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The Viterbi algorithm is a dynamic programming algorithm for obtaining the maximum a posteriori probability estimate of the most likely sequence of hidden states—called the Viterbi path—that results in a sequence of observed events.
Iterative Viterbi decoding is an algorithm that spots the subsequence S of an observation O = {o 1, ..., o n} having the highest average probability (i.e., probability scaled by the length of S) of being generated by a given hidden Markov model M with m states. The algorithm uses a modified Viterbi algorithm as an internal step.
Thus the sampling distribution of the quantile of the sample maximum is the graph x 1/k from 0 to 1: the p-th to q-th quantile of the sample maximum m are the interval [p 1/k N, q 1/k N]. Inverting this yields the corresponding confidence interval for the population maximum of [m/q 1/k, m/p 1/k].
An estimation procedure that is often claimed to be part of Bayesian statistics is the maximum a posteriori (MAP) estimate of an unknown quantity, that equals the mode of the posterior density with respect to some reference measure, typically the Lebesgue measure.
Bayesian optimization of a function (black) with Gaussian processes (purple). Three acquisition functions (blue) are shown at the bottom. [19]Probabilistic numerics have also been studied for mathematical optimization, which consist of finding the minimum or maximum of some objective function given (possibly noisy or indirect) evaluations of that function at a set of points.
It starts from an assumption about a probabilistic distribution of the set of all possible inputs. This assumption is then used to design an efficient algorithm or to derive the complexity of a known algorithm. This approach is not the same as that of probabilistic algorithms, but the two may be combined.
In decision theory, the odds algorithm (or Bruss algorithm) is a mathematical method for computing optimal strategies for a class of problems that belong to the domain of optimal stopping problems. Their solution follows from the odds strategy , and the importance of the odds strategy lies in its optimality, as explained below.
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model , the observed data is most probable.