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The conditional probability density function pdf for bivariate responses y ij is expressed as f y ij ai bi 1 Pij 1 rij Pij ST2 y ij bi rij r 1 Pij 1 rij Pijij ST2 y ij bi rij. Thus the joint posterior density of conditional on D can be given by ni n f D p rij ai f y ij bi wij f wij wij 0 rij f ai bi dai dbi h i 1 j 1 where p rij ai 1 Pij 1 rij Pijij. To make notations more compact given a m rij 1 let y ij yij yij T x ij diag xij xij z ij diag z ij z ij a T m T T a T m T bi bi bi...

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1. Researchers and statisticians who are conducting advanced statistical analyses.
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5. Individuals or organizations interested in analyzing complex datasets to derive insights and make informed decisions.
6. Anyone seeking to contribute to the body of knowledge in advanced statistics or enhance their understanding and application of statistical techniques.

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