Neil G
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 Apr15 awarded Notable Question Dec8 awarded Caucus Dec7 awarded Nice Question Oct31 comment Computing Gradient and Hessian of a vector function @SeeBees: Take a look at Pearlmutter and Schraudolph's work on the R technique that approximates exactly that in linear time. Oct16 awarded Civic Duty Oct16 asked Does the diagonal of a gradient exist? Oct2 revised Finding $E(X \mid X > Y )$ when $X, Y \sim N(0,1)$ added 7 characters in body Oct2 revised Reordering matrix multiplication around diag operator added 72 characters in body Oct2 revised Reordering matrix multiplication around diag operator added 472 characters in body Oct2 answered Finding $E(X \mid X > Y )$ when $X, Y \sim N(0,1)$ Oct2 revised Reordering matrix multiplication around diag operator deleted 18 characters in body Oct2 asked Reordering matrix multiplication around diag operator Sep3 comment Intuitive explanation of a definition of the Fisher information Is there a derivative missing in your definition of the score? Aug30 revised Determinant of Fisher information added 16 characters in body Aug30 revised Determinant of Fisher information added 16 characters in body Aug30 answered Determinant of Fisher information Jul2 awarded Curious Apr10 comment Beta function derivation @EricAuld: Bayes rule is much easier to think about without the denominator, which is just a constant given your observations. So: $P(q\mid a) \propto P(a\mid q) P(q)$. (These terms are called posterior, likelihood, and prior respectively.) Then, you can fill it in: $\int_0^x f(q \mid a) dq \propto \int_0^x f(q)f(a \mid q)dq \implies f(q \mid a) \propto f(q)f(a \mid q)$. And, the likelihood $f(a \mid q)$ is just $q$ for heads and $1-q$ for tails. Feel free to ask a question on stats.stackexchange. There are a lot of very helpful people there. Apr9 comment Beta function derivation @EricAuld: Suppose I give you a coin whose bias $p$ you don't know. You flip the coin $n$ times and get heads $a$ times. Then the likelihood induced on $p$ is a Beta distribution. You can work out the Beta distribution up to normalization by writing out the product of the Bernoulli mass function $p^x(1-p)^{1-x}$ for each realization $x_i \in \{0,1\}$ (where $\sum_i x_i = a$ and $\sum_i 1-x_i = n-a$). Apr2 awarded Tumbleweed