All Questions
Tagged with simulation markov-chain-montecarlo
76
questions
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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, ...
- 41.6k
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18
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Is this a reasonable way to check the quality of simulated data in MCMC inference?
I have a hierarchical Bayesian model that looks like this:
$\alpha_i \sim \mathcal{N}\left(\mu_\alpha, \sigma_\alpha\right) \tag{1}$
$\beta_i \sim \mathcal{N}\left(\mu_\beta, \sigma_\beta\right) \tag{...
- 211
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37
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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
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23
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Metropolis-Hastings on domain $(2, \infty)$
I'm trying to understand the Metropolis Hastings algorithm in depth by solving some exercise problems. On one of them, I'm asked to use MH to generate samples from
$$f(x) = c \frac{1}{\theta}e^{-\frac{...
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119
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How to compute Expected Squared Jump Distance (ESJD) of a Metropolis-Hastings algorithm
The Expected Squared Jump Distance (ESJD) seems to be defined slightly differently in various papers, which makes this very confusing. For instance, Definition 2.2 of Optimal Scaling of Random-Walk ...
- 2,236
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57
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Monte Carlo simulation to get stationary distribution of a complex system
I was wondering if I could get some help with my problem.
I have a complex Markov chain where I cannot track its transition analytically. Instead, I decided to simulate $N$ numbers of particles for $T$...
- 213
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1
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201
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Sampling from the posterior with a constraint on the posterior mean
Background
Under certain assumptions we know that being given the posterior mean and a family of conditional distributions, we can uniquely determine the joint distribution. I quote one of the ...
- 540
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63
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Gillespie's Algorithm's Connection to Kolmogorov's Forward Equations
I've been learning Gillespie's algorithm to simulate continuous time Markov chains. I understand how the algorithm is derived from the reaction probability density function
$P(\tau, \mu)$ = ...
- 31
2
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217
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Why is it easy for the Gibbs sampler to take long time to converge to target distribution?
This is related to Gelman's Bayesian Data Analysis 3rd Edition pg 300 first paragraph of Section 12.4. The book says the following.
"An inherent inefficiency in the Gibbs sampler and Metropolis
...
- 1,445
1
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1
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84
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Metropolis - Hastings algorithm on a set of countable sequences
I want to simulate $\sigma$ from a measure $\pi(\sigma)$ through the Metropolis-Hastings algorithm, where $\sigma$ is a sequence of 0's and 1's on $S = \{0, 1\}^n$, the set of all sequences of 0's ...
- 425
2
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132
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Simulations based noisy likelihood function
I have a problem where I have a measured data vector $D$ with Gaussian uncertainties (covariance matrix $\Sigma$). I am now trying to model this data with a generative model with parameters $\phi$. ...
- 827
2
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1
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380
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How to understand the scaling in Metropolis Hastings MCMC
We know the Metropolis Hastings (MH) in MCMC:
target distribution: $\pi(x)$
proposal distribution: $p(y|x)$
acceptance: $\alpha(x,y) = \min \Big(1, \dfrac{\pi(y)p(y|x)}{\pi(x)p(x|y)}\Big)$
Here are ...
- 1,345
1
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30
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Proving simulation with rejection generates conditional distribution
I'm working with Poisson processes, but the idea is more general. I want to simulate a two-dimensional Poisson process (over the unit square so we can ignore an area factor) with parameter $\lambda,$ ...
- 46
3
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1
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166
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SMC Samplers - Optimal Backward Kernel Explanation
In Sequential Monte Carlo Samplers of Del Moral (2006) we see that the optimal backward kernel is
$$
L_{n-1}^{\text{opt}} (x_{n-1} \mid x_n) = \frac{\eta_{n-1}(x_{n-1}) K_n(x_n \mid x_{n-1})}{\eta_n(...
- 657
1
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28
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Simulations for uniform limit theorems
When it comes to simulations, I am unfortunately new: How can I verify the performance of my theoretical result, being a limit theorem of the following type:
$$\text{sup}_{t\in[0,1]} X_{t}^{n}\overset{...
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