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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Double hierarchical models using MCMCglmm [on hold]

I am new using R and I need a model to fit both the mean and the SD of the model (similar to the Double hierarchical generalized linear models). Is it possible to perform using the MCMCglmm package? I ...
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5 views

Intraspecific variation in MCMCglmm

I want to use MCMCglmm to account for phylogenetic autocorrelation on my GLMM. However I have more than one trait measurement for certain species. Is there a way ...
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5 views

Is it possible to extend dynamic spatial (space-time) panel model to a SARAR (SAC) specification?

I have panel data of 200 regions over 20 years. My goal is to estimate a dynamic spatial (space-time) panel model. I would like to employ an extension of model used in Debarsy/Ertur/LeSage (2009): ...
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24 views

Probability that a large corpus of text is generated with the same parameters as a subset

Let's say I have a process which generates different words at a set (unknown) frequency per word. I sample this process X times, generating the word "yo" Y times. I then look at a subset of my ...
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28 views

pymc implementation of ThinkBayes 1.3 cookie problem

This is obviously overkill for this problem, but I thought it would help cement the concepts for me. The problem: Suppose there are two bowls of cookies. Bowl 1 contains 30 vanilla cookies and 10 ...
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17 views

Combining independent MCMC samplers from different models

I am interested in sampling from the joint posterior $p(\theta_k,k \mid y)$ where $\theta_k$ belongs to the parameter space of model with index $k$. One way of doing this is with the reversible jump ...
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45 views

Hamiltonian Monte-Carlo with piecewise differentiable log likelihood

This is a bit of a curious situation. I have an energy function $E=S+N$ which is the sum of a smooth differentiable function $S$ and a piecewise constant "noise" function $N$. This means that on ...
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1answer
23 views

Combining multiple parallel MCMC chains into one longer chain

Let's say that one has run $m$ parallel MCMC chains where each chain has had burn-in. Let the resulting chains be denoted by $$ x_1^{(i)},\dots,x_N^{(i)} \quad \text{ for } i=1,\dots,m,$$ where $N$ is ...
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1answer
31 views

Gibbs sampler for a particular distribution

I'm trying to implement Gibbs Sampler for the distribution: $$\pi(x,y)=e^{-10(x^2-y)^2-(y-1/4)^4}$$ So, like the first step, I need to find: $$\phi(t) = \int_{-\infty}^{t} e^{-10(x^2-y)^2-(y-0.25)^4} ...
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1answer
23 views

What is this bivariate distribution called and how to make it posterior?

I am trying to make this bivariate density function as posterior f(x,y) = k x^2 exp( - x y^2 - y^2 + 2y - 4x) and try jags instead of implementing in R as in ...
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2answers
77 views

Large? Number of parameters in MCMC model [closed]

I am implementing a Hierarchical Bayesian Modeling in order to model the relation between the independent and dependent parameters $(x, y)$. I assume the relation is: $$ y_i = \alpha + \beta x_i + ...
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27 views

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

In Bayesian analysis, assume a simple linear regression model with two straight lines that meet at a certain changepoint $c$. The basic setup is as following. \begin{align*} Y_i \ & \sim \ ...
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36 views

Setting up posterior and likelihood of Bayesian for more than one model

If I have a data-set and I would like to fit a model and determine its two or three free parameters, while I know that I can fit twice or three times the model to my data and obtains the free ...
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24 views

OpenBUGS example: Stagnant, a changepoint problem and an illustration of how NOT to do MCMC! - Why is the second parameterization better?

I am working on an Bayesian problem from an OpenBugs example: Stagnant, a changepoint problem and an illustration of how NOT to do MCMC!. This is a changepoint problem. Basically we assume a model ...
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37 views

In MCMC simulation, how to deal with very small likelihood values that couldn't be represented by computer? [duplicate]

I am working on a Bayesian project based on Stagnant data from a OpenBugs example, which is a changepoint problem. Basically we assume a model with two straight lines that meet at a certain ...
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15 views

How to interpret the results of geweke.diag() function present in Coda package of R?

