.html (699 words)

	Adaptive Kernel Density Estimation - Sain (ResearchIndex)
		A New Characterization and Estimation of the Zero-Bias Bandwidth - Sain (2000)
		13 Estimation of a Multivariate Density (context) - Cacoullos - 1966
		3 Arbitrariness of the Pilot Estimator in Adaptive Kernel Meth..
	citeseer.ist.psu.edu /sain94adaptive.html (1116 words)

	Adaptive techniques for density estimation
		The equivalence of Poisson regression and density estimation allows to extend both the propagation-separation approach and stagewise aggregation to the problem of density estimation.
		The applicability of the propagation-separation approach is, being based on a local constant structural assumption, currently restricted to densities with pronounced discontinuities.
		The figure illustrates the density estimates obtained by stagewise aggregation (left) and a non-adaptive kernel density estimate (right) for the Old Faithful Geyser data set.
	www.wias-berlin.de /project-areas/stat/projects/density.html (95 words)

	- SHOP.COM
		Density estimation has long been recognized as an important tool when used with univariate and bivariate data.
		By presenting the major ideas in the context of the classical histogram, the text simplifies the understanding of advanced estimators and develops links between the intuitive histogram and other methods that are more statistically efficient.
		Ideal as an introductory textbook, Multivariate Density Estimation is also an indispensable professional reference for statisticians, biostatisticians, electrical engineers, econometricians, and other scientistsinvolved in data analysis.
	www.shop.com /op/aprod-p26281113 (383 words)

	Kernel Density Estimation (Site not responding. Last check: 2007-10-21)
		the number of equally spaced points at which the density is to be estimated.
		the left and right-most points of the grid at which the density is to be estimated.
		computes kernel density estimates with the given kernel and bandwidth (which is the standard deviation of the kernel).
	www.math.montana.edu /Rweb/Rhelp/density.html (282 words)

	Logspline Density Estimation for Binned Data (ResearchIndex)
		An algorithm involving a procedure similar to maximum likelihood, stepwise knot addition, and stepwise knot deletion is proposed for the estimation of the density function based upon binned data.
		15 Density estimation and bump-hunting by the penalized likelih..
		6 Wavelet density estimation by approximation of log-densities (context) - Koo - 1996
	citeseer.ist.psu.edu /267621.html (460 words)

	Kernel Density Estimation (Site not responding. Last check: 2007-10-21)
		Kernel density estimation consists of estimating a posterior density for a function of interest, using samples from the posterior, often drawn using one of the numerical techniques.
		This expected value may be approximated in the usual fashion, as a simple numerical average of the values of the function at each of the sample points.
		Kernel density estimation is a standard method of examining posterior distributions, and properties of functions of the parameters.
	www.maths.tcd.ie /~chas/node46.html (107 words)

	The Wavelet Digest :: View topic - Preprint: Density estimation via wavelets
		Estimating the square root of a density via compactly supported wavelets
		Instead of estimating the unknown density directly, we estimate the
		positiveness and the $L_1$- norm of the density estimate.
	www.wavelet.org /phpBB2/viewtopic.php?t=2937 (176 words)

	Spatial Resolution and Noise Tradeoffs in Pinhole Imaging System Design:A Density Estimation Approach
		We consider image recovery algorithms based on density estimation methods using kernels that are based on apodized inverse filters.
		The analysis shows that the pinhole size that minimizes the estimate variance for a specied reconstructed spatial resolution is directly proportional to that spatial resolution.
		B W Silverman, "On the estimation of a probability density function by the maximum penalized likelihood method," Ann.
	www.opticsexpress.org /abstract.cfm?URI=OPEX-2-6-237 (889 words)

	Efficient Nonparametric Density Estimation on the Sphere with Applications in Fluid Mechanics
		The application of nonparametric probability density function estimation for the purpose of data analysis is well established.
		Accurate and fast estimation of probability density functions is crucial for these calculations since the density estimation is performed at each iteration during the computation.
		We propose a special sequence of weight functions for nonparametric density estimation that is especially suitable for such applications.
	epubs.siam.org /sam-bin/dbq/article/29046 (264 words)

