Questions tagged [map-estimation]

Estimation by maximizing the posterior density function

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2answers
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What is an example of a transformation on a posterior distribution such that the MAP estimate will be non-invariant?

Suppose that we have a posterior distribution $p(\theta\mid y)$ and we wish to define a transformation on $\theta$ such that $\phi = f(\theta)$. I know that generally such transformations will not ...
11
votes
3answers
721 views

MAP is a solution to $L(\theta) = \mathcal{I}[\theta \ne \theta^{*}]$

I have come across these slides (slide # 16 & #17) in one of the online courses. The instructor was trying to explain how Maximum Posterior Estimate(MAP) is actually the solution $L(\theta) = \...
1
vote
1answer
40 views

reference request for the impact of priors in bayesian statistics

It is well known that in bayesian statistics, the prior believe can have a large impact on the estimation result. For example if you flip a coin ten times to determine whether it is loaded, a prior $...