Questions tagged [hamiltonian-monte-carlo]
Tag for questions related to Hamiltonian Monte Carlo.
36
questions
2
votes
0answers
60 views
Hamiltonian Monte Carlo (or Langevin Monte Carlo) on a Sphere
I want to perform Hamiltonian Monte Carlo (HMC) or Langevin Monte Carlo (LMC) on a spherical domain $\mathbb{S}^{D-1}$ embedded in a Euclidean space $\mathbb{R}^D$. My energy function is a deep neural ...
0
votes
0answers
28 views
Typical set clarification
I was reading more about the use of typical sets when it comes to MCMC methods, like this post by the Stan documentation. Unfortunately, I am confused by several points:
One example I have seen ...
1
vote
0answers
19 views
NUTS Sampler: runaway stepsize
I've been trying to implement a NUTS sampler according to the Gelman 2014 paper, and I've been finding that my log-stepsize $\log \epsilon$ runs away towards $-\infty$ for reasonable values of $\delta=...
1
vote
1answer
68 views
Can someone explain how dual averaging helps the No U-Turn Sampler (NUTS) choose step-size adaptively?
I have read both the original NUTS paper and also the dual averaging paper by Nesterov but due to my lack of background knowledge in optimisation, I don't really understand how dual averaging works.
...
10
votes
1answer
222 views
How does Hamiltonian Monte Carlo work?
I made the below graphic to explain how I currently understand the HMC algorithm. I'd like verification from a subject matter expert if this understanding is or isn't correct. The text in the below ...
1
vote
0answers
23 views
What is the inference behind the momentum variable and the Kinetic energy for a weakly non-linear inverse problems in the HMC method?
We generate an auxiliary momentum variable in the HMC method to provide gradient for the propagation of trajectory (m, p) (model or position, momentum) in the phase space.
If we look into Newton's ...
0
votes
1answer
37 views
Can I do HMC with the wrong Hamiltonian?
I am a novice HMC user. I am reading Neal's chapter in the Handbook of MCMC. I think I can present the HMC algorithm as :
Sample a new momentum
Propose a new momentum and a new position using a ...
2
votes
0answers
32 views
Deriving a momentum proposal distribution for Hamiltonian Monte Carlo — non-Gaussian kinetic energies
I am trying to understand how to derive the optimal way to generate momenta in HMC.
In the gaussian case, I think the approach is that if one samples proportional to the Gaussian, the log likelihoods ...
2
votes
1answer
32 views
For Hamiltonian Monte Carlo, what should be done when one of the steps in the leapfrog path yields no solution?
When estimating a very complex (potentially discontinuous) model with Hamiltonian Monte Carlo, what should be done when one of the steps in the leapfrog path yields no solution? The issue is that ...
0
votes
1answer
43 views
Strange substitution in HMC
I try to read paper, MCMC using Hamiltonian dynamics). The author, Neal states(P28):
To begin, Cruetz nodes that the following relationship holds when any Metropolis-style algorithm is used to ...
2
votes
0answers
27 views
Optimal Scaling HMC proof
I'm reading the paper https://arxiv.org/pdf/1001.4460.pdf
I get very confused when reading the author proof of the theorem (4.2)
Here are few points.
(1) The expected squared jump distance is ...
3
votes
1answer
206 views
Why does Stan initialize an MCMC chain with a random value generated uniformly from [-2, 2] instead of a random value generated from the prior?
From Stan reference,
The default is to randomly generate initial values between -2 and 2 on
the unconstrained support
It seems to me that it makes more sense to randomly generate initial values ...
7
votes
2answers
226 views
Reconciling Langevin MC methods as one-step HMC versus as diffusion or brownian motion
I have a basic understanding of Hamiltonian monte carlo and why it works. I've read that Langevin MC is basically a special case of HMC when you only step the dynamics forward a single timestep before ...
2
votes
1answer
53 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}|...
1
vote
0answers
55 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 ...
5
votes
1answer
58 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
vote
0answers
95 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
votes
0answers
22 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.
...
3
votes
0answers
105 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 ...
8
votes
1answer
2k 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 ...
3
votes
0answers
80 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
48 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
887 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
1k 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. ...
10
votes
1answer
1k 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. ...
9
votes
1answer
638 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 $q_1, q_2, \ldots, q_n$ ...
10
votes
1answer
1k 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 ...
11
votes
2answers
860 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 ...
5
votes
2answers
468 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 ...
5
votes
1answer
584 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
206 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 ...
25
votes
1answer
3k 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 ...
17
votes
2answers
931 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
vote
0answers
81 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
746 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
309 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 ...
