Joint Impact of Rain and Incidents on Traffic Stream Speeds

Algorithm 1

The EM algorithm.

	Let be parameter estimates after the kth iteration.
	E-step:
	(1) Estimate the posterior probability of the ith observation comes from component j,
(i)
	where is the probability density function of the jth component.
	M-step:
	(2) Find a new parameter that estimates by maximizing the log-likelihood function in equation
(1) is calculated as follows:
(ii)	and
(iii)
	where X is an predictor matrix, Y is the corresponding nx1 response vector, and W is an nxn diagonal matrix. Now, by having along its diagonal:
(iv)
	(3) Alternate repeatedly between the E-step and M-step until the incomplete log-likelihood converges to an arbitrarily small value as follows:
(v)
	where is a small number.