Computing (ratios of) normalizing constants of probability models is a fundamental computational problem for many statistical and scientific studies. Monte Carlo simulation is an effective technique, especially with complex and high-dimensional models. This paper aims to bring to the attention of general statistical audiences of some effective methods originating from theoretical physics and at the same time to explore these methods from a more statistical perspective, through establishing theoretical connections and illustrating their uses with statistical problems. We show that the acceptance ratio method and thermodynamic integration are natural generalizations of importance sampling, which is most familiar to statistical audiences. The former generalizes importance sampling through the use of a single "bridge" density and is thus a case of bridge sampling in the sense of Meng and Wong (1996). Thermodynamic integration, which is also known in the numerical analysis literature as Oga...

We present a new scalable algorithm for short-range molecular dynamics simulations on distributed memory MIMD multicomputer based on a message-passing multi-cell approach. We have implemented the algorithm on the Connection Machine 5 (CM-5) and demonstrate that meso-scale molecular dynamics with more than 10 8 particles is now possible on massively parallel MIMD computers. Typical runs show single particle update-times of 0:15¯s in 2 dimensions (2D) and approximately 1¯s in 3 dimensions (3D) on a 1024 node CM-5 without vector units, corresponding to more than 1.8 GFlops overall performance. We also present a scaling equation which agrees well with actually observed timings. To appear in Parallel Computing (1993) Present address: Department of Mathematics, University of Oregon, Eugene, OR 97403. y To whom correspondence should be addressed. 1 Introduction The molecular dynamics (MD) method [1, 2, 3] has been known for several decades and has been used successfully in atomistic...

A brief general introduction into Molecular Dynamics methods for polymers is given. For the statics and dynamics of an isolated chain, a simple microcanonical algorithm is severely hampered by ergodicity problems due to mode conservation. Coupling the system to a Langevin heat bath solves this problem, but also screens hydrodynamic interactions for a chain in a bath of solvent molecules. Rouse scaling laws should hold whenever long--range interactions and entanglements are not important; this is important for controlling the relevant time scales as well as for checking the correctness of simulation algorithms. As an application, a single chain in a bath of solvent particles is discussed. In this system, the long--range nature of the hydrodynamic interaction induces pronounced finite size effects, which are analyzed using Ewald summation methods. Furthermore, simulations on the dynamics of entangled melts are considered. Starting from the reptation picture, we discuss the difficulties t...

Abstract. Computing (ratios of) normalizing constants of probability models is a fundamental computational problem for many statistical and scientific studies. Monte Carlo simulation is an effective technique, especially with complex and high-dimensional models. This paper aims to bring to the attention of general statistical audiences of some effective methods originating from theoretical physics and at the same time to explore these methods from a more statistical perspective, through establishing theoretical connections and illustrating their uses with statistical problems. We show that the acceptance ratio method and thermodynamic integration are natural generalizations of importance sampling, which is most familiar to statistical audiences. The former generalizes importance sampling through the use of a single “bridge ” density and is thus a case of bridge sampling in the sense of Meng and Wong. Thermodynamic integration, which is also known in the numerical analysis literature as Ogata’s method for high-dimensional integration, corresponds to the use of infinitely many and continuously connected bridges (and thus a “path”). Our path sampling formulation offers more flexibility and thus potential efficiency to thermodynamic integration, and the search of optimal paths turns out to have close connections with the Jeffreys prior density and the Rao and Hellinger distances between two densities. We provide an informative theoretical example as well as two empirical examples (involving 17- to 70-dimensional integrations) to illustrate the potential and implementation of path sampling. We also discuss some open problems.

The phenomenon of heat conduction in a two-dimensional gas of N hard disks is studied in the hydrostatic regime by means of nonequilibrium molecular dynamics (N ranging from 100 to 8000). For systems with N>~I500 the temperature and density profiles observed are in excellent agreement with the continuous theory, but the conductivity k differs from the one derived from Enskog's theory in a systematic way. This difference seems to slowly decrease with increasing density.

Number of figures: 12