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Density Estimation
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. Example We will consider records of the incidence of diabetes. The following is quoted verbatim from the data set description: :''A population of women who were at least 21 years old, of Pima Indian heritage and living near Phoenix, Arizona, was tested for diabetes mellitus according to World Health Organization criteria. The data were collected by the US National Ins ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blood Plasma
Blood plasma is a light Amber (color), amber-colored liquid component of blood in which blood cells are absent, but which contains Blood protein, proteins and other constituents of whole blood in Suspension (chemistry), suspension. It makes up about 55% of the body's total blood volume. It is the Intravascular compartment, intravascular part of extracellular fluid (all body fluid outside cells). It is mostly water (up to 95% by volume), and contains important dissolved proteins (6–8%; e.g., serum albumins, globulins, and fibrinogen), glucose, clotting factors, electrolytes (, , , , , etc.), hormones, carbon dioxide (plasma being the main medium for excretory product transportation), and oxygen. It plays a vital role in an intravascular osmotic effect that keeps electrolyte concentration balanced and protects the body from infection and other blood-related disorders. Blood plasma can be separated from whole blood through blood fractionation, by adding an anticoagulant to a tube ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Histogram
A histogram is a visual representation of the frequency distribution, distribution of quantitative data. To construct a histogram, the first step is to Data binning, "bin" (or "bucket") the range of values— divide the entire range of values into a series of intervals—and then count how many values fall into each interval. The bins are usually specified as consecutive, non-overlapping interval (mathematics), intervals of a variable. The bins (intervals) are adjacent and are typically (but not required to be) of equal size. Histograms give a rough sense of the density of the underlying distribution of the data, and often for density estimation: estimating the probability density function of the underlying variable. The total area of a histogram used for probability density is always normalized to 1. If the length of the intervals on the ''x''-axis are all 1, then a histogram is identical to a relative frequency plot. Histograms are sometimes confused with bar charts. In a his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean Integrated Squared Error
In statistics, the mean integrated squared error (MISE) is used in density estimation. The MISE of an estimate of an unknown probability density is given by :\operatorname\, f_n-f\, _2^2=\operatorname\int (f_n(x)-f(x))^2 \, dx where ''ƒ'' is the unknown density, ''ƒ''''n'' is its estimate based on a sample of ''n'' independent and identically distributed random variables. Here, E denotes the expected value with respect to that sample. The MISE is also known as ''L''2 risk function. See also * Minimum distance estimation * Mean squared error In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference betwee ... References {{DEFAULTSORT:Mean Integrated Squared Error Estimation of densities Nonparametric statistics Point estimation performance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kernel Density Estimation
In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on '' kernels'' as weights. KDE answers a fundamental data smoothing problem where inferences about the population are made based on a finite data sample. In some fields such as signal processing and econometrics it is also termed the Parzen–Rosenblatt window method, after Emanuel Parzen and Murray Rosenblatt, who are usually credited with independently creating it in its current form. One of the famous applications of kernel density estimation is in estimating the class-conditional marginal densities of data when using a naive Bayes classifier, which can improve its prediction accuracy. Definition Let be independent and identically distributed samples drawn from some univariate distribution with an unknown density at any given point . We are in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Distribution
In probability theory and statistics, a probability distribution is a Function (mathematics), function that gives the probabilities of occurrence of possible events for an Experiment (probability theory), experiment. It is a mathematical description of a Randomness, random phenomenon in terms of its sample space and the Probability, probabilities of Event (probability theory), events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that fair coin, the coin is fair). More commonly, probability distributions are used to compare the relative occurrence of many different random values. Probability distributions can be defined in different ways and for discrete or for continuous variables. Distributions with special properties or for especially important applications are given specific names. Introduction A prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydrology
