Consider the following partially observed 2 by 2 contingency table:
|
| \(Y=0\) |
| \(Y=1\) |
| |
--------- |
--------- |
--------- |
--------- |
\(X=0\) |
| \(Y_0\) |
| |
| \(r_0\) |
--------- |
--------- |
--------- |
--------- |
\(X=1\) |
| \(Y_1\) |
| |
| \(r_1\) |
--------- |
--------- |
--------- |
--------- |
where \(r_0\), \(r_1\), \(c_0\), \(c_1\), and \(N\) are
non-negative integers that are observed. The interior cell entries
are not observed. It is assumed that \(Y_0|r_0 \sim
\mathcal{B}inomial(r_0, p_0)\) and \(Y_1|r_1 \sim
\mathcal{B}inomial(r_1, p_1)\).
This function plots the bounds on the maximum likelihood estimatess for (p0,
p1).