Monte Carlo phase space integration for initial state radiation

Monte-Carlo and Quasi-Monte-Carlo Methods for Numerical Integration

We consider the problem of numerical integration in dimension s, with eventually large s; the usual rules need a very huge number of nodes with increasing dimension to obtain some accuracy, say an error bound less than 10−2; this phenomenon is called ”the curse of dimensionality”; to overcome it, two kind of methods have been developped: the so-called Monte-Carlo and Quasi-Monte-Carlo methods. ...

Improved Monte Carlo Methods for State-Space Models

The recent availability of low cost powerful computational resources has led to the development of a plethora of Monte Carlo based inference mechanisms for use in complex statistical problems, many of which involve temporally evolving systems. Sequential Monte Carlo (SMC), which is based around Sequential Importance Sampling and Resampling, is a class of Monte Carlo algorithm that can be applie...

On Extended State-Space Constructions for Monte Carlo Methods

Numerical Integration and Monte Carlo Integration

Here we will begin by deriving the basic trapezoidal and Simpson’s integration formulas for functions that can be evaluated at all points in the integration range, i.e, there are no singularities in this range. We will also show how the remaining discretization errors present in these low-order formulas can be systematically extrapolated away to arbitrarily high order; a method known as Romberg...

Exponential Integration for Hamiltonian Monte Carlo

We investigate numerical integration of ordinary differential equations (ODEs) for Hamiltonian Monte Carlo (HMC). High-quality integration is crucial for designing efficient and effective proposals for HMC. While the standard method is leapfrog (Störmer-Verlet) integration, we propose the use of an exponential integrator, which is robust to stiff ODEs with highly-oscillatory components. This os...