MCMC using Hamiltonian dynamics
Citations
8,059 citations
4,353 citations
Cites background or methods from "MCMC using Hamiltonian dynamics"
...Currently, these are the static Hamiltonian Monte-Carlo (HMC) Sampler sometimes also referred to as Hybrid Monte-Carlo (Neal 2011, 2003; Duane et al. 1987) and its extension the No-U-Turn Sampler (NUTS) by Hoffman and Gelman (2014)....
[...]
...One of the main problems of these algorithms is their rather slow convergence for high-dimensional models with correlated parameters (Neal 2011; Hoffman and Gelman 2014; Gelman, Carlin, Stern, and Rubin 2014)....
[...]
...In contrast, Stan implements Hamiltonian Monte Carlo (Duane, Kennedy, Pendleton, and Roweth 1987; Neal 2011) and its extension, the No-U-Turn Sampler (NUTS) (Hoffman and Gelman 2014)....
[...]
2,938 citations
Additional excerpts
...An additional benefit of RHMC are transitions that can cover much larger variations in density, making it uniquely suited to these models; see (Neal 2011)....
[...]
2,080 citations
Cites methods from "MCMC using Hamiltonian dynamics"
...In this paper we will consider a class of MCMC techniques called Langevin dynamics (Neal, 2010)....
[...]
...More sophisticated techniques use Hamiltonian dynamics with momentum variables to allow parameters to move over larger distances without the inefficient random walk behaviour of Langevin dynamics (Neal, 2010)....
[...]
1,457 citations
Cites methods from "MCMC using Hamiltonian dynamics"
...However, this dichotomy is not as stark as it appears: many gradient-based optimisation methods can be turned into integration methods through the use of Langevin and Hamiltonian Monte Carlo methods [27, 28], while integration problems can be turned into optimisation problems through the use of variational approximations[24]....
[...]
References
35,161 citations
"MCMC using Hamiltonian dynamics" refers background or methods in this paper
...Chapter 1 MCMC using Hamiltonian dynamics Radford M. Neal, University of Toronto Hamiltonian dynamics can be used to produce distant proposals for the Metropolis algorithm, thereby avoiding the slow exploration of the state space that results from the diffusive behaviour of simple random-walk proposals....
[...]
...Markov Chain Monte Carlo (MCMC) originated with the classic paper of Metropolis et al. (1953), where it was used to simulate the distribution of states for a system of idealized molecules....
[...]
...Chapter 1 MCMC using Hamiltonian dynamics Radford M. Neal, University of Toronto Hamiltonian dynamics can be used to produce distant proposals for the Metropolis algorithm, thereby avoiding the slow exploration of the state space that results from the diffusive behaviour of simple random-walk…...
[...]
14,965 citations
"MCMC using Hamiltonian dynamics" refers background or methods in this paper
...not symmetrical, it must be accepted or rejected based on both the ratio of the probability densities of q∗ and q and on the ratio of the probability densities for proposing q from q∗ and vice versa (Hastings, 1970). To see the equivalence with HMC using one leapfrog step, we can write the Metropolis-Hastings acceptance probability as follows: min " 1, exp(−U(q∗)) exp(−U(q)) Yd i=1 exp − qi − q∗ i +(ε2/2)[∂...
[...]
...Since this proposal is not symmetrical, it must be accepted or rejected based on both the ratio of the probability densities of q∗ and q and on the ratio of the probability densities for proposing q from q∗ and vice versa (Hastings, 1970)....
[...]
11,008 citations
6,901 citations
6,188 citations