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

learn more… | top users | synonyms

3
votes
1answer
32 views

Metropolis-Hastings with two dimensional target distribution

I'm confused in the following situation: I want to sample by writing code (Java) from the following distribution that is characterized by the mean vectors and covariance matrices: $$ p\left ( ...
0
votes
0answers
9 views

Loss Function to Calibrate Kernel - Metropolis Hastings

I was wondering if there is anything I can read about calibrating the variance for the proposal distribution in the random walk metropolis hastings. I was thinking of using an optimizer and creating ...
2
votes
0answers
38 views

Metropolis-Hastings acceptance rate confusion

I ran a Bayesian model that have about 2700 parameters. Among these parameters, Adaptive Metropolis algorithm was implemented to estimate ~790 parameters in the I-group and Metropolis algorithm was ...
4
votes
1answer
50 views

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 ) ...
1
vote
1answer
57 views

In Bayesian analysis, how to sample from full conditional given uniform prior and normal data likelihood?

[EDIT] This question comes from the example of OpenBUGS manual: Stagnant: a changepoint problem and an illustration of how NOT to do MCMC! I also asked another question regarding this example. ...
2
votes
1answer
32 views

Bayesian Mixture Model Gibbs Sampler for two linear relationships

I am attempting to use a Gibbs Sampler to model a mixture of two groups, where the group membership is defined by a linear relationship conditional on x. Both groups have the same slope and intercept, ...
2
votes
1answer
164 views

Metropolis-Hastings MCMC for Bayesian Regression in R

I am looking for a teaching example of a multivariate (not bivariate) implementation of Metropolis-Hastings for MCMC in R. I know several packages implement the algorithm more generally, but the code ...
2
votes
0answers
39 views

Is this how a Bayesian bootstrap works?

I am a bit new to the whole nonparametric and Bayesian idea, so tell me if this is correct: to estimate, say, the mean of a dataset's population we do the following: We define a function $f(x)$ that ...
3
votes
0answers
27 views

Simplification of my Hasting-Metropolis ratio

I am considering the following model : $$ y_{i,j} = f(x_{i,j},\beta,b_{i},d) + \varepsilon_{i,j} $$ where : $1 \leq i \leq s$ $1 \leq j \leq n_{s}$ $\beta$ is a (vector of) fixed effects $b_{i} ...
1
vote
1answer
64 views

Gibbs sampling for reducible chain

I am new to Gibbs sampling and I ran into a problem with irreducibility. For the Gibbs sampler to work the Markov chain has to be irreducible. But that assumption is not satisfied in my probability ...
1
vote
1answer
45 views

How to incorporate parameter constraints in Metropolis Hastings

I am working on parameter estimation of GARCH model with Metropolis Hastings. But the results I have got doesn't look reasonable, actually it is quite different from what I have got from Gibbs ...
1
vote
1answer
41 views

Independence-Metropolis-Hastings Algorithm

IMHA is an importance-sampling version of MCMC, where the proposal is drawn from a fixed distribution g. Usually, g is chosen to be an approximation to f. The acceptance probability becomes ...
0
votes
0answers
12 views

Explanations about the parallel tempering

I am reading this paper on parallel tempering but there are a few things I do not really understand. If I'm not mistaken, parallel tempering is a MCMC method which is quite convenient to sample from ...
3
votes
2answers
156 views

MCMC chain getting stuck

I am trying to use a Metropolis-within-Gibbs type algorithm to sample $\theta$ and $x$ from the following model. Starting with Bayes theorem I can write: $$ P(\theta, x | y) = \frac{P(y | x, \theta) ...
4
votes
1answer
34 views

Why does Slice sampler use the log of the density?

The Slice sampler1 takes as its argument the log of the density to be sampled from. Why is it doing this? A commenter on this question pointed out that it makes no sense to "sample" from the log of ...
0
votes
1answer
97 views

Metropolis-Hastings using log of the density

Does Metropolis-Hastings work with the log of the proposal and the density to be sampled from? That is, say we want to sample from a density $\pi(x)$, using a proposal $q(x|x^{old})$, will the ...
2
votes
2answers
493 views

Metropolis-Hastings Algorithm within Gibbs Sampling

I have this $f$ function below. $$ f(x_1,x_2)\propto \left(\dfrac{x_1}{x_2}\right)\left(\dfrac{\alpha}{x_2}\right)^{x_1-1}exp\left\{-\left(\dfrac{\alpha}{x_2}\right)^{x_1} \right\}I_{R^+}(x) $$ where ...
1
vote
1answer
136 views

Transformation of variables (Metropolis Hastings)

Say I have a bunch of data from a Poisson distribution and I want to find out my posterior i.e. I'm data fitting: $p(\lambda | X) \sim p(X|\lambda)p(\lambda)$ where $p(X|\lambda) = ...
0
votes
0answers
15 views

What sort of data would be appropriate to analyze under an MCMC method?

