Consider the probability problem below:
A test for a rare form of skin cancer shows a positive result in 90% of patients with the disease, and produces a false positive in only 7% percent of individuals who do not have that disorder. If one tenth of 1% of individuals actually have the disease, what is the probability that an individual who shows a positive result actually has skin cancer?
Show the correct Bayesian formula for calculating the answer to this problem and show the answer that would be computed using this formula.
Consider how the posterior probability of a positive result could be computed using a neuron-like processing unit that computes its net input by adding together a bias term plus another term consisting of the product of a connection weight times the input from another unit whose activation is 1 if the test is positive, then passes this net input through the logistic function. State what the bias term and connection weight value correspond to in Bayesian terms, show their numerical values and the resulting value of the net input, and then show the numeric values of the numerator and denominator of the logistic function. The ratio of these values should equal the value you first obtained.
experiment to some aspect of the Bayesian calculation. (200 words)