Efficient Cosmological Parameter Estimation with Hamiltonian Monte Carlo

@misc{hamiltonianMCMC, abstract = {Traditional Markov Chain Monte Carlo methods suffer from low acceptance rate, slow mixing and low efficiency in high dimensions. Hamiltonian Monte Carlo resolves this issue by avoiding the random walk. Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) technique built upon the basic principle of Hamiltonian mechanics. Hamiltonian dynamics allows the chain to move along trajectories of constant energy, taking large jumps in the parameter space with relatively inexpensive computations. This new technique improves the acceptance rate by a factor of 4 and boosts up the efficiency by at least a factor of D in a D-dimensional parameter space. Therefor shorter chains will be needed for a reliable parameter estimation comparing to a traditional MCMC chain yielding the same performance. Besides that, the HMC is well suited for sampling from non-Gaussian and curved distributions which are very hard to sample from using the traditional MCMC methods. The method is very simple to code and can be easily plugged into standard parameter estimation codes such as CosmoMC. In this paper we demonstrate how the HMC can be efficiently used in cosmological parameter estimation.}, author = {Hajian, Amir }, citeulike-article-id = {1445907}, comment = {Fast variant of MCMC. In a D dimensional parameter space one can gain speedups up to D. It avoids the random walk (how?) }, eprint = {astro-ph/0608679}, keywords = {gibbs, mcmctheory}, month = {Aug}, posted-at = {2008-07-15 18:00:33}, priority = {2}, title = {Efficient Cosmological Parameter Estimation with Hamiltonian Monte Carlo}, url = {http://arxiv.org/abs/astro-ph/0608679}, year = {2006} }

TY - ELEC ID - hamiltonianMCMC L3 - citeulike-article-id:1445907 TI - Efficient Cosmological Parameter Estimation with Hamiltonian Monte Carlo N2 - Traditional Markov Chain Monte Carlo methods suffer from low acceptance rate, slow mixing and low efficiency in high dimensions. Hamiltonian Monte Carlo resolves this issue by avoiding the random walk. Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) technique built upon the basic principle of Hamiltonian mechanics. Hamiltonian dynamics allows the chain to move along trajectories of constant energy, taking large jumps in the parameter space with relatively inexpensive computations. This new technique improves the acceptance rate by a factor of 4 and boosts up the efficiency by at least a factor of D in a D-dimensional parameter space. Therefor shorter chains will be needed for a reliable parameter estimation comparing to a traditional MCMC chain yielding the same performance. Besides that, the HMC is well suited for sampling from non-Gaussian and curved distributions which are very hard to sample from using the traditional MCMC methods. The method is very simple to code and can be easily plugged into standard parameter estimation codes such as CosmoMC. In this paper we demonstrate how the HMC can be efficiently used in cosmological parameter estimation. KW - gibbs KW - mcmctheory N1 - Fast variant of MCMC. In a D dimensional parameter space one can gain speedups up to D. It avoids the random walk (how?) AU - Hajian, Amir PY - 2006/Aug/31/ UR - http://arxiv.org/abs/astro-ph/0608679 ER -