# Alexandre Chorin

## Bio

Alexandre Chorin is a UC Berkeley professor of mathematics and a Senior Faculty Scientist in the Mathematics Group. He received his Ph.D. from the Courant Institute of Mathematics at New York University in 1966, becoming an associate professor in 1971 before joining the Berkeley faculty in 1972. He was Head of the LBNL Mathematics Department from 1986-1995. Chorin's awards include the National Academy of Sciences award in applied mathematics and numerical analysis, the Wiener prize of the American Mathematical Society, and the Lagrange prize of the International Council on Applied Mathematics. Chorin is known for his contributions to computational fluid mechanics, turbulence theory, and computational statistics, including the invention of the ubiquitous projection method for modeling incompressible fluids and the random vortex method for computing turbulent flow.

## Journal Articles

### Alexandre J. Chorin, Xuemin Tu, "An iterative implementation of the implicit nonlinear filter", ESAIM: Mathematical Modelling and Numerical Analysis, 2012, 46:535--543,

Implicit sampling is a sampling scheme for particle filters, designed to move particles one-by-one so that they remain in high-probability domains. We present a new derivation of implicit sampling, as well as a new iteration method for solving the resulting algebraic equations.

### Matthias Morzfeld, Xuemin Tu, Ethan Atkins, Alexandre J. Chorin, "A random map implementation of implicit filters", Journal of Computational Physics, 2012, 231:2049--2066, doi: 10.1016/j.jcp.2011.11.022

### M. Morzfeld, A. J. Chorin, "Implicit particle filtering for models with partial noise, and an application to geomagnetic data assimilation", Nonlinear Processes in Geophysics, 2012, 19:365--382, doi: 10.5194/npg-19-365-2012

### Alexandre J. Chorin, Xuemin Tu, "Interpolation and iteration for nonlinear filters", ESAIM: Mathematical Modelling and Numerical Analysis. Submitted, 2010, arXiv:0910,

We present a general form of the iteration and interpolation process used in implicit particle filters. Implicit filters are based on a pseudo-Gaussian representation of posterior densities, and are designed to focus the particle paths so as to reduce the number of particles needed in nonlinear data assimilation. Examples are given.

### Alexandre J. Chorin, Xuemin Tu, Matthias Morzfeld, "Implicit Particle Filters for Data Assimilation", Comm. Appl. Math. Comp. Sc., 2010, 5:221--240,

### Alexandre J. Chorin, Xuemin Tu, "Implicit sampling for particle filters", Proceedings of the National Academy of Sciences, 2009, 106:17249-1725, doi: 10.1073/pnas.0909196106

We present a particle-based nonlinear filtering scheme, related to recent work on chainless Monte Carlo, designed to focus particle paths sharply so that fewer particles are required. The main features of the scheme are a representation of each new probability density function by means of a set of functions of Gaussian variables (a distinct function for each particle and step) and a resampling based on normalization factors and Jacobians. The construction is demonstrated on a standard, ill-conditioned test problem.

## Conference Papers

### J. Bell, A. Chorin, and W. Crutchfield, "Stochastic Optimal Prediction with Application to Averaged Euler Equations", Proc. 7th Nat. Conf. Comput. Fluid Mech., (C.A. Lin, Ed.), pp. 1-13, Pingtung, Taiwan, 2000,

- Download File: bcc001.ps.gz (gz: 79 KB)

## Books

### A. Chorin, O. H. Hald, Stochastic Tools in Mathematics and Science, Surveys and Tutorials in the Applied Mathematical Sciences, (Springer: 2009)

## Book Chapters

### A. J. Chorin, M. Morzfeld, X. Tu, "A survey of implicit particle filters for data assimilation", Statistics for Financial Engineering and Econometrics: State-Space Models and Applications in Economics and Finance, edited by S. Wu, (Springer. In print: 2013)