pretty often a naive compute limited estimate of P(G & E) will be zero with high probability unless you importance sample using T
I’m having troubles parsing what you said here.
The classic case is trying to work out the probability that a photon will hit a speck of dust in a raytraced scene, where introducing the theodicy that a photon will zing straight from the lightbulb filament to your speck produces the correct probability through an expression just like P(G&E) = P(G&E|T)P(T) + P(G&E| ¬T)P(¬T)
Of course it produces the correct probability. Why would anything I said imply that it doesn’t? I’m explicitly appealing to Law of Total Probability, after all.
I’m really interested in figuring out your objections to the post, but for now they seem quite incoherent to me. As if some words were wrongly changed by autocomplete, and, in case with this reply, as if your message was sent before you finished writing it.
Could you try once again and present me a simple and and explicit real world example where my math fails, writing your post not from a phone?
I’m having troubles parsing what you said here.
Of course it produces the correct probability. Why would anything I said imply that it doesn’t? I’m explicitly appealing to Law of Total Probability, after all.
actually, on further thought, it’s worse than that . consider the caustic.
I’m really interested in figuring out your objections to the post, but for now they seem quite incoherent to me. As if some words were wrongly changed by autocomplete, and, in case with this reply, as if your message was sent before you finished writing it.
Could you try once again and present me a simple and and explicit real world example where my math fails, writing your post not from a phone?