Bayes and maximum likelihood

Three small functions that turn this unit's formulas into code.

• posterior(prior, sensitivity, fpr): the probability of having the condition given a positive test. prior is the prevalence, sensitivity is $P(+\mid \text{sick})$, fpr is $P(+\mid \text{healthy})$.
• gaussian_mle(x): return (mu, sigma), the maximum likelihood estimates for a 1-D array of samples. MLE divides by $n$.
• bernoulli_nll(p, flips): the negative log-likelihood of an array of 0/1 flips under probability p of a 1. Use np.log.