\begin{frame}{Estimativa do limite inferior -- procedimento}%{n_g independent samples, each one of size n} \begin{columns} \column[T]{.65\textwidth} \begin{tikzpicture} \draw(0,3) -- (2,3); \draw(2,3) -- (3.5,5.5); \draw(2,3) -- (3.5,4.5); \draw(2,3) -- (3.5,0.5); \only<1->{ \draw(3.5,0) rectangle +(0.5,6) +(0.3,6.5) node {\textcolor{black}{1}} +(0.3,5.5) node {\textcolor{black}{$\xi^1$}} +(0.3,4.5) node {\textcolor{black}{$\xi^2$}} +(0.3,0.5) node {\textcolor{black}{$\xi^n$}} +(0.3,-.3) node {\textcolor{black}{$\widehat{\vartheta}_{n,1}$}}; } \only<2->{ \draw(4.6,0) rectangle +(0.5,6) +(0.3,6.5) node {\textcolor{green}{2}} +(0.3,5.5) node {\textcolor{green}{$\xi^1$}} +(0.3,4.5) node {\textcolor{green}{$\xi^2$}} +(0.3,0.5) node {\textcolor{green}{$\xi^n$}} +(0.3,-.3) node {\textcolor{green}{$\widehat{\vartheta}_{n,2}$}}; } \only<3->{ %\draw(5.5,0) rectangle +(0.5,6) %+(0.3,6.5) node {\textcolor{red}{3}} %+(0.3,5.5) node {\textcolor{red}{$\xi^1$}} %+(0.3,4.5) node {\textcolor{red}{$\xi^2$}} %+(0.3,0.5) node {\textcolor{red}{$\xi^n$}} %+(0.3,-.3) node {\textcolor{red}{$\widehat{\vartheta}_{n,3}$}}; \pause \draw(6.5,0) rectangle +(0.5,6) +(0.3,6.5) node {\textcolor{blue}{$n_g$}} +(0.3,5.5) node {\textcolor{blue}{$\xi^1$}} +(0.3,4.5) node {\textcolor{blue}{$\xi^2$}} +(0.3,0.5) node {\textcolor{blue}{$\xi^n$}} +(0.3,-.3) node {\textcolor{blue}{$\widehat{\vartheta}_{n,n_g}$}};} \end{tikzpicture} \column[T]{.45\textwidth}%\pause \only<4->{ \centering {Problema discretizado} \begin{align*} \widehat{\vartheta}_{n,j} = & \min_{x} \left\{ c^\top x + \widehat{Q}_{n,j}(x) \right\} \\ & \text{s. a} \quad Ax = b \\ & x \geq 0 \end{align*} \begin{itemize} \item[] Obs.: \[ \mathbb{E}[\widehat{\vartheta}_{n,j}] \leq \vartheta^* \] \end{itemize} } \end{columns} \end{frame}