Markov Chain Monte Carlo (MCMC) refers to a class of methods for generating samples from a target distribution by generating random numbers from a Markov Chain whose stationary distribution is the target distribution. MCMC methods are typically used when more direct methods for random number ...

learn more… | top users | synonyms

0
votes
0answers
7 views

fitting a dynamic bayesian model to irregular time data

I have a dynamic epidemiological model which I solve with scipy's ODEint and fit to my data using pymc. My data is irregular in ...
2
votes
0answers
22 views

Hamiltonion monte carlo

Can someone explain the main idea behind Hamiltonion Monte Carlo methods and in which cases they will yield better results than Markov Chain Monte Carlo methods ?
1
vote
2answers
50 views

Why would I use any MC technique other than basic sampling

I'm trying to learn sampling techniques. Lots of tutorials say that they are useful when "you can't sample directly from the pdf...." q1) If I have the algebraic form of the pdf can't I always sample ...
0
votes
0answers
6 views

More variability than Beta posterior suggests - A/B testing

I'm using a Beta-Bernoulli to model conversion rates between two groups, A and B. For each group, my prior is $Beta(a,b)$ and likelihood is $Bernoulli(p)$. My posterior distribution is therefore a ...
0
votes
1answer
26 views

How to include prior information about target pdf in MCMC

Is there a somewhat principled way to include prior information about a target density $f(x)$ in a sampling (MCMC) algorithm? [This is a much better formulated version of this question, which I am ...
10
votes
2answers
336 views

How do ABC and MCMC differ in their applications?

To my understanding Approximate Bayesian Computation (ABC) and Markov Chain Monte Carlo (MCMC) have very similar aims. Below I describe my understanding of these methods and how I perceive the ...
2
votes
2answers
59 views

What to take in consideration when we use Bayesian Methods on Big Data problems?

I was reading the book Bayesian Methods for Hackers by Cameron Davidson-Pilon. He use PyMC for examples. As an experiment, I created a ...
0
votes
0answers
16 views

How to update latent discrete variables in MCMC?

Most of the discussion on Bayesian model with latent variables that I've seen fall into two classes: continuous latent variable underlying the observed discrete outcome (e.g. probit model (Albert ...
0
votes
0answers
6 views

Long-tailed random effect posterior distribution from unbalanced design

I am using MCMCGLMM to estimate the effect of some factors on a trait. The model is constructed with $Y \backsim B*S$ to find an interaction effect of factor B ...
3
votes
0answers
79 views

Sampling from $f(x)$ given approximation $g(x)$

(After some pondering, what I really wanted to ask is how to incorporate prior information about $f$ into a sampling method - see this question.) Suppose you want to draw samples from an ...
1
vote
0answers
26 views

Markov chain Monte Carlo sampling using CDFs instead of PDFs

I wonder if there is any MCMC sampling method which uses the definition of the target CDF instead of the target PDF; however, I may use a proposal PDF. I would like to use Metropolis-Hastings but it ...
0
votes
0answers
9 views

How to sample from Conditional Density Estimation estimated using hdrcde package in R? [closed]

I wanted to use ARMS sampling technique (MCMC method) available in "HI" package in R. I'm not understanding how to give input for ARMS.
0
votes
0answers
19 views

Expected value of inverse-Wishart prior in JAGS

I am trying to estimate a covariance matrix in JAGS, using a prior centered around the expected variances. Thus, I want to assign a prior with expected variances that are about equal to the observed ...
-3
votes
1answer
23 views

Example when $\hat{R}$ diagnostic is failing [duplicate]

I've seen somewhere an example of $\hat{R}$ statistics being close to 1 and the chains not converging. Marc Kery brought up this example: where the chains still converge but they all do not ...
-1
votes
0answers
64 views

Overestimated MCMC standard deviation (SD)

I did a simulation study with 100 replications for a complex model with rstan, and I found the standard deviation (SD) of posterior samples is larger than the true ...
3
votes
1answer
40 views

What is causing autocorrelation in MCMC sampler?

