bayes_corona.md

There is a new test for corona antibodies. The manufacturer of the test claims the following features of the test.

Sensitivity of the test is 93 %, which means in 93% of the cases where an infected person receives a postitive result from the test, the person is actually infected (true positives) and in 7% of the cases, the test provides false negatives. An infected person recieves a negative result from the test:

Specifity of the test is 90 %, which means in 90 % of the cases where a non-infected person receives a negative result form the test, the person is actually not infected (true ngatives) and in 10 % of the cases, the test provides false positives. A non-infected person receives a postive result from the test but is actually not infected.

Virologists estimate that during the pandemic 1 % of the population is infected.

Questions:

1. What is the propability of having corona antibodies when a person recieves a postive test result from the test ?
2. What is the propability of not having corona antibodies when a person recieves a negative test result from the test ?

Bruger man Bayes:

1 ) Sandsynligheden for at have sygdommen, ved en positiv test med 1% general population infected
P( Sygdom | positiv test) =
= 0.085

Sygdommen / Anti bodies, whatever

Omvendt er P(ingen sygdom | negativ test) (Sandsynligheden for ikke at have sygdommen hvis testen er negative)
= 0.9992149 ...

1. Som en tabel. Baseret på 10000 personer :

	1% har det	Positiv test	Negativ test
Har antistoffer	100	93	7
Har ikke antistoffer	9900	990	8910
Ialt	10000	1083	8917

93/1083=0.085