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 ...

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18 views

Translate glmer (lme4) model specification into MCMCglmm

I am having some computational trouble estimating the following model with the glmer function in lme4: ...
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1answer
26 views

High dimensional sampling with low measurement noise

Assume that you have a model $$ Y = G(\Theta) + \varepsilon,$$ where $\Theta$ is a parameter vector with $\sim 8$ dimensions, $G$ is a highly nonlinear function of the parameters, $Y$ is observed ...
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20 views

Using MCMC to calculate log likelihood

I have an analytical solution to finding $p(y|\beta)$ and $p(\beta)$. My goal is to find $\log p(y)$. However, the integral $\int p(y|\beta)p(\beta)\,d\beta$ is not analytical. I did manage to use a ...
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2answers
27 views

Suspiciously high Multivariate PSRF from gelman.diag()

I am using "Multivariate PSRF" statistics from gelman.diag() function to analyze my MCMC chains. Now I analyzed convergence 471 variables (parameters for each ...
2
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1answer
51 views

How is ABC more computationally efficient than exact Bayesian Computation for parameter estimation in dynamical systems (ODE) models?

Approximate Bayesian Computation has been suggested as an approach to parameter estimation for computationally intensive simulations, most commonly in population genetics, but also in dynamical ...
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1answer
20 views

One-Step ahead predictive likelihood for time series forecasting

I am still new to Bayesian forecasting, so I am hoping to get some clarification on a simple concept (by the sounds of it). Suppose that we are interested in forecasting some time series one-step ...
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11 views

Monte Carlo for Multivariate Distribution with $x_i > 0$

I am trying to sample from a continuous posterior density $f$, where $f({\bf x}) = 0$ if any $x_i<0$ (can think of the marginals as looking like some sort of gamma distribution). I have coded a ...
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31 views

MCMC: The posteriors are too narrow

I have this very simple MCMC there I have ...
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1answer
53 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 ...
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32 views

MCMC convergence: why Heidelberg's test says normal samples are non-stationary?

I am learning about and playing with Heidelberg's convergence test to automatically stop a MCMC sampling. I would have said that if I sample, for instance, from a normal distribution, the test ...
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2answers
478 views

When is MCMC useful?

I am having trouble in understanding in which situation the MCMC approach is actually useful. I am going through a toy example from the Kruschke book "Doing Bayesian Data Analysis: A Tutorial with R ...
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14 views

How many random effects to specify in glmmADMB?

I am not sure if I could use 4 random effects in a glmmADMB model. According to Bolker et al. (TREE 24: 127-131, 2009) when there are more than 3 random effects MCMC should be used. However, I do not ...
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11 views

PyMC Noob: Zero Prob error: Web Site Counts [migrated]

I'm trying to learn and use PyMC with real data I've collected and basing my code and approach on the Hacker's Guide: here My data are views of a web site. I've linearly detrended the data, as I ...
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14 views

Efficient generation of graph structured correlated random variables via MCMC/Gibbs

Sometime back I had asked this question about generating correlated random draws based on the correlation structure given by a graph. Link Here The solution there requires to create $n\times n$ ...
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20 views

Adaptive MCMC for discrete random variables

Let {$Y_1,Y_2, \cdots, Y_n$} be a sequence of random variables where $Y_t$ follows a multinomial distribution with $n=1$ (the number of trials) and $\pi_t = (\pi_{t1}, \pi_{t2}, \cdots, \pi_{tk})'$ be ...
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40 views

How to use MCMC samples for parameter estimation

My background is in optimization, and I am new in Bayesian inference. Very broadly speaking, I am trying to reproduce a latent feature model (see, Miller et al) for graphs. I want to uncover the ...
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1answer
42 views

JAGS, cannot evaluate upper index of counter

I asked this question at the JAGS sourceforge help forum but didn't get response there. I have the following JAGS model: ...
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20 views

Base sales in multivariate time series | MCMC model

I have been looking around online for good resources that explain how one would go about calculating base sales when preforming marketing mix modeling. I was told by a colleague that essentially they ...
5
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2answers
152 views

Dirichlet Processes for clustering: how to deal with labels?

Q: What is the standard way to cluster data using a Dirichlet Process? When using Gibbs sampling clusters appear and dissapear during the sampling. Besides, we have a identifiability problem since ...
2
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44 views

Likelihood maximization: MCEM algorithm versus MCMC algorithm

Hello Everyone this is my first question. I am a particle physicist and I am doing some empirical studiues on parameters estimation using different methods (this might give me some handle to study on ...
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12 views

Symmetric Distribution for MCMC Continuous Distribution

I have a sampling distribution $g(X^{'}| X=x)$ such that $$ \log(X^{'})|X=x\sim N(\log(x), \sigma^2)$$ This ensures that our samples are in $(0, \infty)$. Now I would like to use the Metropolis ...
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1answer
22 views

Interpretation of absurdly large (but probably correct) Bayes Factors?

I estimated a Bayes factor to compare a hypothetical model against a null-model (which obviously by visual comparison of the posterior predictive with the data) fails to capture a certain aspect in ...
2
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54 views

how to determine if two dice are fair using pymc and roll data

My scenario is that I have two six-sided dice (D1 and D2), either of which may be fair or loaded (biased). I have samples of combined roll data (i.e. D1 + D2). I would like to view the posterior ...
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47 views

Book recommendation on statistical computing? [closed]

Topics on importance sampling, Monte Carlo, MCMC etc.
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15 views

Bayesian inference of marginal likelihood using ABC

I have the following situation: suppose data $D = \{x_i\}$ iid are generated through some process with density function $f(x_i | \alpha, \beta)$ (which I think will be negative binomial) and we'd like ...
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20 views

How to evaluate a Bayesian forecast?

