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It is closely related to the method of maximum likelihood (ML) estimation, but employs an augmented optimization objective which incorporates a prior density over the quantity one wants to estimate. MAP estimation is therefore a regularization of maximum likelihood estimation, so is not a well-defined statistic of the Bayesian posterior ...
From a given posterior distribution, various point and interval estimates can be derived, such as the maximum a posteriori (MAP) or the highest posterior density interval (HPDI). [4] But while conceptually simple, the posterior distribution is generally not tractable and therefore needs to be either analytically or numerically approximated.
The rabbit test became a widely used bioassay (animal-based test) to test for pregnancy. The term "rabbit test" was first recorded in 1949, and was the origin of a common euphemism, "the rabbit died", for a positive pregnancy test. [4] The phrase was, in fact, based on a common misconception about the test.
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 ...
A maximum likelihood estimator coincides with the most probable Bayesian estimator given a uniform prior distribution on the parameters. Indeed, the maximum a posteriori estimate is the parameter θ that maximizes the probability of θ given the data, given by Bayes' theorem:
The control line of this pregnancy test is blank, making the test invalid. The control line on the left of this pregnancy test is visible, suggesting that the test result is valid. A pale purple line has also appeared on the right hand side (the test line) which clearly signifies that the subject is pregnant.
In contrast, the related method of maximum a posteriori estimation is formally the application of the maximum a posteriori (MAP) estimation approach. This is more complex than maximum likelihood sequence estimation and requires a known distribution (in Bayesian terms, a prior distribution) for the underlying signal.
Mrs. Thompson set a record for the longest sextuplet pregnancy in the United States at 29 weeks and six days. One girl was stillborn; the five survivors are four girls (Octavia Daniela, Stella Kimberly, Ann Marie Amanda, and Emily Elizabeth) and one boy (Richard Linden). They are the first African-American sextuplets.