I am using geweke.diag() to check the convergence of an MCMC chain, I am using following R-Code for the purpose ...
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33 views

Is there good introduction to scala for MCMC simulation

https://darrenjw.wordpress.com/2011/07/16/gibbs-sampler-in-various-languages-revisited/ It seems scala is the way to go for MCMC for complex models, Is there any good introduction for scala to get ...
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36 views

Analyzing output in MCMC

I am using emcee to do inference on some data. I am trying to fit my data to a line of equation $ y = mx + b $. ...
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53 views

Fitting a Bayesian Hierarchical Poisson Regression in R

I'm trying to fit a Bayesian hierarchical poisson regression. To do so, I'm using MCMChpoisson function from MCMCpack in R. Based on this package, the model is: $$Y_i \sim Poisson(\lambda_i)$$ ...
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13 views

How can I smooth a set of distributions?

I have a set of results from MCMC modelling of a variable at discrete time points and I would like to know what kind of approaches I could take to smooth the results, given I would expect some kind of ...
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2answers
1k views

Priors in Bayesian MCMC

I am trying to understand how the choice of priors affects a Bayesian model estimated using MCMC. At a basic level I understand that the product of the prior and the likelihood are proportional to the ...
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20 views

What are good values for autocorrelation, Gelman, and cross-correlation in rjags?

I don't want to post my whole code since it is long, so I will only post part of it: ...
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1answer
29 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
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1answer
121 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 ...
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90 views

When should I be worried about the Jeffreys-Lindley paradox in Bayesian model choice?

I am considering a large (but finite) space of models of varying complexity which I explore using RJMCMC. The prior on the parameter vector for each model is fairly informative. In what cases (if ...
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36 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 ...
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19 views

How to interpret a multilevel model that repeats variables for fixed and random effects (like in MCMhregress)?

I came across a specification of a multilevel model that I'd never seen before. It looks like the R function MCMChregress (see: ...
2
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1answer
119 views

Bayesian meta analysis: implementation in BUGS/JAGS/STAN

I would like to conduct a meta analysis in order to collate the information from a number of studies. The parameter of interest is a probability $\theta$. In each of the studies, the observed data ...
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1answer
45 views
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2answers
146 views

What are the options when statisticians who only know R need more computing speed

Speed isn't a concern for many statistics projects but sometimes it is, for example MCMC. Assume that hardware improvement is not an option (looking for relatively free solutions that produce orders ...
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23 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} ...
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2answers
38 views

Return value of uniform distributions for MCMC simulations

I am confused about how what value should be returned from a uniform distribution when using MCMC simulations. The proper normal distribution is define as $$ p(\theta) = \left\{ \begin{array}{cc} ...
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1answer
61 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 ...
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44 views

How do I sample from a black-box model of a probability distribution?

I have a function 'P(x)' where we query for any 'x' it gives a probability value. This function 'P' does not have a closed form and the evaluation is costly. Now 'x' is a set of vectors(matrix whose ...
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1answer
36 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 ...
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1answer
33 views

Gibbs Sampler output: how many Markov chains?

When running a Gibbs sampler (for $n=200$ Iterations) with two full conditionals, I get the output $\mathbf{x} = (x_1^{(n)},x_2^{(n)})_{n =1,...,200}$. So $\mathbf{x}$ is the realizations of a Gibbs ...
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25 views

Calculating Marginal Data Density for VAR Model

I am currently estimating Bayesian vector autoregressive (BVAR) models and I would like to do model comparison with Bayes factors. I have read about the Gelfand-Day method, the Geweke (1999) modified ...
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1answer
67 views

MCMC/EM limitations? MCMC over EM?

I am currently learning hierarchical Bayesian models using JAGS from R, and also pymc using Python ("Bayesian Methods for Hackers"). I can get some intuition from this post: "you will end up with a ...
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52 views

GridWalk sampler with pymc3

I am trying to build a GridWalk sampler (actually PolicyWalk as in BIRL by Ramachandran et. al.. Edit More info: The distribution I am interested in is the reward posterior given by, $$ P(R|D) = ...
2
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21 views

Cluster Assignment in Bayesian perspective

I am going to study clustering methods in the Bayesian perspective. I understood how k-means works, and I found it pretty clear, due to the notion of distance and assignments to specific centers. I ...
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9 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 ...
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17 views

Sampling from a set of non-nested models

Consider a collection $\mathcal{M}$ of $m$ different model classes $\mathcal{M} = \{M_1,\dots,M_m\}$, where each model class has a parameter set $\Theta_i$, $i=1,\dots,m$. The model classes are not ...
2
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2answers
136 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) ...
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1answer
48 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
35 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 ...
2
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36 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
39 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
61 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
40 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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15 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 ...