Markov Chain Monte Carlo 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 less computationally expensive methods for random ...

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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 ...
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13 views

When to use skew normal regression via MCMC (mixture models)?

when do i use skew normal or skew t Regression via MCMC? Do I use them when the data are heavily skewed, for example income data? Or do I fit a normal Regression model first and inspect the residuals ...
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9 views

Error using “cengaussian” family with MCMCglmm

I'm trying to run a model using a cengaussian family distribution with the function MCMCglmm. The model is: ...
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21 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 | ...
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117 views

What makes a GLM Hierarchical?

Wikipedia defines a Hierarchical GLM as: Hierarchical linear models (or multilevel regression) organizes the data into a hierarchy of regressions, for example where A is regressed on B, and B ...
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56 views

How to interpret autocorrelation plot in MCMC

I am getting familiar with Bayesian statistics by reading the book Doing Bayesian Data Analysis, by John K. Kruschke also known as the "puppy book". In chapter 9, hierarchical models are introduced ...
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9 views

Discrete time generator of stochastic process

While looking at one paper about Metropolic Hasting optimal convergence rates, I came accross a discrete time generator of Markov chain. It is defined as follows: $$G V(x)=nE\left [ \left( ...
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92 views

Does the Gibbs Sampling algorithm guarantee detailed balance?

I have it on supreme authority1 that Gibbs Sampling is a special case of the Metropolis-Hastings algorithm for Markov Chain Monte Carlo sampling. The MH algorithm always gives a transition probability ...
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17 views

Checking the mixing of an MCMC chain by testing its gaussianity

As I was running several Monte-Carlo runs and trying to find the mixing time by doing traceplots. I had the idea of instead running $N$ chains $X^{l}_i$ with $l$ the chain label (in $1,..., n$) and ...
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18 views

Verifying propriety of MCMC

I have a posterior I'd like to sample: $p(\theta\mid Y)\propto L(Y\mid \theta) p(\theta)$ where $p(\theta)$ is proper, so the posterior is proper. I can write $L(Y\mid\theta) = \int f(Y, Z\mid ...
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28 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 ...
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32 views

Using interaction terms in an MCMCglmm

I am using MCMCglmm models in R, with hierarchically nested data. The basic structure of the data is as follows - each dyad is a unique combination of focal/other: ...
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17 views

MCMCglmm interpretation of effective sample size

I'm running a selection of MCMCglmm models in R, and have a basic question about the outputs. Based on what I've been reading, one indication that the model is mixing well is a large effective ...
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32 views

Rstan model for a simple mixture of normals

This blog post from Rbloggers describes how to code a simple three-part normal mixture model with known mixing coefficients, means and standard deviations. While it describes the procedures in some ...
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11 views

validity of MCM proposal distribution? uniform prior?

I am writing a program to compute estimated values. Suppose I I have a prior (discrete) distribution T that I can sample from, but don't know the analytic PMF. That is to say I have a program that ...
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25 views

Inference methods for multimodality and label switching

Imagine that there are three professions in the world $a,b,c$ (astronauts, doctors and statisticians) and that the Gross Domestic Product (GDP) of a city can be modeled as a linear regression of its ...
3
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45 views

Bayesian inference MCMC model for interval censored data

I have interval censored data for incubation period and I suppose that the exact time Ti included in each interval of the data [L;U] follows a lognormal distribution (mu,sigma2). I would like to use a ...
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24 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 ...
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2answers
92 views

Is my Bayesian analysis correct?

This is my first time doing a Bayesian analysis, so I'm not sure whether what I did makes perfect sense. I'm trying to tell if two samples come from the same distribution, more specifically, if they ...
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29 views

MCMC-Draws from different MCMC- chains

I have questions about the usage of draws from a MCMC. I estimate a hierarchical bayesian Multinomial Logit model (using bayesm in R). I am interested in the ratio of two coefficients 1 and 2, say ...
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21 views

Covariance for a multivariate Bayesian Additive Regression Tree

Chipman, George, and McCullogh (2010) state that: One can also extend the sum-of-trees model to a multivariate framework such as: $$ (29) \qquad\qquad Y_i = h_i\left( x_i \right) + ...
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1answer
21 views

MCMC sampling with noisy likelihood

A surprising results is that MCMC sampling remains unbiased if instead of computing the likelihood $p(x)$ ones compute an estimate $\hat{p}(x)$ as long as $\hat{p}$ is an unbiased and positive ...
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14 views

Univariate fixed effect Vs Multivariate model -Negative Covariance, positive parameter estimate, but why?

I am trying to compare the results of two models. The first model looks at y with x as a fixed effect. The second looks at the covariance between x and y. Both models have repeated measures for x ...
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16 views

How adapt MCMC when (constant) weights for oberservations are introduced?

I have the following problem: I have already set up a model and MCMC sampler for a mixed model without weights, i.e., every observation contributes the same amount of information. Now I would like to ...
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2answers
205 views

MCMC packages in R

Is there an R package for MCMC that can accept my self-defined (log)likelihood function (can be done in MCMCpack) and lets the user define contraints to the ...
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1answer
44 views

PYMC Confusion: are observed nodes fixed or stochastic?

