Tagged Questions

Refers to a special case of Markov Chain Monte Carlo algorithm used to sample from probability distributions.

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Metropolis algorithm to solve a problem [migrated]

I need to implement the metropolis algorithm to solve the example titled Cheating among students here. In summary the aim is to estimate the frequency of students cheating in an exam. The experiment ...
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What is the difference and relationship between posterior distribution function and likelihood function in MCMC?

I am learning MCMC in class, and I encounter one question about the relationship between posterior probability and likelihood function. In our lecture, the professor asked us to take samples from ...
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Metropolis-Hasting: compute acceptance based on asymmetric continous independent chain proposal

The title is a mouthful, but here is what it amounts to: Under a proposal distribution using an independent chain, the probability of jumping to point $x$ is independent of the current position $y$ ...
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Proposal distribution - Metropolis Hastings MCMC

In Metropolis-Hastings Markov chain Monte Carlo, the proposal distribution can be anything including the Gaussian (according to the Wikipedia). Q: What's the motivation for using anything other than ...
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Symmetric PDFs in Metropolis-Hastings

My textbook says that a symmetric PDF satisfies $$f(x|y)=f(y|x).$$ Can anyone explain this? Is it equivalent to $f(x+a)=f(x-a)$?
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MCMC Metropolis-Hastings initial values [closed]

my posterior values that I obtained via Metroplis-Hasting are always around my initial values. For instance if I chose $\theta_0 =(1,2)$ my posterior values, after either taking mean or median, are ...
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dmvnorm produce 0 likelihood

I am implementing an MCMC algorithm in R using the "mvtnorm" package. The data is about 150 dimensions so the likelihood produced by dmvnorm is usually zero (or -inf if "log=TRUE" is set), which make ...
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Multiple-Try Metropolis question

I read Multiple-Try Metropolis from Wikipedia and I do not understand some points. Suppose the current state is $\mathbf{x}$. The MTM algorithm is as follows: Draw ''k'' independent ...
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Are there analytically derivable posteriors that save from doing MCMC other than conjugate priors? [duplicate]

Posteriors for conjugate priors can be analytically derived and save us from doing MCMC. Conjugate priors simply have a posterior in the same family as the prior distribution. Are there other ...
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Singular proposal in MCMC

Suppose we want to obtain samples of the density $f(\mathbf{x})$ where $\mathbf{x}$ is a $d$-dimensional vector, i.e. $\mathbf{x} = (x_1, x_2, \dots, x_d)$. To that end, we choose the Metropolis-...
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Fitting power function to data

I am trying to implement an MH algorithm to fit a power function to my data. The power function has the following form: $\hat{y} = a * x^b$ The data are assumed to be normally distributed ...
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A question about the choice and interpretation of the jumping distribution in Metropolis-Hastings algorithm

In order to implement the MH algorithm you need a proposal density or jumping distribution $q(⋅|⋅)$, from which it is easy to sample. If you want to sample from a distribution $f(⋅)$, the MH algorithm ...
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For Metropolis-Hastings algorithm, should target density and proposal distribution have the same distribution?

I watched some youtube videos about the Metropolis-Hastings algorithm. They used a Gaussian as a proposal function to estimate an unknown Gaussian, or used a Gamma function as the proposal function to ...
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MCMC with dependent variables

I want to run Metropolis-Hastings on a problem which involves two parameters that are not independent. I.e. I want to estimate both of these parameters. At the moment I'm trying to understand if this ...
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Metropolis : Set first sample value instead of randomly generate an arbitary value

According to Metropolis-Hasting algorithm, the first sample is an arbitrary value generated randomly at the Initialization step. ( http://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm ) ...