Thread: Bayesian Statistics - Posterior Assessments

Hi all, wordy tough question that i dont have a clue how to do!

Experience with the electric sewing machines used in a dress factory has shown that
the only source of malfunctioning are a faulty tension spring and a needle misalign-
ment, and that simultaneous faults in these two sources never occur. Experience
has shown that malfunctions are caused by a faulty tension spring about seventy
per cent of the time. Unfortunately there appears to be no completely reliable
guide to correct diagnosis, but it is known that three types of malfunctioning –
missing stitches only, breaking thread only, missing stitches and breaking thread –
occur with probabilities 0.5, 0.1, 0.4 when the fault is in the tension spring, and
with probabilities 0.2, 0.4, 0.4 when there is a needle misalignment.

(i) Construct rules for differential diagnosis on the basis of the posterior assess-
ments for each type of malfunctioning displayed.
(ii) What proportion of malfunctioning sewing machine will be wrongly diagnosed
by your set of rules?

Originally Posted by sirellwood

Hi all, wordy tough question that i dont have a clue how to do!

Experience with the electric sewing machines used in a dress factory has shown that
the only source of malfunctioning are a faulty tension spring and a needle misalign-
ment, and that simultaneous faults in these two sources never occur. Experience
has shown that malfunctions are caused by a faulty tension spring about seventy
per cent of the time. Unfortunately there appears to be no completely reliable
guide to correct diagnosis, but it is known that three types of malfunctioning –
missing stitches only, breaking thread only, missing stitches and breaking thread –
occur with probabilities 0.5, 0.1, 0.4 when the fault is in the tension spring, and
with probabilities 0.2, 0.4, 0.4 when there is a needle misalignment.

(i) Construct rules for differential diagnosis on the basis of the posterior assess-
ments for each type of malfunctioning displayed.
(ii) What proportion of malfunctioning sewing machine will be wrongly diagnosed
by your set of rules?

The first thing you have to do is compile a table of the posterior probability of a tension fault (T) and a needle fault (N) given malfunction type: missing stitches (s), breaking thread (t), both (b).

CB