Populations of models, Experimental Designs and coverage of parameter space by Latin Hypercube and Orthogonal Sampling

TL;DR

This paper investigates the coverage properties of Latin Hypercube and Orthogonal Sampling methods in high-dimensional parameter spaces, proposing a coverage formula and comparing their effectiveness for experimental design.

Contribution

It introduces a conjectured coverage formula for Latin Hypercube sampling in high dimensions and demonstrates Orthogonal Sampling's superior uniformity in coverage.

Findings

Coverage formula for Latin Hypercube sampling is independent of total dimension d.

Orthogonal sampling provides more uniform coverage of subspaces.

The proposed model links Populations of Models with experimental design strategies.

Abstract

In this paper we have used simulations to make a conjecture about the coverage of a $t$ dimensional subspace of a $d$ dimensional parameter space of size $n$ when performing $k$ trials of Latin Hypercube sampling. This takes the form $P(k,n,d,t)=1-e^{-k/n^{t-1}}$. We suggest that this coverage formula is independent of $d$ and this allows us to make connections between building Populations of Models and Experimental Designs. We also show that Orthogonal sampling is superior to Latin Hypercube sampling in terms of allowing a more uniform coverage of the $t$ dimensional subspace at the sub-block size level.