No. 12 (00081)

Family name : Tkachov
Given name : Fyodor
Affiliation : Institute for Nuclear Research of RAS
Abbreviation : INR RAS
E-mail address : ftkachov@ms2.inr.ac.ru
Title : POUZYRY: a new class of algorithms for modelling a function from
        a random sample
Authors : F.V.Tkachov
Abstract : 
Reexamined are mathematical foundations of the fundamental problem of
modelling a function from a random sample, which has two important
applications: multi-dimensional adaptive MC integration and construction
of quasi-optimal observables (hep-ph/0001019) for data analysis.
The concept of week convergence, although largely ignored beyond
abstract mathematics, is central for a systematic exploration of
algorithmic solutions for the problem, and is the basis of POUZYRY, a
novel class of algorithms which has a considerable flexibility of
implementation including: iterative schemes; applicability to
non-positive functions; a relatively small number of random points
required; a weak sensitivity to the dimensionality of the function's
domain of definition; insensitivity to the choice of coordinate axes.
POUZYRY is ideologically related to, and borrows some algorithmic
solutions (without which it would be prohibitively slow) from, the
Optimal Jet Finder (hep-ph/0301185), which also exploits the concept of
weak convergence; this relation explains why POUZYRY can locate peaks of
a distribution with a relative ease.
A simple exploratory implementation of POUZYRY written in
Oberon/Component Pascal is compared with VEGAS on some simple tests.