# Questions tagged [markov-chain-montecarlo]

Markov Chain Monte Carlo (MCMC) refers to a class of simulation methods for generating samples from a complex 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 generation (e.g. inversion method) are infeasible. The very first MCMC method was the Metropolis (et al.) algorithm, later expanded by Hastings.

1,638 questions
Filter by
Sorted by
Tagged with
29 views

### Bayesian MCMC and Only Updating Some Variables at a Time

I want to do Bayesian MCMC on a Gaussian Mixture Model. But, I want to update the means, weights, and covariance matrix for a single component separate from the others. Would there be the issue of ...
1 vote
47 views

### My MCMC Simulation

I am new to MCMC Simulation and Bayesian Analysis, so I wonder if my simulation has converged. My posterior is highly correlated by nature, so I'm facing some difficulty to ensure a sufficient number ...
• 41
1 vote
12 views

### Recycling MCMC samples for another data set from the same distribution

Suppose I'm given $\theta_0$ and I want to sample data from a density $f(Y|\theta_0)$ and then sample from the posterior of $\theta|Y$ (given, obviously, some prior). I want to do this lots of times, ...
• 41.8k
11 views

### two-step gibbs sampling vs block gibbs sampling

While reading Bayesian-related technical articles, I can see algorithms such as two-step Gibbs sampling and block gibbs sampling ...
• 5,222
18 views

• 66
45 views

### How to tune the unadjusted Langevin algorithm?

I want to start investigating the (unadjusted) simulation of the Langevin process $${\rm d}X_t=b(X_t){\rm d}t+\sigma{\rm d}W_t,$$ where $$b:=\frac{\sigma^2}2\nabla\ln p.$$ I don't want to simulate ...
• 303
18 views

### Is it possible to use Particle Marginal Metropolis Hastings to estimate the transition matrix and input?

A state space model is defined as: $$x_{t+1} = A_tx_t + B_tu_t$$ $$y_{t+1} = H_tx_{t+1}$$ So my question is: is it possible to use Particle Marginal Metropolis Hastings to estimate the transition ...
53 views

### Metropolis-Hastings algorithm doesn't converge to the global minimum

I calculated the total root mean squared error of 24 parameters that are estimated with metropolis hastings, I ran the algorithm for 100.000 iterations, and as the chain forward it reached a global ...
1 vote
27 views

• 13
24 views

### How to do prediction (evaluate marginal likelihood) in generative latent variable classifier?

The dataset is $\{\boldsymbol x_t,y_t\}$ for $t=1,\dots,T$, where $y_t \in \{0,1\}$. Define a generative latent variable classifier whose plate diagram is shown above. For each data point, a local ...
• 81
1 vote
22 views

### How to leverage the separable functions in MCMC sampling? [closed]

I'm considering the posterior of a parametric model via the Bayesian approach. More specificity, I have a parametric model $u(p_1,p_2, p_3) = u_1(p_1) \times u_2(p_2) \times u_3(p_3)$ and I want to ...
• 11
144 views

### Can MCMC sample any probability distributions?

I have three fundamental questions related to MCMC. I would appreciate the help on any one of those. The most fundamental question in MCMC field, which I can't find a reference, is: Can MCMC generate ...
28 views

### Particle Marginal Metropolis Hastings - How to multiply the proposal distribution by the distribution of x?

When we are using particle marginal metropolis hastings, we will approximate the distribution of x with particle filter, in this pdf written below says: In such situations it is natural to suggest ...
6 views

### Expectation of Changes in Top K Elements Amongst Randomly Generated Numbers

I am conducting a Monte Carlo simulation where: I generate n random numbers uniformly. Select the top k of these numbers. Then regenerate c of the n numbers at random. I aim to compute the mean ...
20 views

### How to do Bayesian MCMC with Compositional Parameter Constraints

So I know that if you have parameter constraints and you were to do a random walk MH without them, you can use a truncated normal distribution as your proposal instead (and of course, this would be ...
44 views

• 303
6 views

### generalized progressive hybrid censoring scheme type 1 and Muth distribution

I have data concerning failure of sodium sulfur battery cells with the following numeric values: 76,82,210,315,385,412,491,504,522,646+,678,775,884,1131,1446,1824,1827,2248,2385,3077. This dataset ...
22 views

### MCMC for correlated Posterior

I'm simulating the posterior of a (as it seems) highly correlated Posterior distribution using MCMC (DREAM Algorithm). My setting is that I have 7 parameters where x1/x3 and x2/x4 is highly correlated,...
• 41
31 views

### Sampling from a binomial and get stuck in boundaries

I am trying to use the Metropolis-Hasting in order to obtain a sample for X that is a vector of length N of values that go from 0 to K (in this case K=3). So X ~ Binom(K, p) and p ~ Beta(1,1). For ...
• 57
27 views

### Is MCMC on log-likelihood valid? [duplicate]

Hi it occurred to me that for numerical stability people often use the log-likelihood instead of a real pdf/likelihood. And while this might work fine for MAP & MLE it's not obvious that it works ...
• 411
10 views

### x value in MCMC - log(Obs/Exp)

My company recently implemented software that uses an MCMC method. In that program, a handful of randomly generated nuisance parameters are used to calculate expected values which are then compared to ...
• 101
13 views

### Using PCA to check if parameters simulated from a hierarchical Bayesian model are close to real parameters

I have a hierarchical Bayesian model that learns a 5-parameter function for each of the N participants. The priors on each of the 5 parameters are parameterized by a scale parameter, so, it also ...
• 111
38 views

### How can I determine if a system is equilibrated?

Cross-posted in SCSE and MMSE I am experimenting with a new MCMC protocol and new research. In the context of Monte Carlo simulation, a "state of equilibrium" refers to a condition where the ...
• 2,201
16 views

### Is this a correct way of resampling the MCMC chain?

Please understand I am not familiar to the statistical languages. All I want is to resample a probability distribution from an existing sample drawn from another distribution using MCMC, without ...
• 131
60 views

### MCMC seems very sensible to the evidence

currently starting to study bayesian ML, and specifically MCMC, in order to compute the posterior: $$P(\theta|D) = \frac{P(D|\theta)P(\theta)}{P(D)}$$ Now, I see how the acceptance ratio makes sense ...
• 1,217
69 views

### How should you determine the probability returned by a flat uniform prior function

I am currently doing an analysis that involves fitting a model to a 1D graph. Following the example on the emcee documentation, I started with Maximum likelihood estimation and am now looking at using ...
• 33
40 views

### Is there a way to restrict the relationship of parameters in MCMC?

I have seen some discussion on the restriction on the parameter space such as MCMC on a bounded parameter space? this post, but I am wondering if there is a method to restrict the function or ...
• 1
11 views

### Parallel Tempering and Bayesian Non-Parametrics

In parallel tempering, we run multiple MCMC chains in an ascending temperature ladder, where the posterior density of the $i$th chain is exponentiated to the reciprocal of the temperature of the $i$th ...
• 225
1 vote
35 views

### Enumerating feasible solutions to the subset sum problem using Gibbs sampling

Given a set of $m$ strictly positive real numbers $W = \{ w_{1}, \dots, w_{m} \}$, I want to find subsets of $W$ whose sum is less than or equal to a maximum value $N$ using Gibbs sampling. To do this,...
• 101
I am curious about whether a Markov Chain $X_n$ is recurrent implies that for any $k > 0$, $X_{kn}$ is also recurrent. Here are my observations. If $X_n$ is transient, $X_{kn}$ must be transient by ...