Nonparametric probability density estimation

Problem statement: Identify underlying probability density function for random variable such that for

We make no prior assumptions on the form of .

Useful links

• Introductory chapter from Density Estimation for Statistics and Data Analysis - B.W. Silverman

• 1991 Review article, J. Am. Statistical Association 86(413):205-224, A.J. Izenman, Recent Developments in Nonparametric Density Estimation

Background on optimal transport

Links to papers by Brenier, Evans on optimal transport:

• Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq Equations

• Topics on Hydrodynamics and volume preserving maps

• Extended Monge-Kantorovich theory

• Partial Differential Equations and Monge–Kantorovich Mass Transfer

Optimal transport kernel images

OptTanNov06.pdf test1.m

Data sets

A collection of some data sets on which to test p.d.f. estimation algorithms.

Slepyan breaking string model

• Fortran 90 MPI-parallelized code: string.f90 , initial data: string.dat