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Questions tagged [hmc]

Tag for questions related to Hamiltonian Monte Carlo.

2
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0answers
24 views

NUTS algorithm efficient transition kernel

I'm reading this paper, but I'm struggling to understand the following transition kernel. $T(w^{'}|w,\mathcal{C})=\left\{\begin{matrix} \frac{\mathbb{I}[w^{'}\in\mathcal{C}^{new}]}{|\mathcal{C}^{new}|...
0
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0answers
24 views

Bayesian chi-squared tests

I have a dataset with two groups of participants. Each participant performed a repeated measures task on which three types of errors could be made. I want to measure the difference in distributions of ...
1
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0answers
23 views

Does specifying normalizing constant significantly improves Hamiltonian Monte Carlo?

From my understanding the energy function needs only be specified such that it is proportional to the log density, and not specifying the normalizing constant should not greatly impact the sampling ...
3
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0answers
29 views

Is there an HMC algorithm that estimates a model with noncontinuous parameters?

Is there an HMC algorithm that estimates a model with noncontinuous parameters? All of the intuition I have for how HMC surfs around in the phase space is based on examples for posterior distributions ...
1
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0answers
44 views

Why volume preservation is important for Metropolis update? [duplicate]

I think my question is naive but I would like to ask why why volume preservation is important for MCMC and specifically Metropolis update.I'm reading the following paper https://arxiv.org/pdf/1206....
0
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0answers
26 views

Hamiltonian Monte Carlo Recover the Marginal distribution

Let $x$ be the random variable of interest and $v$ be the momentum variable. Let $U(x)$ be the potential energy function (log-negative of target distribution) and $K(v)$ be kinetic energy. For ...
0
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0answers
20 views

Hamiltonian MCMC information gathering [duplicate]

I started gathering information about Hamiltonian MCMC and I would like to ask if someone knows some good papers or books.If it possible notes that give a detailed explanation of Hamiltonian MCMC. ...
2
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0answers
44 views

Is the MC produced by HMC reversible?

I know that the deterministic dynamics in Hamiltonian Monte Carlo/Hybrid Monte Carlo are reversible and the numerical integrators one uses to approximate them are reversible too. But HMC consists of 2 ...
3
votes
1answer
301 views

What is the purpose of “transformed variables” in Stan?

I find references to transformed values in the Stan Reference and User Guides, and example code but no clear tutorial explanation. I'd be grateful for a link. Michael Betancourt, in his Stan ...
2
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0answers
40 views

Adaptive selection of Mass values in Hamiltonian Monte-Carlo?

I know there are good solutions for adaptive selection of path lengths and step-size for Hamiltonian Monte-Carlo (e.g. the NUTS sampler), but for the sampler to work efficiently we also require that ...
1
vote
1answer
42 views

Can I use Hamiltionian Monte Carlo when my likelihood is not a direct function of my parameters?

By "not a direct function of my parameters" I mean the following. I have some observed K-dimensional data and a model that can generate synthetic data based on 6 free parameters. I use this model to ...
8
votes
0answers
491 views

No-U-Turn Sampler (NUTS) for Hamiltonian Monte Carlo (HMC): how do I understand the doubling process?

I'm reading the original NUTS paper by Hoffman and Gelman, but couldn't fully understand the recursively doubling process. The following figure is taken from the paper. The NUTS process starts ...
14
votes
1answer
933 views

Hamiltonian Monte Carlo for dummies

Could you provide a step-by-step for dummies explanation of how Hamiltonian Monte Carlo work? PS: I've already read the answers here, Hamiltonian monte carlo, and here, Hamiltonian Monte Carlo vs. ...
8
votes
1answer
689 views

Hamiltonian Monte Carlo: how to make sense of the Metropolis-Hasting proposal?

I am trying to understand the inner working of Hamiltonian Monte Carlo (HMC), but can't fully understand the part when we replace the deterministic time-integration with a Metropolis-Hasting proposal. ...
5
votes
1answer
285 views

Understanding the Typical Set for Markov chain Monte Carlo sampling

I started reading "A Conceptual Introduction to Hamiltonian Monte Carlo" today, and I've gotten stuck on understanding Betancourt's explanation of what a "typical set" is. If $q_1, q_2, \ldots, q_n$ ...
6
votes
1answer
358 views

Hamiltonian Monte Carlo (HMC): what's the intuition and justification behind a Gaussian-distributed momentum variable?

I am reading an awesome introductory HMC paper by Prof. Michael Betancourt, but getting stuck in understanding how do we go about the choice of the distribution of the momentum. Summary The basic ...
5
votes
2answers
370 views

For Hamiltonian Monte Carlo, why does negating the momentum variables result in a symmetric proposal?

I have been going through Radford Neal's excellent HMC book chapter in detail. However, there is one detail that I'm really obsessing with now, and I'm not sure if I'm thinking about it right. When ...
3
votes
2answers
258 views

Proposal distribution in Hamiltonian Monte Carlo

I have been reading A Conceptual Introduction to Hamiltonian Monte Carlo by Betancourt (https://arxiv.org/abs/1701.02434), which is a great introduction to HMC, but there is one part that I can't get ...
3
votes
1answer
211 views

Plotting the typical set of a Gaussian distribution

There is this article where the author Michael Betancourt uses this image to convey the concept of the typical set in a distribution. I would like to plot the typical set of a univariate or a ...
3
votes
1answer
163 views

How to know if the derivatives exist in Hamiltonian Monte Carlo?

In section 3.2 of Radford Neal's take on HMC he says: We must also be able to compute the partial derivatives of the log of the density function. These derivatives must therefore exist, except ...
22
votes
1answer
2k views

Hamiltonian Monte Carlo vs. Sequential Monte Carlo

I am trying to get a feel for the relative merits and drawbacks, as well as different application domains of these two MCMC schemes. When would you use which and why? When might one fail but the ...
13
votes
2answers
538 views

Hamiltonian monte carlo

Can someone explain the main idea behind Hamiltonian Monte Carlo methods and in which cases they will yield better results than Markov Chain Monte Carlo methods ?
1
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0answers
77 views

Hamiltonian Monte Carlo with large parameter values fail to converge

I'm trying to learn about Hamiltonian Monte Carlo. Therefore I tried to infer the Parameters of a Multivariate Normal given some samples. My procedure is the following: Define $\mu$ and $\Sigma$ ...
3
votes
1answer
455 views

Interesting / strange behavior of one chane on different [unrelated] variables in STAN

I have a quite complex hierarchical model for which I'm estimating parameters and producing posterior predictive using STAN (rstan) for some psychophyiscal data. I'm (sometimes) observing some ...
7
votes
1answer
225 views

Hamiltonian Monte-Carlo with piecewise differentiable log likelihood

This is a bit of a curious situation. I have an energy function $E=S+N$ which is the sum of a smooth differentiable function $S$ and a piecewise constant "noise" function $N$. This means that on ...