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PhD candidate in computer science at Brigham Young University, studying programming languages for probabilistic modeling and inference. Current topics of interest: formal languages, foundations of mathematics, measure-theoretic probability, applied probability, topology, and computation in the limit.

In my spare time, I learn piano arrangements of great music from video games. Current favorite composers: Yasunori Mitsuda (Chrono Trigger, Chrono Cross), and Koji Kondo and his protégés (Legend of Zelda, Super Mario). These guys are terrific.


Sep
24
awarded  Autobiographer
Jul
2
awarded  Curious
Apr
3
awarded  Popular Question
Mar
15
comment Domain of a random variable - sample space or probability space?
The OP is struggling with the fact that the formal definition doesn't seem to impart intrinsic properties to random variables (i.e. a probability distribution), but that philosophically, we regard them has having these intrinsic properties. The best way forward is not to insist that our philosophy is formal truth, but to demonstrate how our philosophy is only an interpretation of the facts.
Mar
15
comment Domain of a random variable - sample space or probability space?
Convergence in distribution is a property that arises from the combined properties of a probability space and random variables, or if you like, the measure-theoretic model. Such properties are not intrinsic to the random variables, which are well-defined, deterministic functions with or without a probability measure defined on their domains.
Mar
15
answered Domain of a random variable - sample space or probability space?
Oct
23
awarded  Commentator
Oct
23
comment Inverses of two argument functions with respect to one argument
Asked at mathoverflow.net (mathoverflow.net/questions/145676/…)
Oct
21
awarded  Yearling
Oct
21
comment Inverses of two argument functions with respect to one argument
Should this get moved to mathoverflow.net?
Oct
21
revised Inverses of two argument functions with respect to one argument
correction
Oct
19
asked Inverses of two argument functions with respect to one argument
Aug
8
accepted Preimages of Jordan-measurable sets
Aug
8
comment Preimages of Jordan-measurable sets
Do you happen to have a reference for the "homeomorphism with Luzin N inverse" property? I might need to investigate this deeply.
Aug
7
asked Preimages of Jordan-measurable sets
Jun
3
asked When does the existence of an iterated limit imply the existence of a double limit?
May
21
awarded  Nice Question
May
9
accepted What's the name of this function property?
May
8
comment What's the name of this function property?
@Asaf: I'm totally down with Mr. Knaster and Mr. Tarski. But I'm after a more constructive fixed point - one that's built "from below" by transfinite recursion instead of "from above" by an intersection. Most of what I find on fixed-point theory uses continuity (supremum/join/union-preserving) to do it, but I don't think I have continuity.
May
8
comment What's the name of this function property?
Thanks for the quick answer! I guess I'm expecting too much of English, because most hits for "increasing" take it to mean what you called "isotone". Also, I've just discovered that what you called "increasing" is also called "extensive," but most hits for "extensive" are talking about extensionality. Geez.