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As a prelude to a transition-probability definition, we first motivate the definition of a regular rate matrix. We will use the transition-rate matrix Q {\displaystyle Q} to specify the dynamics of the Markov chain by means of generating a collection of transition matrices P ( t ) {\displaystyle P(t)} on S {\displaystyle S} ( t ∈ R ≥ 0 ...
The principle of maximum caliber (MaxCal) or maximum path entropy principle, suggested by E. T. Jaynes, [1] can be considered as a generalization of the principle of maximum entropy. It postulates that the most unbiased probability distribution of paths is the one that maximizes their Shannon entropy. This entropy of paths is sometimes called ...
[2] [3] [4] Modeling the probability of financial ruin as a first passage time was an early application in the field of insurance. [5] An interest in the mathematical properties of first-hitting-times and statistical models and methods for analysis of survival data appeared steadily between the middle and end of the 20th century.
Viterbi path and Viterbi algorithm have become standard terms for the application of dynamic programming algorithms to maximization problems involving probabilities. [3] For example, in statistical parsing a dynamic programming algorithm can be used to discover the single most likely context-free derivation (parse) of a string, which is ...
Given an initial path, TPS provides some algorithms to perturb that path and create a new one. As in all Monte Carlo walks, the new path will then be accepted or rejected in order to have the correct path probability. The procedure is iterated and the ensemble is gradually sampled. A powerful and efficient algorithm is the so-called shooting ...
1.9×10 −3: Probability of being dealt a flush in poker 2.7×10 −3: Probability of a random day of the year being your birthday (for all birthdays besides Feb. 29) 4×10 −3: Probability of being dealt a straight in poker 10 −2: Centi-(c) 1.8×10 −2: Probability of winning any prize in the UK National Lottery with one ticket in 2003 2. ...
In the theory of probability for stochastic processes, the reflection principle for a Wiener process states that if the path of a Wiener process f(t) reaches a value f(s) = a at time t = s, then the subsequent path after time s has the same distribution as the reflection of the subsequent path about the value a. [1]
Seidel's algorithm is an algorithm designed by Raimund Seidel in 1992 for the all-pairs-shortest-path problem for undirected, unweighted, connected graphs. [1] It solves the problem in () expected time for a graph with vertices, where < is the exponent in the complexity () of matrix multiplication.