Bayes Classifiers
		Maximum Likelihood						K=	1	Laplacian Smoothing
	word class	count|S	count|~S	P(w|S)	P(w|~S)			word class	count|S	count|~S	P(w|S)	P(w|~S)
totals:	12	9	15	words:	24		totals:	12	21	27	words:	48
data:							data:
	offer	1	0	0.111111	0			offer	2	1	0.095238	0.037037
	is	1	1	0.111111	0.066667			is	2	2	0.095238	0.074074
	secret	3	1	0.333333	0.066667			secret	4	2	0.190476	0.074074
	click	1	0	0.111111	0			click	2	1	0.095238	0.037037
	sports	1	5	0.111111	0.333333			sports	2	6	0.095238	0.222222
	link	2	0	0.222222	0			link	3	1	0.142857	0.037037
	play	0	2	0	0.133333			play	1	3	0.047619	0.111111
	today	0	2	0	0.133333			today	1	3	0.047619	0.111111
	went	0	1	0	0.066667			went	1	2	0.047619	0.074074
	event	0	1	0	0.066667			event	1	2	0.047619	0.074074
	costs	0	1	0	0.066667			costs	1	2	0.047619	0.074074
	money	0	1	0	0.066667			money	1	2	0.047619	0.074074
	messages:	3	5	total M:	8			messages:	4	6	total M:	10
	for some reason he uses the			P(S) =	P(~S) =						P(S) =	P(~S) =
	message rather than word ratio!!?			0.375	0.625						0.4	0.6
Message:	"secret","is","secret"							"today","is","secret"
bayes:	P(S | "secret","is","secret") =							P(S | "today","is","secret") =
	P("secret","is","secret" | S)  * P(S) / P("secret","is","secret")							P("today","is","secret" | S)  * P(S) / P("today","is","secret")
P(M | S):	P("secret","is","secret" | S) = P(s|S)*P(i|S)*P(s|S) * P(S) =							P("today","is","secret" | S) = P(t|S)*P(i|S)*P(s|S) * P(S) =
	0.0046296							0.0003455
P(M | ~S):	P("secret","is","secret" | ~S) = P(s|~S)*P(i|~S)*P(s|~S) * P(~S) =							P("today","is","secret" | ~S) = P(t|~S)*P(i|~S)*P(s|~S) * P(~S) =
	0.0001852							0.0003658
totalP(M):	P(M | S)  + P(M | ~S) =							P(M | S)  + P(M | ~S) =
	0.0048148							0.0007113
P(S | M):	P(S | "secret","is","secret") =							P(S | "today","is","secret") =
	0.9615385							0.4857571