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How do I determine how likely some data was drawn from a distribution?

In general there're many ways to achieve your request in statistics such as goodness-of-fit chi-squared test, likelihood function as mentioned in another answer, KL-Divergence, etc. And perhaps in ...
cinch's user avatar
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How do I determine how likely some data was drawn from a distribution?

Yes, it exists, and it's called the likelihood function (but if you want to actually calculate that "scalar", you better use the log likelihood)
Alberto's user avatar
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Trying to understand some derivation in the paper: Deep Unsupervised Learning using Nonequilibrium Thermodynamics

Question 1 is indeed correct. From there, the integral for $\int dx^{(t)} q(x^{(t)}|x^{(t-1)})$ is also correct. The problem is that this expression does not appear in your intended integral. In $$\...
ThunderSmotch's user avatar

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