# Tagged Questions

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

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### Use of Metropolis-Hastings in Bayesian Inference

I am now studying the Metropolis-Hastings algorithm and I want to apply it in order to made a Bayesian Inference of a function $y=f(x)$ to a dataset $D=\{x_i,y_i\}$. Five parameters of the function ...
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### Multi parameter Metropolis-Hastings

I need to formulate a multi parameter Metropolis-Hastings algorithm. My question is related to how to define the condition to accept or not the candidate value. In my problem (it is a curve fitting)...
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### METROPOLIS-HASTINGS with likelihood

I am trying to set up a Metropolis-Hastings algorithm in Matlab in order to estimate the parameters ${\theta}$ (it is a vector of 5 elements) to fit a curve to a set of data $D={X_i,Y_i,\delta_i}$. $X$...
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### Metropolis-Hastings Convergence in R

I'm trying to implement the algorithm Metropolis Hastings for the next FDP. f_{X}(x)=(5+\exp(5/2))*\sqrt{2\pi}\left[\exp\left\{-\frac{(x-2)^{2}-2x}{2}\right\}+5\exp\left\{-\frac{x+2}{...
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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 ...