Hydrology () is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle, water resources, and drainage basin sustainability. A practitioner of hydrology is called a hydrologist. Hydrologists are scientists studying earth science, earth or environmental science, civil engineering, civil or environmental engineering, and physical geography. Using various analytical methods and scientific techniques, they collect and analyze data to help solve water related problems such as Environmentalism, environmental preservation, natural disasters, and Water resource management, water management. Hydrology subdivides into surface water hydrology, groundwater hydrology (hydrogeology), and marine hydrology. Domains of hydrology include hydrometeorology, surface-water hydrology, surface hydrology, hydrogeology, drainage basin, drainage-basin management, and water quality. Oceanography and meteorology are not included beca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Novelty Detection
Novelty detection is the mechanism by which an intelligent organism is able to identify an incoming sensory pattern as being hitherto unknown. If the pattern is sufficiently salient or associated with a high positive or strong negative utility, it will be given computational resources for effective future processing. The principle is long known in neurophysiology, with roots in the orienting response research by E. N. Sokolov in the 1950s. The reverse phenomenon is habituation, i.e., the phenomenon that known patterns yield a less marked response. Early neural modeling attempts were by Yehuda Salu. An increasing body of knowledge has been collected concerning the corresponding mechanisms in the brain. In technology, the principle became important for radar detection methods during the Cold War, where unusual aircraft-reflection patterns could indicate an attack by a new type of aircraft. Today, the phenomenon plays an important role in machine learning and data science, where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anomaly Detection
In data analysis, anomaly detection (also referred to as outlier detection and sometimes as novelty detection) is generally understood to be the identification of rare items, events or observations which deviate significantly from the majority of the data and do not conform to a well defined notion of normal behavior. Such examples may arouse suspicions of being generated by a different mechanism, or appear inconsistent with the remainder of that set of data. Anomaly detection finds application in many domains including cybersecurity, medicine, machine vision, statistics, neuroscience, law enforcement and financial fraud to name only a few. Anomalies were initially searched for clear rejection or omission from the data to aid statistical analysis, for example to compute the mean or standard deviation. They were also removed to better predictions from models such as linear regression, and more recently their removal aids the performance of machine learning algorithms. However, in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gumbel Distribtion , a fictional character from ''The Simpsons''
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Gumbel or Gumble is a surname. Notable people with the surname include: * Albert Gumble (1883–1946), American musician * Bryant Gumbel (born 1948), American television sportscaster, brother of Greg * David Heinz Gumbel (1906–1992), Israeli designer and silversmith * Emil Julius Gumbel (1891–1966), German mathematician, pacifist and anti-Nazi campaigner * Greg Gumbel (1946–2024), American television sportscaster, brother of Bryant * Nicky Gumbel (born 1955), Anglican priest and author * Thomas Gumble (died 1676), English biographer * Wilhelm Theodor Gumbel (1812–1858), German bryologist * Wilhelm von Gumbel (1823–1898), German geologist Fictional * Barney Gumble Barnard "Barney" Gumble is a recurring character in the American animated TV series ''The Simpsons''. He is voiced by Dan Castellaneta and first appeared in the series premiere episode " Simpsons Roasting on an Open Fire". Barney is the town ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayes' Rule
Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting conditional probabilities, allowing one to find the probability of a cause given its effect. For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to someone of a known age to be assessed more accurately by conditioning it relative to their age, rather than assuming that the person is typical of the population as a whole. Based on Bayes' law, both the prevalence of a disease in a given population and the error rate of an infectious disease test must be taken into account to evaluate the meaning of a positive test result and avoid the '' base-rate fallacy''. One of Bayes' theorem's many applications is Bayesian inference, an approach to statistical inference, where it is used to invert the probability of observations given a model configuration (i.e., the likelihood function) to obtain the probability o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean
A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statistics. Each attempts to summarize or typify a given group of data, illustrating the magnitude and sign of the data set. Which of these measures is most illuminating depends on what is being measured, and on context and purpose. The ''arithmetic mean'', also known as "arithmetic average", is the sum of the values divided by the number of values. The arithmetic mean of a set of numbers ''x''1, ''x''2, ..., x''n'' is typically denoted using an overhead bar, \bar. If the numbers are from observing a sample of a larger group, the arithmetic mean is termed the '' sample mean'' (\bar) to distinguish it from the group mean (or expected value) of the underlying distribution, denoted \mu or \mu_x. Outside probability and statistics, a wide rang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
