cognitive psychology. PhD 
Time to live-tweet the probabilistic graphical models course I'm taking. Prepare for a quarter of Hot Takes on how probabilistic programming languages are the future. cc @stephtwang
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... a joint distribution (comma separated), a joint distribution (\cap separated). You can write P(X) to represent the probability distribution over x. You can write P(X = x) to represent the probability of a single thing happening. You can write p(..), P(..), P[..].
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My goal is to learn probability as a tool of thought. What is a general process for destructuring problems with incomplete information into programs/algorithms? I've always felt like these notational mishaps have been an impediment to me learning this process.
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"Ok I don't know this piece of information... so is that an event? Err no a random variable. I know it's a categorical variable, so my prior should be drawn from a categorical distribu... hmm or multinomial... Dirichlet.......?"
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From lecture: converting a Bayes net into a Markov net is called "moralization" because it involved "marrying the parents of a node". Perhaps the most unnecessary use of personal principles in the naming of math that I've ever seen.
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Marginalization is such a powerful concept in probability. In decision-making, I think we humans tend to infer from context a few most likely possibilities for unobserved quantities. Marginalizing, by contrast, is like simultaneously imagining every possible state of the world.
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While classic strategy algorithms like minimax employ similar kinds of search, they make assumptions like "I know how to play the game, and the opponent thinks like me." Marginalization (and expectation) allow inference of optimal strategy just based on previous observations.
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Love it when physicists invent algorithms instead of mathematicians. They give names with wonderful analogies to the real world, like using "temperature" in simulated annealing as a metaphor for concentration of "energy".
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A good reminder that most statistical methods don't just arise out of a vacuum, but rather from people who had really concrete needs (simulating atomic bombs on extremely primitive hardware, etc.). Another data point in the "does important math come from mathematicians" debate!
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Summarized some thoughts from the quarter in "Compiling Knowledge into Probabilities." Why can't we design probabilistic programs the same way we design deterministic ones? http://willcrichton.net/notes/compiling-knowledge-probability/ …
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Thanks again @stephtwang (and other hardworking TAs) for a fun quarter!
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