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Up-and-Down Designs
Up-and-down designs (UDDs) are a family of statistical experiment designs used in dose-finding experiments in science, engineering, and medical research. Dose-finding experiments have ''binary responses'': each individual outcome can be described as one of two possible values, such as success vs. failure or toxic vs. non-toxic. Mathematically the binary responses are coded as 1 and 0. The goal of dose-finding experiments is to estimate the strength of treatment (i.e., the "dose") that would trigger the "1" response a pre-specified proportion of the time. This dose can be envisioned as a percentile of the distribution of response thresholds. An example where dose-finding is used is in an experiment to estimate the LD50 of some toxic chemical with respect to mice. Dose-finding designs are sequential and response-adaptive: the dose at a given point in the experiment depends upon previous outcomes, rather than be fixed ''a priori''. Dose-finding designs are generally more efficie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bruceton Analysis
A Bruceton analysis is one way of analyzing the sensitivity of explosives as described originally by Dixon and Mood in 1948. Also known as the " Up and Down Test" or "the staircase method", a Bruceton analysis relies upon two parameters: first stimulus and step size. A stimulus is provided to the sample, and the results noted. If a positive result is noted, then the stimulus is decremented by the step size. If a negative result occurs, the stimulus is increased. The test continues with each sample tested at a stimulus 1 step up or down from the previous stimulus if the previous result was negative or positive. The results are tabulated and analyzed via Bruceton analysis, a simple computation of sums that can be performed by pencil and paper, to provide estimates of the mean and standard deviation. Confidence estimates are also produced. Other analysis methods are the Neyer d-optimal test and Dror and Steinberg 008sequential procedure. Bruceton analysis has an advantage over the mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical
Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Matrix
In mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability. It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix. The stochastic matrix was first developed by Andrey Markov at the beginning of the 20th century, and has found use throughout a wide variety of scientific fields, including probability theory, statistics, mathematical finance and linear algebra, as well as computer science and population genetics. There are several different definitions and types of stochastic matrices: :A right stochastic matrix is a real square matrix, with each row summing to 1. :A left stochastic matrix is a real square matrix, with each column summing to 1. :A doubly stochastic matrix is a square matrix of nonnegative real numbers with each row and column summing to 1. In the same vein, one may define a stochastic vector (also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isotonic Regression
In statistics and numerical analysis, isotonic regression or monotonic regression is the technique of fitting a free-form line to a sequence of observations such that the fitted line is non-decreasing (or non-increasing) everywhere, and lies as close to the observations as possible. Applications Isotonic regression has applications in statistical inference. For example, one might use it to fit an isotonic curve to the means of some set of experimental results when an increase in those means according to some particular ordering is expected. A benefit of isotonic regression is that it is not constrained by any functional form, such as the linearity imposed by linear regression, as long as the function is monotonic increasing. Another application is nonmetric multidimensional scaling, where a low-dimensional embedding for data points is sought such that order of distances between points in the embedding matches order of dissimilarity between points. Isotonic regression is use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probit Model
In statistics, a probit model is a type of regression where the dependent variable can take only two values, for example married or not married. The word is a portmanteau, coming from ''probability'' + ''unit''. The purpose of the model is to estimate the probability that an observation with particular characteristics will fall into a specific one of the categories; moreover, classifying observations based on their predicted probabilities is a type of binary classification model. A probit model is a popular specification for a binary response model. As such it treats the same set of problems as does logistic regression using similar techniques. When viewed in the generalized linear model framework, the probit model employs a probit link function. It is most often estimated using the maximum likelihood procedure, such an estimation being called a probit regression. Conceptual framework Suppose a response variable ''Y'' is ''binary'', that is it can have only two possible outcomes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abscissa
In common usage, the abscissa refers to the (''x'') coordinate and the ordinate refers to the (''y'') coordinate of a standard two-dimensional graph. The distance of a point from the y-axis, scaled with the x-axis, is called abscissa or x coordinate of the point. The distance of a point from x-axis scaled with the y-axis is called ordinate. For example, if (x, y) is an ordered pair in the Cartesian plane, then the first coordinate in the plane (x) is called the abscissa and the second coordinate (y) is the ordinate. In mathematics, the abscissa (; plural ''abscissae'' or ''abscissas'') and the ordinate are respectively the first and second coordinate of a point in a Cartesian coordinate system: :abscissa \equiv x-axis (horizontal) coordinate :ordinate \equiv y-axis (vertical) coordinate Usually these are the horizontal and vertical coordinates of a point in plane, the rectangular coordinate system. An ordered pair consists of two terms—the abscissa (horizontal, usually '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Misrak Gezmu
Misrak Gezmu is an Ethiopian-American statistician who works as a mathematical statistician and grant officer for the Biostatistics Research Branch of the National Institute of Allergy and Infectious Diseases. She is known for her pioneering doctoral research on the statistics of up-and-down designs. Gezmu is originally from Ethiopia. She earned a Ph.D. in statistics from American University in Washington, D.C. in 1996; Her doctoral dissertation, ''The Geometric Up-and-Down Design for Allocating Dosage Levels'', was supervised by Nancy Flournoy. While still a doctoral student, she became an assistant professor of decision sciences at Norfolk State University in Virginia in 1993. She moved to the National Institute of Allergy and Infectious Diseases in 1998. Gezmu is a Fellow of the American Statistical Association Like many other academic professional societies, the American Statistical Association (ASA) uses the title of Fellow of the American Statistical Association as its h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton–Raphson
In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a single-variable function defined for a real variable , the function's derivative , and an initial guess for a root of . If the function satisfies sufficient assumptions and the initial guess is close, then :x_ = x_0 - \frac is a better approximation of the root than . Geometrically, is the intersection of the -axis and the tangent of the graph of at : that is, the improved guess is the unique root of the linear approximation at the initial point. The process is repeated as :x_ = x_n - \frac until a sufficiently precise value is reached. This algorithm is first in the class of Householder's methods, succeeded by Halley's method. The method can also be extended to complex functions an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mode (statistics)
The mode is the value that appears most often in a set of data values. If is a discrete random variable, the mode is the value (i.e, ) at which the probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled. Like the statistical mean and median, the mode is a way of expressing, in a (usually) single number, important information about a random variable or a population. The numerical value of the mode is the same as that of the mean and median in a normal distribution, and it may be very different in highly skewed distributions. The mode is not necessarily unique to a given discrete distribution, since the probability mass function may take the same maximum value at several points , , etc. The most extreme case occurs in uniform distributions, where all values occur equally frequently. When the probability density function of a continuous distribution has multiple local maxima it is common to refer to all of the local ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
