evidence given x2 so if you multiply all three of these together we get exactly this quantity over here which is to join between x2 and all the evidences and so he think to observe here is that evidence that comes from the past is just a standard forward filter being run that's shown over here Adams coming from the future is some kind of backwards filter running that does these updates here that work from the back of the chain back to x2 and give you a condition of all future evidence given x2 and of course you need the evidence