Questions tagged [map-estimation]

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Distance correlation and a corresponding mapping

I have two long vectors, say X and Y (of equal length). I computed the Distance Correlation as implemented in Scipy and I got a ...
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Can you find the posterior mode of an unknown distribution without MCMC?

I was wondering if you wanted to compute the MAP estimate of an unknown posterior distribution, is there a non-sampling based method that would suffice? As in, if you don’t need to know anything more ...
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How to choose estimates after Bayesian regression?

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 ...
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1answer
28 views

Finding MAP estimate

I think after all the reading I've done I still don't fully understand MAP estimation. I came across a problem that's leaving me dumbfounded. Suppose $A$ ~ $N(0,\sigma^2_1) $ and $\epsilon$ ~ $N(0,\...
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1answer
48 views

What are the possible estimates of the parameters of the multinomial distribution?

The expected value of the parameters of the multinomial distribution (taking into account the Dirichlet prior $D(\alpha)$ and the posterior Dirichlet-Multinomial) is: $\pi_i = α_i+ x_i / \sum_{j} α_j+...
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Predictive Distribution using MAP

I'm facing the following problem. Suppose that you are a part of a team that has trained $n$ temperature prediction models. The models use readings from a set of sensors that measure weather ...
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1answer
28 views

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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16 views

meanAveragePrecision(mAP) score calculated for the object detection with class imbalance

How is the meanAveragePrecision(mAP) score calculated for the object detection? How can I modify it to take class imbalance into account? Should I make it weighted meanAveragePrecision(mAP) where I ...
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37 views

Loss decreases but mAP is dropping

I'm using the RetinaNet model for object detection in images. When I train the model, I all ways see the same behavior: For the first three - four epochs the mAP increases and then it decreases again. ...
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1answer
45 views

Confused about maximum a posteriori estimation [closed]

I am new to Bayesian statistics, and I just came across MAP. When our prior is a continuous distribution (pdf) on $\theta$ how can we calculate $g(\theta)$ in the numerator? Edit: I assumed $g(\...
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1answer
33 views

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 ...
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261 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) = \...
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1answer
349 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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1answer
211 views

MAP estimation for multiple parameters

Consider $N$ observed data points $x_i$ ($i=1,..,N$), and a likelihood that depends on $p$ parameters: $f(x_i|\theta_n)$ ($n=1,..p$). From Bayes' theorem $$p(\theta_n|x_i) = \frac{f(x_i|\theta_n)g(\...
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2answers
364 views

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 ...
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1answer
76 views

For a posterior $p(\theta |y)$, if I specify a one-to-one transformation $\phi = g(\theta)$, how can I apply the transformation? [duplicate]

Suppose I have a posterior distribution, $p(\theta \mid y)$, where $y$ was my data and $\theta$ is a random variable with some prior distribution. If I specify a one-to-one transformation $\phi = g(\...
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1answer
78 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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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 ...