I've been trying to gain a better understanding of factor potentials in PYMC. In reading this article by Cam Davidson-Pilon on Yhat, I got confused about how observed nodes are understood by PYMC. ...
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63 views

Is rstan or my grid approximation incorrect: deciding between conflicting quantile estimates in Bayesian inference

I have a model to achieve Bayesian estimates the population size $N$ and probability of detection $\theta$ in a binomial distribution solely based on the observed number of observed objects $y$: $$ ...
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155 views

MCMC of a mixture and the label switching problem

I generated some data according to a mixture of two lognormals: $f(x) = p \cdot \mathcal LN(\mu_1, \sigma) + (1-p) \cdot \mathcal LN (\mu_2, \sigma)$. given $p$ and $\sigma$, this is my code to find ...
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1answer
107 views

what to chose for prior and proposal function for MCMC of a mixture

I generated some data according to a mixture of two lognormals: $f(x) = p \cdot \mathcal LN(\mu_1, \sigma) + (1-p) \cdot \mathcal LN (\mu_2, \sigma)$ Now I want to use MCMC to find the parameters $p, ...
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34 views

Point Estimate of normally distributed threshold parameter with unknown mean and variance

I'm new to Bayesian analysis an applied what I learned in John Kruschke's book to simplified versions of a model I previously fitted with non-Bayesian methods. For those simplified versions, even ...
0
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1answer
73 views

Defining the Stochastic and Deterministic variables with pymc3

I am trying to use write my own stochastic and deterministic variables with pymc3, but old ...
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28 views

Fitting Model with MCMC?

In fitting a model with several variable I have found extremely useful a method involving the minimization of the Chi Square using a MCMC approach. In particular, I followed this tutorial ...
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53 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 ...
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51 views

What does drawing sample using Metropolis-Hastings algorithm mean?

I am confused with the word "draw samples from any probability distribution P(x)", mean I apologize for my ignorance, but, drawing sample as i understand, is for example, tossing a coin and writing ...
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30 views

Sampling methods and parallelization

A couple of years ago I learned about recent work in parallelizing slice sampling methods. More recently, I have read great things about NUTS and Hamiltonian Monte Carlo methods (HMC) in general (e.g. ...
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1answer
44 views

MCMC algorithm to generate samples

I read that MCMC algorithm is used to draw samples from a distribution. The example mentioned in the text book is about a 6x6 matrix which after 1000 iterations will converge to a steady state 1x6 ...
3
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1answer
76 views

Is there an R package for MCMC estimation of Generalized Method of Moments?

I'm looking for an R package (or a combination of packages) that would allow me to perform MCMC estimation of a GMM model, with a user-specified moments function. I've looked at the CRAN Bayesian ...
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1answer
117 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 ...
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64 views

Effective Sample Size for posterior

I am trying to implement unsuccessfully a function in matlab, to compute the effective sample size after a MCMC chain, with a posterior with 3 coefficients. Source: Sims MCMC $ VAR(1) / Y_t=\mu ...
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17 views

How to find the pdf of a time-dependent parameter in a linear regression model with drift?

Suppose there exists a simple linear equation, where the dependent variable y(time series; measurements available) depends on x1 and x2. If the parameter multiplier of x2 is time dependent and the ...
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36 views

Gibbs sample from AR(1) of exogenous input

I am trying to fit a model where there is a sequence of exogenous "shocks", $X_1, X_2, ..., X_T$, and a AR(1) of these shocks explain $Y_1, Y_2, ..., Y_T$. Specifically, Data (known): $X_1, X_2, ...
3
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1answer
92 views

Use only the last sample as the posterior in MCMC

I am new to statistics. After an MCMC sampler warmed up, the posterior is better estimated as the mean of several samples. (e.g. related question: http://stats.stackexchange.com//questions/56077) ...
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41 views

HMM-forward backward algorithm

Let $x_t, \, t=1, \dots ,T$ be a time series and suppose that $x_t | \xi_t \sim N(\mu_{\xi_t},\sigma^2_{\xi_t})$, where $\xi_t \in [1, \dots,K]$ is a group indicator (or regime or state), the ...
2
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2answers
92 views

Why is it desirable to have low auto-correlation in MCMC?

I keep reading about the need to check for autocorrelation in MCMC. Why is it important that the autocorrelation is low? What does it measure in the context of MCMC?
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27 views

What is the best ensemble sampler for highly correlated parameter space?

I have a likelihood that I want to estimate the free parameters for it and I am using MCMC to estimate the parameters. Two of the free parameters are positions and I defined uniform priors and one has ...
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2answers
83 views

Binary version of Probabilistic Matrix Factorization in pymc?

I'm a newby in statistics, this is my first post, sorry for any possible mistake. There is a good Bayesian Probabilistic Matrix Factorization model introduced in: Bayesian Probabilistic Matrix ...
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46 views

Defining constraint on prior with potential class

I have written an MCMC code in order to estimate parameters Xpos, Ypos, MASS and concentration with a set of input data gal_pos, ...
4
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1answer
60 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 ...
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56 views

Mixture of probits: understanding truncated-based likelihoods

I am trying to implement a mixture model of probits to infer the best decision boundary for every latent subpopulation. When doing Gibbs sampling, we eventually have to compute $P(y^* | w_c)$ where ...
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40 views

MCMC for Bayesian Inference (Gibbs Sampling) Varying Observed Data

At every step $k$, a Markov chain Monte Carlo algorithm for Bayesian inference with Gibbs sampling draws a parameter of the model to fit, $\beta_i^{(k)}$, from the conditional ...