Search results
Results from the WOW.Com Content Network
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.
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.
The EM method was modified to compute maximum a posteriori (MAP) estimates for Bayesian inference in the original paper by Dempster, Laird, and Rubin. Other methods exist to find maximum likelihood estimates, such as gradient descent, conjugate gradient, or variants of the Gauss–Newton algorithm. Unlike EM, such methods typically require the ...
where ^ is the location of a mode of the joint target density, also known as the maximum a posteriori or MAP point and is the positive definite matrix of second derivatives of the negative log joint target density at the mode = ^. Thus, the Gaussian approximation matches the value and the log-curvature of the un-normalised target density at the ...
Posterior probability is a conditional probability conditioned on randomly observed data. Hence it is a random variable. For a random variable, it is important to summarize its amount of uncertainty. One way to achieve this goal is to provide a credible interval of the posterior probability. [11]
Bayesian linear regression is a type of conditional modeling in which the mean of one variable is described by a linear combination of other variables, with the goal of obtaining the posterior probability of the regression coefficients (as well as other parameters describing the distribution of the regressand) and ultimately allowing the out-of-sample prediction of the regressand (often ...
In Bayesian statistics, Laplace's approximation can refer to either approximating the posterior normalizing constant with Laplace's method or approximating the posterior distribution with a Gaussian centered at the maximum a posteriori estimate. [1] [2] Laplace approximations are used in the integrated nested Laplace approximations method for ...
If the probability of a transition from one state to the other is defined as in both directions, then the probability to remain in the same state at each time step is . The probability to measure the state correctly is γ {\displaystyle \gamma } (and conversely, the probability of an incorrect measurement is 1 − γ {\displaystyle {1-\gamma }} ).