Questions tagged [hamiltonian-monte-carlo]
Tag for questions related to Hamiltonian Monte Carlo.
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What is a representation of positive numbers summing to one that can be sampled via HMC?
I have a probability density $f(x): \mathbb{R}^n \rightarrow \mathbb{R}$ whose argument vector $x$ satisfies the constraints that all elements are positive and sum to unity. I need to generate samples ...
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Combining MCMC with Variatonal Inference
I have a Gibbs sampler that is mixing terribly slowly. I have a hunch that if I sample a parameter pair as a single block, it would improve convergence.
I tried HMC within Gibbs, but it's also slow. I ...
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How to diagnose HMC results like r-hat for a Mixture Model?
I have the following distribution $$
\begin{align}
\boldsymbol \pi&\sim\text{Dirichlet}([1,\cdots 1]\in R^K)\\
\boldsymbol \theta&\sim P(\boldsymbol \theta)
\\
\mathbf y&\sim \sum _{i=1}^K\...
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Lots of variability in the effective sample size but stable parameter estimates?
I ran 4 chains with NUTS and made a forest plot, but I cannot show the plot here. In words, what I am seeing is the there is a lot of variability in the effective sample size (ESS) in the chains. ...
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What is the intuition for the limited variation in potential energy for HMC?
In A General Metric for Riemannian Manifold Hamiltonian Monte Carlo (Betancourt, 2013), the author writes:
The first [5] and still most common choice of the conditional density, $\pi(p|q)$, is a ...
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Prior term in SGHMC implementation
I am working with SGHMC (Stochastic Gradient Hamiltonian Monte Carlo) models.
I found an implimentation of the algorithm in pytorch here. The part of the code that represents momentum variable update (...
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139
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What could lead to this misbehavior for the expected sample size (ESS)?
I am using Hamiltonian Monte Carlo (HMC) to sample the posterior of a continuous-time Markov Chain (CTMC).
However, after running 10 parallel chains with 100 draws each, the effective sample size (ESS)...
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The guidelines for choosing different MCMC algorithms [closed]
MCMC has several types of algorithms: Metropolis-Hastings, Gibbs, Adaptive MH, Hamiltonian Monte Carlo. What are their respective pro/cons, and how to choose them in the Bayesian analysis?
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What does it mean to have a "transient state" or a "transient phase" in an Ising model?
I downloaded a simple implementation of the Ising model in C# from this link.
I have understood more or less the entire code except the following routine:
...
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Hamiltonian Monte Carlo vs. "Metropolis-Hastings with a Hamiltonian step"
In Hamiltonian Monte Carlo the proposal is accepted with probability:
$$
\alpha\left(\mathbf{x}_n(0),\mathbf{x}_n(L\Delta t)\right)
=
\min\left(1, \frac{\exp\left[-H\left(\mathbf{x}_n(L\Delta t),\...
- 4,439
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Hamiltonian trajectory stays in the typical set?
I'm currently studying Hamiltonian MCMC by reading Betancourt's 2014 and Neal's 2011 pedagogical papers, but I still don't understand why following a Hamiltonian trajectory for our proposed update ...
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volume preservation in MCMC
In the paper of MCMC using Hamiltonian dynamics, there is the following statement on volume preservation. What does it mean exactly? I am not very clear about the ...
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what is the advantage of using Hamilton dynamics in sampling methods? [duplicate]
I am wondering apart form being gradient based sampling methods, what is the advantages of using Hamiltonian MCMC?
- 135
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Use Monte Carlo to produce new 'p' correlated data from existing data [duplicate]
As mentioned above, I have a problem where I need to generate new data Y from an existing data X such that Y is p correlated to X.
I know their are several ways to do it but I want to know if monte ...
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Step-size adaptation of NUTS within Gibbs
I am trying to solve a hierarchical problem with a Gibbs sampler. I do not have closed-form expressions for the conditionals, thus I have to use another MCMC method within the Gibbs scheme to sample ...
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