Questions tagged [map-estimation]

Estimation by maximizing the posterior density function

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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 ...
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Does it make sense to condition on fixed values of some parameters before doing MCMC on the other parameters?

I have a Bayesian model with a large number of parameters (around 50), and as usual my goal is to infer the posterior distribution for the parameters, with MCMC. However, I am only interested in the ...
138 views

The explanation for the need to compute (rather then optimize) the posterior of latent variables

The most common usage of the variational inference looks like to be in computing the marginal distribution $P(X)$ in the denominator of the Bayes formula when computing the posterior probability of ...
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Multidimensional Bayes point estimates

Consider the posterior distribution $p(\theta|x)$. We aim to find a "good" estimate of the random variable $\theta$. The Bayes risk associated with the loss function $L(\hat{\theta}, \theta)$ is ...
967 views

How can (L1 / L2) regularization be equivalent to using a prior when priors can't be changed?

I understand the argument for how training with an L1/L2 regularizer is the same thing as finding the MAP estimate when the prior is Gaussian/Laplace. But there's a crucial difference. In Bayes' ...
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Example of maximum a posteriori that does not match the mean of a marginalized posterior

Given a N-parameter likelihood and prior, I can obtain the marginalized posterior for each parameter through Bayesian MCMC. I can also estimate the maximum a posteriori (MAP) of the N-parameter ...
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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 ...
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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 $Beta (\alpha - 1 + k , \beta - 1 + n- k$). ...
In a Bayesian logistic regression with two predictor variables $x_{1}$ and $x_{2}$, I did MCMC (2000 samples) to estimate posterior distribution. Now it's done, how can I choose the final estimates ...