Chapter III. The Sampler module

Abstract

This is a description of the Sampler module whose main goal is to produce a design-of-experiments, starting from the description of the model provided by the user, and that would be used to investigate the sensitivity and/or propagate uncertainty for the requested analysis.
The source files are in souRCE.git/meTIER/sampler/souRCE and the corresponding namespace is URANIE::Sampler.

Table of Contents

III.1. Introduction
III.2. The Stochastic methods
III.2.1. Introduction
III.2.2. The main sampler classes
III.2.3. Simple example
III.2.4. TConstrLHS example
III.3. Description of a correlation
III.3.1. Imposing the correlation coefficients
III.3.2. The copula classes
III.4. QMC method
III.5. The random fields
III.6. OAT Design
III.6.1. Introduction
III.6.2. OAT design in Uranie
III.6.3. TOATDesign
III.7. The Vectorial Quantification method

III.1. Introduction

The Sampler module is used to produce design-of-experiments knowing the expected behaviour of the input variables for the problem under consideration. The framework of our approach can be illustrated in the following schematic view:

Figure III.1. Schematic view of the input/output relation through a code

Schematic view of the input/output relation through a code


  • We will denote as the studied computational code which, generally, has two types of inputs:

    • The constant parameters which are gathered in the vector . They represent constants.

    • The uncertain parameters which are gathered in the vector

      It shall be noticed that these parameters are supposed to be uncertain either because of a lack of knowledge on their actual value or because of their intrinsic random nature.

  • The result of the code for a given set of parameters gives the vector which contains all the output variables of the analysis.

Different methods exist to obtain a design-of-experiments from uncertain parameters which can be classified into two categories:

  1. stochastic methods (see Section III.2). These methods consist in using a random number generator to produce new samples. This is also called Monte-Carlo.

  2. deterministic methods (see Section III.4). Two distinct calls with the same parameters will always give the same point in a design-of-experiments. Some of these methods (those discussed below) are sequences which are sometimes called quasi-Monte Carlo (qMC).