MCMC methods describe stochastic sampling but I'm not entirely sure the contexts in real datasets one would wish to apply MCMC methods. What kind of data could I gain insight into with MCMC methods?
2
votes
0answers
36 views

Comparison of MCMC methods? [closed]

Where can I find a good comparison of Gibbs, Metropolis, and Hybrid MCMC in R or Python? I have thus far found this ...
3
votes
1answer
63 views

Why is acceptance prob $A(x \rightarrow x')=min\left[1,\frac{\pi(x')Q(x'\rightarrow x)}{\pi(x)Q(x\rightarrow x')}\right]$ for Metropolis-Hastings?

In the Metropolis-Hasting algorithm we choose the acceptance probability $A(x \rightarrow x')$ as following: $$A(x \rightarrow x') = min \left[1, \frac{\pi(x')Q(x' \rightarrow x)}{\pi(x)Q(x ...
0
votes
1answer
30 views

Why accept Metropolis-Hastings sample if more probable than previous sample?

One step in the Metropolis-Hastings sampling algorithm is to determine whether a sample $x_i$ is to be accepted based on the previous sample $x_{i-1}$. My understanding is that $x_i$ is accepted with ...
2
votes
1answer
117 views

Sampling with Metropolis-Hastings

In Metropolis-Hastings sampling, if every draw of my proposal distribution (Q) is independent from the previous draw, is the convergence to the stationary distribution still guaranteed? To be more ...
0
votes
1answer
50 views

Systematic change of proposal density of metropolis algorithm - still a markov chain?

The problem is that I have a Gibbs-Sampler where one of the parameters has to be sampled via a Metropolis-Step from the respective FCD. I have problems finding a suitable scale for the Gaussian ...
1
vote
0answers
30 views

Monte carlo integrations with metropolis hastings step

Consider the following problem: Suppose we want to compute the following integral $$ f(y_1|y_2) = \int_{\theta} \int_{x_1} \int_{x_2} f(y_1| x_1,x_2,\theta, y_2) f(x_1,x_2|\theta,y_2) f(\theta | ...
1
vote
1answer
43 views

Metropolis-Hastings sample reusal

I have a posterior distribution from which I calculate some statistics using sampling, for example I calculate expectation. So I draw 1000 samples using Metropolis-Hastings and then I calculate their ...
2
votes
0answers
52 views

Computing a Metropolis-Hastings target distribution?

In implementations of the Metropolis-Hastings algorithm, how is the target distribution $\pi(\mathbf{x}) = P(\mathbf{x}|\mathbf{e})$ computed or estimated while ...
1
vote
0answers
78 views

Understanding a measure of convergence of MCMC simulations

I am trying to better understand better the Gelman/Rubin measure of convergence of MCMCs. The method starts off by defining two quantities: $B$ and $W$. $B$ is said to be the between chain variance ...
1
vote
1answer
153 views

Gibbs Sampling Detecting Change point in time series

I was reading through this one page paper on using Gibbs sampling for detecting a change point in a time series like data. While I understand the part where the $\lambda$ and $\phi$ are chosen from a ...
4
votes
1answer
155 views

MCMC: examples of when direct sampling is difficult (but Metropolis Hastings is easy)

The Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution for which direct sampling is difficult. Would ...
3
votes
1answer
463 views

Island Hopping with Metropolis Algorithm

From John Kruschke's book, Chapter 7, Pg. 120 (summarised for succinctness): A politician is constantly travelling from island to island on a chain of islands... His goal is to visit all the ...
1
vote
0answers
47 views

Viterbi-like algorithm with a single observation

Consider a Metropolis-Hastings walk over an exponentially large, known state space S. The proposal/transition matrix P is known, as is the target stationary distribution. In fact, assume there is an ...
1
vote
0answers
28 views

