Fast Hamiltonian sampling for large-scale structure inference

In this paper we present a new and efficient Bayesian method for non-linear three-dimensional large-scale structure inference. We employ a Hamiltonian Monte Carlo (HMC) sampler to obtain samples from a multivariate highly non-Gaussian lognormal Poissonian density posterior given a set of observations. The HMC allows us to take into account the non-linear relations between the observations and the underlying density field which we seek to recover. As the HMC provides a sampled representation of the density posterior any desired statistical summary, such as the mean, mode or variance, can be calculated from the set of samples. Further, it permits us to seamlessly propagate non-Gaussian uncertainty information to any final quantity inferred from the set of samples. The developed method is extensively tested in a variety of test scenarios, taking into account a highly structured survey geometry and selection effects. Tests with a mock galaxy catalogue based on the Millennium Run show that the method is able to recover the filamentary structure of the non-linear density field. The results further demonstrate the feasibility of non-Gaussian sampling in high-dimensional spaces, as required for precision non-linear large-scale structure inference. The HMC is a flexible and efficient method, which permits for simple extension and incorporation of additional observational constraints. Thus, the method presented here provides an efficient and flexible basis for future high-precision large-scale structure inference.