Questions tagged [langevin-diffusion]

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4
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2answers
163 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 ...
4
votes
1answer
341 views

Does Langevin MCMC with decreasing step size require Metropolis-Hastings?

We want to sample from the distribution $P(\theta \mid X)$, which we only know up to a multiplicative constant. In Langvin MCMC, our Markov Chain is $$ \theta_{t+1} = \theta_t + \frac{\epsilon_t}{2}\...
5
votes
0answers
466 views

Tuning MALA (Metropolis-adjusted Langevin) proposal

I'd like to implement a version of Metropolis-adjusted Langevin sampling, but I'm unsure how to go about tuning the parameters of the proposal density. My understanding is that in MALA, a proposal ...
2
votes
2answers
148 views

How to solve MALA when the target density is known up to a constant?

If you look at the wikipedia explanation of Metropolis adjusted Langevin Algorithm, the acceptance ratio is given by The second equation involves taking the gradient of the log of $\pi(x)$. However, ...