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615
bio website suitdummy.blogspot.com
location Cambridge, MA
age
visits member for 2 years, 4 months
seen Jul 8 at 19:04

I once launched swi-prolog and asked it a question:

ely:~/home$ prolog
Welcome to SWI-Prolog (Multi-threaded, 64 bits, Version 5.10.1)
Copyright (c) 1990-2010 University of Amsterdam, VU Amsterdam
SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
and you are welcome to redistribute it under certain conditions.
Please visit http://www.swi-prolog.org for details.

For help, use ?- help(Topic). or ?- apropos(Word).

?- love(math) is unrequited.
true.

Mar
18
revised What is the expected number of dice one needs to roll to get any monotonically increasing series of 1 to 6?
edited body
Mar
18
comment What is the expected number of dice one needs to roll to get any monotonically increasing series of 1 to 6?
I wanted the top row and the first column to give headers about what is in those rows/columns. It makes it easier to interpret than just putting a matrix.
Mar
18
comment What is the expected number of dice one needs to roll to get any monotonically increasing series of 1 to 6?
Any help getting mathjax to understand tabulars? It's not math mode, so how do I signal non-math TeX?
Mar
18
answered What is the expected number of dice one needs to roll to get any monotonically increasing series of 1 to 6?
Mar
18
comment Conditional independence
Ok, but I'm heading to bed for tonight. I'll pick it up tomorrow.
Mar
18
comment Conditional independence
Ah, yes, you're right. I was mis-reading it.. but it just results in a typo. Where I had written $1/2$ before, it should be $P(D_{j})/2$ because the LTP means the terms add up to $P(D_{j})$, not to 1 as I mistakenly claimed. But I think this still could be fruitful in terms of yielding a system of equations in the $D_{j}$, then applying the given conditions as constraints.
Mar
18
revised In search of memorable example of “(Pearson-)uncorrelated $\not\Rightarrow$ independent”
added 990 characters in body
Mar
18
comment Conditional independence
Because the whole sample space $\Omega_{i} = H_{i}\cup\bar{H_{i}}$ by definition in that case, and because $H_{i}$ is disjoint from its negation... again, unless you're using 'negation' in some non-obvious way, in which case my interpretation is off.
Mar
18
answered In search of memorable example of “(Pearson-)uncorrelated $\not\Rightarrow$ independent”
Mar
18
comment Conditional independence
If I am understanding the notation (which maybe I am not), then $\bar{H_{i}}$ is the negation of $H_{i}$, basically like the complement if you want to think of $H_{i}$ as a set/event. Then the law of total probability gives my statement. That may not be what the symbol $\bar{H_{i}}$ is actually meant for though... Does it explain that in any more detail?
Mar
18
awarded  Commentator
Mar
18
comment Conditional independence
If I am understanding the notation correctly, then in order for those fractions to be unity, we must have $P(D_{j}|H_{i}) = P(D_{j}|\bar{H_{i}}) = 1/2$, because $P(D_{j}|H_{i}) + P(D_{j}|\bar{H_{i}}) = 1$. So given that it's this specific, I'm guessing you can derive a system of equations for determining the different probabilities by assuming each fraction equals some value $f_{ij}$, possibly not unity. Then that system probably will only have non-trivial solutions under the stated result. At least, this is the line of thinking I'd look down first.
Mar
17
comment Computing the derivative of a quadratic form and matrix chain rule
If it makes you feel better, most of the work I do is Bayesian computational statistics, so.. functional analysis and Markov chain sampling theory. But I have to pay the bills too... :)
Mar
17
comment Computing the derivative of a quadratic form and matrix chain rule
Yes, I am also working with wage data to predict yogurt brand purchase decisions based on wage data. The wage data comes from a well-known paper, Abowd and Card (1989) "On the Covariance Structure of Earnings and Hours Changes," Econometrica, 57 (2), 441-445. This GMM part is about estimating a parameter for an autoregressive model on the earnings.
Mar
17
awarded  Student
Mar
17
asked Computing the derivative of a quadratic form and matrix chain rule
Mar
17
awarded  Critic
Mar
16
comment Solving SDE's on subsets of $R^n$.
I think Theorem 1.18 on pages 12-15 specifically addresses the uniqueness issues in depth.
Mar
15
comment Recurrence relations on a continuous domain
It's not clear what you mean. Are you talking about difference equations, and their well-understood analog with differential equations? I mean, for that you can Google 'recurrence relation' and most sources will point you towards the mathematical theory. I would say that generating functions definitely apply to this field of study.
Mar
15
comment Convergence of $\int\int_{|x|\geq 1,|y|\geq 1} \frac{1}{|x|^\alpha+ |y|^\beta} \;dx\;dy$
This seems like a homework question; I vaguely remember it from Folland's book (or at least the class I took that used Folland's book). If it is homework, add the homework tag so we don't give away answers.