# Questions tagged [map-estimation]

Estimation by maximizing the posterior density function

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0answers
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### Is there a reason to use variational inference for point estimates?

I have seen Bayesian hierarchical models, particularly in computational biology, that use variational inference, but do not use the uncertainty provided by a variational solution. For example, MOFA is ...
1answer
26 views

### MCMC with using MAP as starting value

let $X$ be a random variable from my target distribution $\pi(x)$, which I know up to a normalizing constant, and I want to calculate $Ef(X)$ for some know function $f$. The dimensions of $X$ are ...
1answer
64 views

### Why should MAP be invariant under reparameterization?

I learned why MAP suffers from being reparametrization invariance while MLE not from this answer, but I don't know why reparametrization invariance even matters? What is the non-linear mapping ...
1answer
56 views

### Why is MAP and ML widely accepted? [closed]

(ML as in Maximum Likelihood and MAP as in Maximum A-posteriori) I'm going trough a course book on my own, and without really having peers to talk to I'm turning to stack exchange with these rather ...
3answers
210 views

### Differences between MLE and MAP estimators

Generally speaking, what are the differences between an MLE and a MAP estimator? If I wanted to improve the performance of a model, how would these differences come into play? Are there specific ...
0answers
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### Quantifying uncertainty in MAP nonlinear regression

I am interested in clinical pharmacokinetics, where we have a given medicine's population model, with its parameters (mean and standard deviation), and our goal is take one or two blood samples from a ...
0answers
26 views

### Bayesian Inference Intuition: Beta and Binomial vs Gamma and Poisson

When the data is assumed to be binomial distributed, and the prior probability is assumed to be a beta distribution, the posterior follows the distribution $Beta (\alpha - 1 + k , \beta - 1 + n- k$). ...
1answer
293 views

### MLE and MAP with Naive Bayes

From what I understand, Naive Bayes classifies by doing: $$y \leftarrow argmax_{y_k}P(Y=y_k)\prod_{i}P(X_i|Y=y_k)$$ There are two things there we need to know: $P(Y=y_k)$ and all the $P(X_i|Y=y_k)$ ...
0answers
19 views

### Bayesian inference MAP question

Hello I am stuck with this problem and was wondering if someone can solve it for me. Thanks
1answer
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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 ...
1answer
266 views

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### confusion related to maximum a posteriori estimation [duplicate]

I was reading this article in wikipedia related to MAP http://en.wikipedia.org/wiki/Maximum_a_posteriori_estimation. However, I had this confusion when it says MAP estimation is a limit of Bayes ...