Method of estimating the parameters of a statistical model
This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Maximum a posteriori estimation" – news · newspapers · books · scholar · JSTOR(September 2011) (Learn how and when to remove this message)
Part of a series on
Bayesian statistics
Posterior = Likelihood × Prior ÷ Evidence
Background
Bayesian inference
Bayesian probability
Bayes' theorem
Bernstein–von Mises theorem
Coherence
Cox's theorem
Cromwell's rule
Principle of indifference
Principle of maximum entropy
Model building
Weak prior ... Strong prior
Conjugate prior
Linear regression
Empirical Bayes
Hierarchical model
Posterior approximation
Markov chain Monte Carlo
Laplace's approximation
Integrated nested Laplace approximations
Variational inference
Approximate Bayesian computation
Estimators
Bayesian estimator
Credible interval
Maximum a posteriori estimation
Evidence approximation
Evidence lower bound
Nested sampling
Model evaluation
Bayes factor
Model averaging
Posterior predictive
Mathematics portal
v
t
e
In Bayesian statistics, a maximum a posteriori probability (MAP) estimate is an estimate of an unknown quantity, that equals the mode of the posterior distribution. The MAP can be used to obtain a point estimate of an unobserved quantity on the basis of empirical data. It is closely related to the method of maximum likelihood (ML) estimation, but employs an augmented optimization objective which incorporates a prior distribution (that quantifies the additional information available through prior knowledge of a related event) over the quantity one wants to estimate. MAP estimation can therefore be seen as a regularization of maximum likelihood estimation.
and 26 Related for: Maximum a posteriori estimation information
generally equivalent to maximumaposteriori (MAP) estimation with uniform prior distributions (or a normal prior distribution with a standard deviation of...
maximumaposterioriestimation is formally the application of the maximumaposteriori (MAP) estimation approach. This is more complex than maximum likelihood...
Bayesian statistics is maximumaposterioriestimation. Suppose an unknown parameter θ {\displaystyle \theta } is known to have a prior distribution π {\displaystyle...
of the maximum entropy principle is in discrete and continuous density estimation. Similar to support vector machine estimators, the maximum entropy...
various point and interval estimates can be derived, such as the maximum a posteriori (MAP) or the highest posterior density interval (HPDI). But while conceptually...
algorithm from maximumaposterioriestimation (MAP estimation) of the single most probable value of each parameter to fully Bayesian estimation which computes...
proportional to this product: P ( A ∣ B ) ∝ P ( B ∣ A ) P ( A ) {\displaystyle P(A\mid B)\propto P(B\mid A)P(A)} The maximumaposteriori, which is the mode of the...
g., by maximum likelihood or maximumaposterioriestimation (MAP)—and then plugging this estimate into the formula for the distribution of a data point...
known as the maximumaposteriori or MAP decision rule. The corresponding classifier, a Bayes classifier, is the function that assigns a class label y...
parametric empirical Bayes point estimation, is to approximate the marginal using the maximum likelihood estimate (MLE), or a moments expansion, which allows...
function, as observed by Laplace. maximumaposteriori (MAP), which finds amaximum of the posterior distribution; for a uniform prior probability, the MAP...
parameter. In maximum likelihood estimation, the arg max (over the parameter θ {\displaystyle \theta } ) of the likelihood function serves as a point estimate...
a set which encloses the pose of the robot and a set approximation of the map. Bundle adjustment, and more generally maximumaposterioriestimation (MAP)...
q_{\phi }(\cdot |x)} balances between being a uniform distribution and moving towards the maximumaposteriori arg max z ln p θ ( z | x ) {\displaystyle...
regularity conditions, this process converges on maximum likelihood (or maximum posterior) values for parameters. A more fully Bayesian approach to parameters...
determining a non-informative prior is the principle of indifference, which assigns equal probabilities to all possibilities. In parameter estimation problems...
). Maximum Entropy and Bayesian Methods. Dordrecht: Kluwer. pp. 29–44. doi:10.1007/978-94-015-7860-8_2. ISBN 0-7923-0224-9. Halpern, J. (1999). "A counterexample...
unimodal distribution, this interval will include the mode (the maximum a posteriori). This is sometimes called the highest posterior density interval (HPDI)...
the maximum likelihood by adding parameters, but doing so may result in overfitting. Both BIC and AIC attempt to resolve this problem by introducing a penalty...
was Resolution enhancement of hyperspectral imagery using maximumaposterioriestimation with a stochastic mixing model. Eismann is Chief Scientist at the...
regression. A similar analysis can be performed for the general case of the multivariate regression and part of this provides for Bayesian estimation of covariance...
time. For related approaches, see Recursive Bayesian estimation and Data assimilation. Suppose a rental car service operates in your city. Drivers can...
Global Information