Suppose that I have a predictive posterior, which is an attempt to predict some one-step ahead forecasted value $\hat{y}_{T+1}$. How do I assess if my posterior has done a good job or not? If we had ...
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1answer
30 views

marginal conditional distribution from MCMC output [duplicate]

I have a MCMC sampler that targets $$\mathbb{P}(U_1,U_2,...U_n \mid G(U) \leq 0)$$ where $U=(U_1,U_2,...U_n)^T$. I realize now I am more interested in estimating the conditional density $$p_k = p(u_k ...
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2answers
406 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 ...
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1answer
57 views

Marginal Likelihood in PYMC

I am using the PYMC toolbox in python in order to carry out a model selection problem using MCMC. What I would like to have for each model is the marginal log-likelihood (i.e. model evidence). The ...
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42 views

Generating a skewed distribution given the median and left and right “$1\sigma$” limits [duplicate]

Edit: I found a solution to the problem, which is at the bottom of the post. I'm going to leave the post as it is in case someone else encounters a similar problem! I was banging my head to a ...
4
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1answer
87 views

What is the simple standard error for MCMC?

Simply put: suppose that we have observed $X=\left\{ X_{1},\ldots,X_{n}\right\}$. We then need to calculate some statistic $T$ using MCMC, using $M$ loops (By "loops" I mean the number of times the ...
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1answer
35 views

MCMC sampling with sum constraints

I'm interested in sampling a collection of variables with a sum constraint on them. For a simplified example: Prior: $X \sim \mathcal{N}(0, 1)$ $Y \sim \mathcal{N}(0, 1)$ Observation: $X + Y = 1$ ...
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1answer
65 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) = ...
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1answer
34 views

Gibbs Sampling for Boltzmann Machines

David Mac Kay, in his book on machine learning talks about Boltzmann machines, and on pg. 3 here http://www.inference.phy.cam.ac.uk/itprnn/ps/521.526.pdf He says "the second equation ...
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2answers
432 views

Is Markov chain based sampling the “best” for Monte Carlo sampling? Are there alternative schemes available?

Markov Chain Monte Carlo is a method based on Markov chains that allows us to obtain samples (in a Monte Carlo setting) from non-standard distributions from which we cannot draw samples directly. My ...
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38 views

“Observed node inconsistent ” when binomial success rate exactly one

I observed some curious behavior in JAGS (rjags). There probably is a good reason for it, but I can't figure it out: As part of a more complex model I have these statements: ...
3
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36 views

Fast Algorithm for Bayesian Measurement Model

I want to estimate a Bayesian Measurement model. That is I am concerned with the rating of each judge $j$ of the value of some trait $z$ for each observation $i$. Not all raters will have rated each ...
5
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1answer
54 views

How to derive Gibbs sampling?

I'm actually hesitating to ask this, because I'm afraid I will be referred to other questions or Wikipedia on Gibbs sampling, but I don't have the feeling that they describe what's at hand. Given a ...
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19 views

Overestimating variance with MCMC

I'm working with a very specific type of proposal distribution in MCMC algorithm. To validate it I use a simple multivariave Gaussian with $\mu=0$ and $\Sigma$ an identity matrix. The proposal ...
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21 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 ...
4
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1answer
191 views

computing the posterior of two Gaussian probability distributions

I am a bit confused how to solve a Bayesian statistics problem. I have a parameter $\epsilon^s$ which is defined as following: $$\epsilon^s=\frac{\epsilon-g(\pi,z)}{1-g^*(\pi,z)\epsilon}$$ where ...
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1answer
39 views

Constructing Bayesian model for randomly picked points from a sine wave

I am trying to apply some data analysis on data which is generated by picking points from a sine wave with some noise added in. I am purposefully ignoring the time dependence, so just collecting data ...
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16 views

Gibbs sampler with beta posterior

Drive the Gibbs sampler for the joint posterior for a beta distribution X~Beta (a,b) with parameters alpha and phi, also stating the conditional distribution
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2answers
110 views

What is going on in an MCMC chain?

I'm currently running some data through the MCMCglmm package in R. I was wandering what actually happens in the chain that is created? I have a multiresponse model (as a quick overview of the data: ...
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45 views

how to integrate over product of two inverse-gammas

I'm trying to find a nice closed form for an integral which has the following form: $\int_{0}^{\infty} x^{-\theta_1 -1} \exp \bigl( - \frac{\beta_1}{x} \bigr) (ax +b)^{-\theta_2 -1} \exp \bigl( - ...
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22 views

Gibbs Sampling with given Posterior Distribution

I'm trying to implement an algorithm from a paper which assigns three types of labels $m_i, m_d$ and $m_s$. Here $m_i$ labels a collection of documents $G_i , m_d$ a subcollection of them and $m_s$ ...
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1answer
66 views

Skewed posterior distribution on constrained parameter space for Bayesian inference of MCMC. Advice on what to do?

I am running a fully Bayesian MCMC procedure to estimate some time series models, and my model has a lot of parameter estimates. In particular, one of these parameters, $\phi$, is $\in [-1,1]$. The ...
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27 views

PANEL model (MCMC): Equivalent of system GMM in MCMC

I want to fit a PANEL model via MCMC. I am concerned, that I got some covariates that are endogenous. I use MCMC for various reasons, particularly cause I got some spatial dependencies in my model. I ...
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1answer
54 views

General questions on MCMC

This is a continuation of the following question. The previous link was related to rejection sampling. This is related to MCMC. General questions on rejection sampling 1a. As far as I understand, ...
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1answer
51 views

General questions on rejection sampling

I am new to Bayesian methods. I was going through a chapter on sampling. I have a few questions related to it. Please help me get these clarified. As far as I understand, rejection sampling will not ...