Questions tagged [langevin-diffusion]

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 is generated as: $$ X^*=X+\tau\nabla…

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 resampling the momentum -- and I see how this…

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}\left ( \nabla P(\theta_t) + \sum_{i = 1}^n \nabla…

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, the whole reason for doing MCMC is that you do…