When running a Bayesian analysis, one thing to check is the autocorrelation of the MCMC samples. But I don't understand what is causing this autocorrelation. Here, they are saying that High ...
0
votes
0answers
10 views

Approximating KL-Divergence for 2-D Random Variables with Scatter Plots

I have lots of experience computing KL divergences for straightforward discrete distributions where I have access to complete probability tables, etc. But I'm a little concerned about my current ...
12
votes
2answers
259 views

Sampling from an Improper Distribution (using MCMC and otherwise)

My basic question is: how would you sample from an improper distribution? Does it even make sense to sample from an improper distribution? Xi'an's comment here kind of addresses the question, but I ...
3
votes
1answer
32 views

Effective sample size for MCMC with multimodal target

I am trying to evaluate an adaptive MCMC algorithm on a multimodal target density. Among other performance measures, I would like to evaluate the sampler in terms of Effective Sample Size (ESS). The ...
1
vote
0answers
52 views

Inverse gamma posterior

I am working on bayesian analysis and I have a normal likelihood function and an inverse gamma (IG) prior for the parameter $\lambda$. I have the following posterior: $$ \propto ...
0
votes
0answers
37 views

PYMC error:pymc.Node.ZeroProbability: Stochastic A's value is outside its support, or it forbids its parents' current values

I asked this question in stackoverflow but closed it after 4 days since I didn't get any answer. I am using this example as a basis for my work: I am trying to use pymc MCMC to fit the parameters of a ...
1
vote
2answers
59 views

Gibbs sampling and mixed distribution

For a project, I need to simulate from a joint distribution with both continuous and discrete variables that are dependent. The conditional distribution of any variable given the rest is known. I ...
2
votes
1answer
40 views

Evaluating two sets of random samples

Let $p$ be a probability distribution that can be computed tractably for any given point. I use two MCMC methods to generate samples from the distributions. For each MCMC method, I run 1000 Markov ...
10
votes
1answer
186 views

Computation of the marginal likelihood from MCMC samples

This is a recurring question (see this post, this post and this post), but I have a different spin. Suppose I have a bunch of samples from a generic MCMC sampler. For each sample $\theta$, I know the ...
2
votes
2answers
70 views

Predictions from BSTS model (in R) are failing completely

After reading this blog post about Bayesian structural time series models, I wanted to look at implementing this in the context of a problem I'd previously used ARIMA for. I have some data with some ...
3
votes
2answers
83 views

Markov chain Monte Carlo (MCMC) for Maximum Likelihood Estimation (MLE)

I am reading a 1991 conference paper by Geyer which is linked below. In it he seems to elude to a method that can use MCMC for MLE parameter estimation This excites me since, I have coded BFGS ...
1
vote
0answers
33 views

Hierarchical modelling - partial pooling with correlation

I am doing a Bayesian regression. I have groups of data $(y_1 ~X_1), (y_2~X_2),...$, where each $y$ and $X$ is a vector. The subscript is regarded as group number. The completely unpooled regression ...
2
votes
2answers
35 views

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 ...
2
votes
0answers
39 views

Population Monte Carlo Algorithm

I am trying to wrap my head around the Population Monte Carlo Algorithm. I want to implement it for a mixture model, but I am uncertain on how to proceed. I am mostly looking for references or ...
0
votes
0answers
21 views

Warning message after a MCMCglmm call in R

I have a Warning message after a MCMCglmm call in R. Let me first write about the aims of the study : 1) describe whether a set of seven different behavioural traits vary (or are consistent) in time ...
0
votes
0answers
49 views

What are examples where only a single sample is needed?

Consider the following setup: Let $\Omega$ be a finite (but humongous) state space and $\pi:\Omega\to[0,1]$ be a probability mass function. It seems to me that when people want to "sample" in this ...
0
votes
0answers
8 views

How to determine and use the sampling lag in the collapsed Gibbs sampler?

