Concepts inAutomatic sampling with the ratio-of-uniforms method
Logarithmically concave function
In convex analysis, a non-negative function f : R → R+ is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it satisfies the inequality for all x,y ∈ dom f and 0 < θ < 1. If f is strictly positive, this is equivalent to saying that the logarithm of the function, log ∘ f, is concave; that is, for all x,y ∈ dom f and 0 < θ < 1.
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Random variate
A random variate is a particular outcome of a random variable: the random variates which are other outcomes of the same random variable would have different values. Random variates are used when simulating processes driven by random influences.
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Uniform distribution (continuous)
In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable. The support is defined by the two parameters, a and b, which are its minimum and maximum values. The distribution is often abbreviated U(a,b).
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Expected value
In probability theory, the expected value (or expectation, or mathematical expectation, or mean, or the first moment) of a random variable is the weighted average of all possible values that this random variable can take on. The weights used in computing this average correspond to the probabilities in case of a discrete random variable, or densities in case of a continuous random variable.
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Closed-form expression
In mathematics, an expression is said to be a closed-form expression if it can be expressed analytically in terms of a finite number of certain "well-known" functions. Typically, these well-known functions are defined to be elementary functions—constants, one variable x, elementary operations of arithmetic (+ − × ÷), nth roots, exponent and logarithm (which thus also include trigonometric functions and inverse trigonometric functions).
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Efficiency (statistics)
In statistics, efficiency is a term used in the comparison of various statistical procedures and, in particular, it refers to a measure of the optimality of an estimator, of an experimental design or of an hypothesis testing procedure. Essentially, a more efficient estimator, experiment or test needs fewer samples than a less efficient one to achieve a given performance.
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Parameter
Parameter (from Ancient Greek παρά also “para” meaning “beside, subsidiary” and μέτρον also “metron” meaning “measure”) can be interpreted in mathematics, logic, linguistics, environmental science and other disciplines. In its common meaning, the term is used to identify a characteristic, a feature, a measurable factor that can help in defining a particular system.
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Polygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain or circuit. A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments (i.e. , by a closed polygonal chain). These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices or corners. An n-gon is a polygon with n sides.
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