Simultaneous multiple perturbations in Markov chain Monte Carlo

I'm coding a McMC algorithm for geophysical applications. Using the Metropolis–Hastings scheme to accept/reject the proposed models is something that I thought I understood completely, but I don't. ...
1
vote
1answer
176 views

burn in for Metropolis Hastings MCMC

I was wondering if there is a principled way to figure out how many samples to discard during the MH-MCMC burn-in stage. So, as I understand it, the initial samples can introduce bias in the ...
2
votes
1answer
186 views

Gibbs sampling versus general MH-MCMC

I have just been doing some reading on Gibbs sampling and Metropolis Hastings algorithm and have a couple of questions. As I understand it, in the case of Gibbs sampling, if we have a large ...
1
vote
1answer
57 views

Simplex Random Walk Mean

Hi I have two questions related to a previous question I asked here: Simplex Random Walk In this link it describes how to perform a random walk on the simplex. ...
2
votes
0answers
23 views

What methodology should I choose? If hiearchical, what model design?

I am working on a problem that has can beyond my level of understanding. I am quite familiar with R, so that would be my preferred choice but I also have access to SAS. Data I have created a fake ...
0
votes
1answer
73 views

Simplex Random Walk

This link describes how to perform a random walk on the simplex using the Metropolis-Hastings algorithm: http://en.wikipedia.org/wiki/User:Skinnerd/Simplex_Point_Picking The description says: "The ...
1
vote
0answers
41 views

Analysis of mcmc output

I have a sequence of Bayesian Networks for del with more epochs. For example if i work with trafic on street I can have a BN for morning, one for afternoon e one for evening. If i collect data for ...
0
votes
1answer
247 views

Metropolis Random Walk Algorithm in Python

I am trying to implement random walk metropolis in Python for generate from a pdf $f$, which is defined in the domain: $$(0, \infty) \times [3, 4] \times (0, \infty)$$ I am using Metropolis Random ...
2
votes
1answer
113 views

Metropolis independence sampler

I need to implement an algorithm of Metropolis Independence Sampler, where the proposal distribution is a Multivariate Normal with 3 parameters. Since my function $f$ is really difficult to ...
1
vote
0answers
58 views

Metropolis Hastings when acceptance rate is not a probability

I need to implement a Metropolis Hastings where the acceptance probability $\alpha$ is not a probability but a logarithm of a score. The logarithm of a score is a negative float. In original ...
1
vote
1answer
202 views

Metropolis random walk using multivariate normal

I need to implement a program that generates a sample from a really complicated distribution $f$ of 3 variables. I need to implement it using Metropolis-Hastings Algorithm's and its variation and I ...
2
votes
0answers
35 views

Metropolis Algorithm for a 3 variated function

I need to implement a program that generate a sample from a 3 variated $pdf$ using the Metropolis algorithm (and its variations). I was thinking to use a 3-variated normal distribution as my proposal ...
3
votes
1answer
221 views

MCMC with Metropolis-Hastings algorithm: Choosing proposal

I need to do a simulation to evaluate an integral of a 3 parameter function, we say $f$, which has a very complicated formula. It is asked to use MCMC method to compute it and implement the ...
0
votes
1answer
74 views

Simple question on acceptance rate in Metropolis Hasting

When we say acceptance rate in a MH algorithm (for examples, suppose it's recommended to have 40% acceptance rate), do we mean overall acceptance rate or we mean acceptance rate after burn in? It's a ...
0
votes
1answer
150 views

pymc random seed doesn't guarantee the same posterior samples?

If pymc.numpy.random.seed(0) guarantee the same random number sequence to initialize a stochastic variable (say a Uniform distribution), why does its posterior samples (from trace plot) don't have the ...
0
votes
0answers
279 views

Choosing an appropriate proposal distribution for metropolis hastings

So far the only constraint I've found for sampling from some target distribution $\pi(x)$ is that the proposal distribution must include the support of $\pi(x)$. That's very vague. What makes a ...
0
votes
0answers
73 views

Proper likelihood function in acceptance probability of Gibbs Sampler

I have a question about the acceptance ratio used when implementing a random walk M-H in a gibbs sampler to generate sample paths of an unobservable process. When computing the likelihood of a set of ...
1
vote
1answer
56 views

Metropolis Ergodicity

I have encountered one last problem with regarding to the Metropolis-Hastings algorithm. I know that ergodicity is needed in the algorithm to imply convergence to a unique stationary distribution. But ...