I am implementing a collapsed Gibbs sampler for LDA model. According to this technical note's word, average a number of samples, and often it is desirable to leave an interval of L iteration ...
3
votes
1answer
69 views

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 ...
0
votes
0answers
16 views

How does GibbsLDA++ ensure that we are sampling from a good posterior?

This is an extending of this question, which asked that whether we should do some estimating to ensure that we are really using a likely topic assignment instead of the one happened with low ...
1
vote
0answers
77 views

How to check the convergence in the collapsed Gibbs sampling of LDA? [closed]

I am trying to implement the LDA model fit by collapsed Gibbs sampling by myself. I have go through this article. And there is a clear pseudo code (section 5.5), ...
3
votes
1answer
22 views

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 $f(x+a)=f(x-a)$?
5
votes
0answers
28 views

Dirichlet process mixture MCMC

I'm reading Markov Chain Sampling Methods for Dirichlet Process Mixture Models by Radford M. Neal. Equation (3.6) states that If $c=c_{j}$ for some $j\neq i $: $P\left(c_{i}=c\;|\;c_{-i}, y_{i}, ...
3
votes
1answer
32 views

MCMC using GIBBS sampling: can different burn-in be used for different parameters?

I have run a stochastic volatility model with 4 parameters. I have used the Heidelberg and Welch convergence diagnostic. The result shows 3 out of 4 parameters have passed the stationary and ...
1
vote
1answer
48 views

How can the (Ensemble) Kalman filter be viewed as a MCMC algorithm?

I am struggling with quotes like The EnKF applies a Markov chain Monte Carlo (MCMC) method ... (1, p. 6) or In fact, the Kalman filter is a MCMC algorithm in the case of a linear and ...
2
votes
1answer
52 views

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 ...
0
votes
0answers
45 views

Normalization factor of truncated multivariate normal distributions (Normalization factor from samples)

I would like to evaluate an expectation of the form $\int p(x) \;\mathbb{1}_\left(Bx \leq 0\right) dx$, where p(x) is a multivariate normal distribution. I.e. the probability of a linear constraint ...
2
votes
0answers
37 views

MCMC efficiency and nonlinear reparametrizations

The efficiency (e.g., effective sample size per density evaluation) of most MCMC methods depends on the parametrization. However, so far I have come across little work in the MCMC literature that ...
3
votes
2answers
129 views

The Harris recurrence of a stepping-out slice-sampling-within-Gibbs MCMC

I want to use a multistage version of the MCMC here. That is, I want to use a Gibbs sampler to draw from a general joint distribution $p(x_1, x_2, x_3, \ldots)$ with a Gibbs step for each full ...
1
vote
1answer
37 views

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 ...
2
votes
1answer
39 views

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 ...
4
votes
3answers
107 views

How to generate the transition matrix of Markov Chain needed for Markov Chain Monte Carlo simulation?

I'm conducting a sensitivity analysis of a model using MCMC approaches. By reading the code of the sensitivity test procedure, I find the steps in Markov Chain is quite similar to random walk. Also, ...
1
vote
1answer
84 views

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 ...
5
votes
2answers
90 views

Performance benchmarks for MCMC

Have there been large scale studies of MCMC methods that compare the performance of several different algorithms on a suite of test densities? I am thinking of something equivalent to Rios and ...
3
votes
1answer
32 views

Combining transition operators in MCMC

Many MCMC papers usually present a new single transition operator (or a family thereof) such as different proposals for Metropolis-Hastings, new forms of slice sampling, etc. I am interested in ...
0
votes
0answers
25 views

Joint modelling or two-step sampling

I am interested in sampling from the joint posterior $\pi(\theta,\lambda, G \mid X,Y)$ using MCMC. $X$ and $Y$ represent unrelated data and they are assumed to be generated along a graph $G$ by two ...