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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106 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
50 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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0answers
24 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
20 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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0answers
22 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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0answers
44 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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2answers
44 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 ...
3
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0answers
28 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
43 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
69 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 ...
1
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1answer
111 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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0answers
57 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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15 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 ...
2
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0answers
34 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
votes
1answer
79 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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0answers
30 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
votes
2answers
80 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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0answers
20 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 ...
0
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2answers
72 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 ...
2
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0answers
37 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
42 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 ...
2
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0answers
54 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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0answers
34 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 ...
5
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1answer
172 views

Stochastic Programming with MCMC

I have just started learning about MCMC (using PyMC), and it seems to be a hammer that can be used to solve a large class of inference and optimization problems. While I understand that there are ...
4
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1answer
39 views

Geweke diagnostic of a Markov chain: why does the first window have to cover the burn-in?

I read the following statement in this document$^{[1]}$, at the bottom of page 11: Too wide A will some times “hide” the burn in part within the converged part of the chain and the difference in ...
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1answer
39 views

MCMC model from CDF values?

I am looking for a working example of an MCMC Bayesian model (for JAGS, etc.) when random variates, from a given distribution with unknown parameters, are observed only via their CDF values. For ...
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1answer
52 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 ...
1
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1answer
43 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 ...
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0answers
41 views

How to implement a metropolis hastings algorithm to find the posterior pdf of a time-dependent parameter?

Assume that I have a time series observations denoted by Yi where i is from 1-5000. yi=β1 x1i + β2 x2i + β3 x3i + Ci; Here x is the input. I have to find the values of Betas. But, I'm taking all ...
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0answers
35 views

Covariance update from Jacobian of transition function

In this paper on particle filtering with gradient descent, the authors sample Xk+1 through gradient descent, then update the covariance matrix P associated with Xk+1 as follows: Pi+1(k + 1|k + 1) = ...
3
votes
1answer
86 views

How do MCMC methods allow the estimation of the posterior distribution in this example?

I am reading a book example (diagram from p10) in which a person scores 9/10 on which we assumed a uniform prior. The posterior distribution could be easily worked out analytically, but the book gives ...
2
votes
0answers
43 views

Dummy coding from a bayesian stand of view

If we want to use categorical variables in regression context we are allowed to use dummy codings such as: http://www.ats.ucla.edu/stat/r/library/contrast_coding.htm Is this also required in ...
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0answers
28 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 ...
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0answers
44 views

How do we build a model with pyMC

I am a newbie programmer with pyMC. I have a model given as following $$\rho=\sqrt(x^2+y^2)$$ $$z=f(x,y)=\frac{c^3}{\log(c)+1}\frac{\log\rho}{\rho^2}+\frac{5.3}{r^2}\rho^{-3}$$ and I want to find the ...
0
votes
1answer
83 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 ...
0
votes
1answer
41 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
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1answer
73 views

Using PyMC to obtain the posterior for the parameters of a parametric model?

I am a newbie with pyMC and I want to program an MCMC sampling for a complicated problem. I have a function given by in the following: $$g(r,c,\theta_1,\theta_2)=\frac{\delta_c}{\Sigma ...
0
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0answers
36 views

MCMC Standard error

I need to make a simulation to calculate the integral of a pdf $f(x|D)$ over a region $T$.That is, I need to evaluate $$\int_T f(x|D)\; dx$$ to do this, I just defined the function $g(x)=1$ if $x \in ...
0
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0answers
27 views

Proper proposal distribution in Metropolis-Hastings for a 2-state discrete process

This question is related to Understanding Metropolis-Hastings with asymmetric proposal distribution. I'm trying to draw sample paths from a 2-state markov chain using M-H. Unfortunately, I've only ...
0
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0answers
31 views

MC Standard Error for Metropolis Random-Walk Algorithm

I need to calculate some integrals using MCMC with Metropolis Random-Walk Algorithm. To decide the value I will accept as my integral, I will calculate 5 simulations of MCMC with size 2000, but I ...
0
votes
0answers
30 views

Metropolis Random Walk Algorithm - Covariance Matrix

I need to calculate an integral of a 3 variable density $f(x_1, x_2, x_3)$, defined in a domain $D$, in the region $$T=\{x \in R³|f(x) \geq M \}$$ using MCMC , where $M$ is a given positive constant. ...
4
votes
1answer
200 views

MCMC Modelling - can this even be solved?

I am very new to Bayesian modelling and MCMC - I would like to know if the problem I describe below can be solved. It seems to be there is too much missing information but I wanted to get your ...
4
votes
2answers
84 views

Metropolis Hastings algorithm

I need to study Markov Chain Monte Carlo methods, to be more specific i need to study Metropolis Hastings algorithm and all about it like convergence criteria. Who can prescribe me a book, or a ...
0
votes
1answer
72 views

Can I subsample a large dataset at every MCMC iteration?

I have a large dataset from which I want to perform a bayesian probit regression using Gibbs sampling 1. Since the dataset has one milion rows, and variables from a truncated normal must be sampled ...
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0answers
36 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
41 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
25 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
95 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 ...
1
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1answer
64 views

Evaluating an integral using MCMC algorithm

Consider the problem of evaluating the following integral $$ \int_T f(\theta_1, \theta_2, \theta_3| D) d\Theta$$ where $f$ is a posterior density and the values of $D = (d_1, ..., d_n)$, given ...
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0answers
29 views

Explaining MCMC sampling for a Multinomial Distribution and missing at random

I understand how MCMC works, and I understand how Multinomial Distribution works. I have a dataset some of the data are missing at random (MAR). I cannot connect these two dots together (MCMC -> ...