Estimation in the Presence of Hidden Variables

Abstract

Let us consider a statistical model $M= \left\{ p({\varvec{x}}, {\varvec{\xi }}) \right\}$, where vector random variable ${\varvec{x}}$ is divided into two parts ${\varvec{x}}= \left( {\varvec{y}}, {\varvec{h}}\right)$ so that $p({\varvec{x}}, {\varvec{\xi }}) = p ({\varvec{y}}, {\varvec{h}} ; {\varvec{\xi }})$. When ${\varvec{x}}$ is not fully observed but ${\varvec{y}}$ is observed, ${\varvec{h}}$ is called a hidden variable.