Exercício 4

Jacques Wainer

Fazer o exercicio individualmente

Para o dia 3/5 antes da meia noite

Submeter o pdf com a sua solucão via moodle. A solucao nao deve ser apenas um numero mas tambem uma explicacao curta do resultado.

Baseado no Exercício 14.12 do livro texto mas eu modifiquei a parte a) e removi a parte b) da questão original. Eu nao coloquei a parte e) neste exercicio.

A versão em ingles:

Two astronomers in different parts of the world make measurements M1 and M2 of the number of stars N in some small region of the sky, using their telescopes. Normally, there is a small possibility e of error by up to one star in each direction. Each telescope can also (with a much smaller probability f) be badly out of focus (events F1 and F2), in which case the scientist will undercount by three or more stars (or if N is less than 3, fail to detect any stars at all)

  1. Draw the bayesian network that more naturally represents of the preceding information.

  2. Write out a conditional distribution for P(M1|N), for the case where N \in \{1,2,3\} and M1 \in \{0, 1, 2, 3, 4\}. Each entry in the conditional distribution should be expressed as a function of the parameters e and/or f .

  3. Suppose M1 = 1 and M2 = 3. What are the possible numbers of stars if you assume no prior constraint on the values of N ?

Alguns pontos,