Sequential Designs

Abstract

We recall our objective. The Fisher information matrix about θ arising from a single observation made at the value u of the vector of control variables is J(u,θ); that from n independent observations at u₍₁₎,…,u_(n) respectively is $L\left( {{{\mathbf{u}}_n},\theta } \right) = \sum\nolimits_{i = 1}^n {J\left( {{u_{\left( i \right)}},\theta } \right)}$,where u _n =(u₍₁₎,…,u_(n)). We wish to choose u _n to maximize a real-valued function $\phi \left\{ {L\left( {{{\mathbf{u}}_n},\theta } \right)} \right\}$ for the true parameter θ. The maximizing u _n usually depends on θ and since we do not know its true value we cannot achieve this objective in practice.