Density estimation

: The true density is a mixture of two Gaussians centered around 0 and 3, shown with a solid blue curve. In each frame, 100 samples are generated from the distribution, shown in red. Centered on each sample, a Gaussian kernel is drawn in gray. Averaging the Gaussians yields the density estimate shown in the dashed black curve. In statistics, probability density estimation or simply 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, including vector quantization. The most basic form of density estimation is a rescaled histogram.

: The true density is a mixture of two Gaussians centered around 0 and 3, shown with a solid blue curve. In each frame, 100 samples are generated from the distribution, shown in red. Centered on each sample, a Gaussian kernel is drawn in gray. Averaging the Gaussians yields the density estimate shown in the dashed black curve. In statistics, probability density estimation or simply 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, including vector quantization. The most basic form of density estimation is a rescaled histogram. The first figure shows density estimates of p(glu | diabetes=1), p(glu | diabetes=0), and p(glu). 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. From the density of "glu" conditional on diabetes, we can obtain the probability of diabetes conditional on "glu" via Bayes' rule. For brevity, "diabetes" is abbreviated "db." in this formula. p(\mbox{diabetes}=1\mid\mbox{glu}) = \frac{p(\mbox{glu}\mid\mbox{db.}=1)\,p(\mbox{db.}=1)}{p(\mbox{glu}\mid\mbox{db.}=1)\,p(\mbox{db.}=1) + p(\mbox{glu}\mid \mbox{db.}=0)\,p(\mbox{db.}=0)} The second figure shows the estimated posterior probability p(diabetes=1 | glu). From these data, it appears that an increased level of "glu" is associated with diabetes. ==Kernel density estimation== ==External links== CREEM: Centre for Research Into Ecological and Environmental Modelling Downloads for free density estimation software packages Distance 4 (from Research Unit for Wildlife Population Assessment "RUWPA") and WiSP. UCI Machine Learning Repository Content Summary (See "Pima Indians Diabetes Database" for the original data set of 732 records, and additional notes.) MATLAB code for one dimensional and two dimensional density estimation libAGF C++ software for variable kernel density estimation.

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