Maximum Likelihood Estimation illustrated with an example

Predicting the risk of Zika Virus infection

Here the concept of MLE explained in the blog on June 6 is explained with an example. Denoting by P the proportion  of babies infected by the Zika virus,  among the population of Zika virus infected pregnant mothers in an  area like say Brazil, this P is a population parameter. P is unknown, but we want to know its true value. But it is impossible to know the entire population and the population parameter due to time and monitory constraints. 10 samples of size 50 each are selected for the estimation of P. That is 10 samples of 50 Zika infected pregnant women are selected. So, n = 50 and m = 10. We are interested in finding the number of babies infected with zika virus among 50 zika infected pregnant women selected in 10 batches. So Xi is the random variable denoting number of zika infected babies in a sample of size 50. So, Xi = 0, 1, 2, ....50. So the MLE is the number of zika infected pregnant women bearing zika infected babies divided by 500. This gives the fraction of zika infected pregnant women bearing zika infected babies among 500 zika infected pregnant women and this is the MLE of P.