	Semiparametric density estimation under a two-sample density ratio model, K.F. Cheng, C.K. Chu
		A semiparametric density estimation is proposed under a two-sample density ratio model.
		Our proposed density estimate is therefore an extension of the kernel density estimate suggested by Jones for length-biased data.
		We show that under the model considered the new density estimator not only is consistent but also has the `smallest' asymptotic variance among general nonparametric density estimators.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.bj/1093265631 (645 words)

	Chameleon Statistics - Density Estimation (Site not responding. Last check: 2007-10-21)
		The goal of density estimation is to model the distribution of data in the population based upon the distribution of the samples.
		Accurate estimation of population distributions from samples of limited size is an important but challenging problem.
		We would like to estimate the population distribution from which these samples are derived.
	www.seventh-sense-software.com /Chameleon/density.htm (109 words)

	Mixture Density Estimation - Li, Barron (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		In both cases, it is possible to give simple expressions for the iterative improvement of performance as components of the network are introduced one at a time.
		In particular, for mixture density estimation we show that a k-component mixture estimated by maximum likelihood (or by an iterative likelihood...
		...in density estimation, the goal is to find a model that has the smallest negative log likelihood.
	citeseer.ist.psu.edu /li99mixture.html (477 words)

	Demetrius at The Australian National University: Item 1885/40365 (Site not responding. Last check: 2007-10-21)
		In this paper, we consider the non-parametric, kernel estimate of the density, f(x), for data drawn from stratified samples.
		A weighted estimator is developed which provides asymptotically unbiased density estimation for stratified samples.
		The weighted estimator and proposed bandwidth are shown to give smaller mean squared error for stratified samples than an unweighted estimator and a commonly used method of choosing the bandwidth.
	hdl.handle.net /1885/40365 (216 words)

	Pareto Density Estimation \| Databionics (Site not responding. Last check: 2007-10-21)
		The difficult problem of empirical probability density estimation is solved using information optimla sets in form of the Pareto Density Estimation (PDE) gelöst (Ultsch 2003).
		For high dimensional data the PDE gives a density estimation especially suited for the discovery of clusters (Ultsch 2004).
		The multidimensional PDE is also used for the visualization of Emergent SOM in form of the P-Matrix.
	www.mathematik.uni-marburg.de /~databionics/en?q=pde (186 words)

	PCA and VQ as density estimation (Site not responding. Last check: 2007-10-21)
		In one dimension, the Gaussian density is defined by
		According to the Cramer-Rao bound, the ML estimator performs optimally in a certain sense, in the limit of infinite data.
		Vapnik's critique of density estimation the model is never correct not "consistent" procedure in the statistical sense example of two Gaussians with different sizes
	hebb.mit.edu /courses/9.641/2000/lectures/lecture23.html (495 words)

	Global Illumination via Density Estimation (Site not responding. Last check: 2007-10-21)
		This paper presents the density estimation framework for generating view-independent global illumination solutions.
		It works by probabilisticly simulating the light flow in an environment with light particles that trace random walks originating at luminaires and then using statistical density estimation techniques to reconstruct the lighting on each surface.
		A new local linear density estimation technique eliminates boundary bias and extends to arbitrary polygons.
	www.graphics.cornell.edu /~bjw/detog.html (217 words)

	Probability Density Estimation from Optimally Condensed Data Samples (Site not responding. Last check: 2007-10-21)
		The requirement to reduce the computational cost of evaluating a point probability density estimate when employing a Parzen window estimator is a well-known problem.
		This paper presents the Reduced Set Density Estimator that provides a kernel-based density estimator which employs a small percentage of the available data sample and is optimal in the L_2 sense.
		It is also demonstrated that the proposed density estimator consistently provides superior density estimates for similar levels of data reduction to that provided by the recently proposed Density-Based Multiscale Data Condensation algorithm and, in addition, has comparable computational scaling.
	csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/trans/tp/&toc=comp/trans/tp/2003/10/ixtoc.xml&DOI=10.1109/TPAMI.2003.1233899 (788 words)

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