# 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.

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### Why model order selection is a big problem in statistics?

I’m learning statistical signal processing for my studies. I was doing a bit of literature review on model order selection and I didn’t want to miss out on techniques that I might not have seen. I ...
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### The gradient vector in Hamiltonian Monte Carlo (leapfrog method)

Let $x_{t}, \omega_{t} \in \mathbb{R^{d}}$ The Hamiltonian Monte Carlo says this: Deterministic: it relies on the Hamiltonian dynamics so given an initial state, at any time $t$, specified by the ...
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### What is a perfect distribution to consider for the step increase/ decrease for the reversible jump MCMC

I am trying to understand the hyper parameters in the paper  for the model order selection with reversible jump MCMC (RJ-MCMC). There is a hyper parameter $\Lambda$ (The parameter of the Poisson ...
• 111
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### Binned resampling of correlated data with bootstrap method

The goal Compute the Binder cumulant defined as the estimator $$\text{B.C.}=\frac{\langle x^4\rangle}{\langle x^2\rangle^2}$$ and its statistical error on a sample of normally distributed data points ...
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### Why Reversible jump mcmc has only one step increase/ decrease?

I was applying reversible jump MCMC for joint estimation of model order and parameter estimation. I've a conceptual question in my mind. First of all, the algorithm has 3 steps, namely the birth, ...
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### Why do we sample from the uniform distribution in Metropolis-Hastings for acceptance?

For each iteration of the MH, sample $x'=q(x|x')$, then the acceptance probability is computed:$$A=\min(1,a)$$ where $$\alpha=\frac{p(x')q(x|x')}{p(x)q(x'|x)}$$ Now, I've seen that the algorithm ...
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### MCMC__ std of the posterior nearly 0

I am new to MCMC. I am trying to use Metropolis-Hastings MCMC to update a parameter set for a model based on measurements. But the posterior I got seems to be little bit wired as the std values for ...
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### Updated book or review paper on MCMC methods (2022)

For a self-study course, I'm looking for bibliography that describes current MCMC algorithms. I'd prefer a book or a review paper. My background knowledge is at the level of Gamerman-Lopes or Gilks-...
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### Is it appropriate to discretize conditional posteriors in an MCMC as an alternative to techniques like Metropolis-Hastings or slice-sampling?

Background Suppose I am interested in sampling the posterior distribution defined by $p(\theta_1,\theta_2|y)$, where $\theta_1,\theta_2$ are parameters of interest and $y$ is a vector of observations. ...
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