meta user
network profile
| bio | website | |
|---|---|---|
| location | ||
| age | ||
| visits | member for | 1 year, 1 month |
| seen | 2 hours ago | |
| stats | profile views | 280 |
|
2h |
comment |
Find the Cramer-Rao bound for an unbiased estimate of $b^2$ I didn't check the details, but if $g(b) = b^2, g^{\prime} = 2b$. |
|
May 18 |
comment |
Decompose $P$ into the direct sum of irreducible representations. the vector of all 1's is an eigenvalue for all the permutation matrices, which should reduce to a 2-d problem. you probably get $A_{\sigma}$ if the determinant is -1. |
|
May 17 |
comment |
discrete harmonic extension (an exercise of Grimmett's “probability on graphs”) yes, I looked in a graph theory book to see how one produce a flow in the source-trough formulation. They had a longish argument starting from minimizing sum of absolute values rather than squares. A flow has a value of 0 for that, by definition, as it has for this quadratic. Then you move on to minimizing the energy, and it seemed that as long as you know that the class of flow with some prescribed values over which you are minimizing is non-empty, minmizing the energy, which has the 'r' in it, works. |
|
May 16 |
comment |
discrete harmonic extension (an exercise of Grimmett's “probability on graphs”) do you know the energy minimization formulation ? I think the hard part of the question is to show that there are flow with $x_{\nu}$ as stated. There are, with the given condition. One can be produced as the minimizer of $\sum_V (\sum_{w \sim v} i_{vw})^2$. Then a second round of minimizing over the energy of flows satisfying the condition produces the flow you are looking for. |
|
May 15 |
comment |
finding the probability density function of $ dY_t = - Y_t X_t dW_t$ i don't think martingales can have (non-trivial) stationary distributions. If they converge in distribution optional stopping tells you that they want to be constants. There is a square-root model, maybe hanson is the name, where you can find the distribution explicitly |
|
May 15 |
comment |
For which p>0 does $S_t=W_t+t^p$ admit an equivalent martingale measure? o.k. let's put it this way: I think NFLVR is too much and a brutally direct effort to construct the likeihood ratios show they want to be $e^{\int f^{\prime}(t) dW_t - \frac 12 \int (f^{\prime})^2 (t) dt}$. Also, you can rule out small p by law of iterated logarithm |
|
May 14 |
comment |
For which p>0 does $S_t=W_t+t^p$ admit an equivalent martingale measure? cameron-martin deals with $W_t + f(t)$ and their condition is $\int^t_0 | f^{\prime} |^2 < \infty$. |
|
May 14 |
comment |
Gaussian vectors formula i think it's integration by parts. $\mathbb E(\nabla F(X)) = \int \nabla F(x) e^{- \frac 12 x^t\Sigma^{-1}x} dx =\int F(x) -\nabla e^{- \frac 12 x^t\Sigma^{-1}x} dx = \int F(x) \Sigma^{-1}x e^{- \frac 12 x^t\Sigma^{-1}x}$ where I've left out some normalizing constants that don't matter and the last is the chain rule |
|
May 13 |
comment |
Gaussian vectors formula covariance matrix of X, covariance between Y and X ... notations are pretty standard for joint gaussian ... wikipedia article uses $\Sigma_{11}, \Sigma_{12}$ for same |
|
May 13 |
comment |
L1 penalty can serve as a convex surrogate for an L0 penalty. Why? the original insight was not much more than that the $\mathbb L^1$ norm was closer to $\mathbb L^0$ than the tractable $\mathbb L^2$ norm, but now see candes-tao, www-stat.stanford.edu/~candes/papers/OptimalRecovery.pdf |
|
May 13 |
comment |
Gaussian vectors formula use that ( in standard gaussian notation) $Y - \Sigma_{YX} \Sigma_{XX}^{-1} X$ is independent of X and hence $F(X)$ to say $ 0 = \mathbb E((Y - \Sigma_{YX} \Sigma_{XX}^{-1} X) F(X)$ and conclude that $\mathbb E(Y F(X) = \Sigma_{YX} \mathbb E( \Sigma_{XX}^{-1} X) F(X) = \Sigma_{YX} \mathbb E( \nabla F(X)$ |
|
May 10 |
comment |
Minimizing the expectation over a set, wrt to the Gaussian measure Isn't it obvious that a symmetric interval about 0 is the minimizer ? Mabe use the neman-pearson lemma to compare $\phi(x) , \vert x \vert \phi(x)$ (normailzed if necessary . |
|
May 10 |
comment |
A Boundary crossing result for discrete brownian bridge I agree with Tim. The error term should be an excess over the boundary term and of order $\frac 1 {\sqrt{n}}$. I think problem must be susceptible to martingale methods as in Siegmund, Sequential Analysis, chapt 3. Siegmund & Yuh may have random walk case in some detail |
|
May 7 |
comment |
Analytic proof that $\log{\Phi(x)}$ is concave? I don't agree that it is easy, except for $x > 0$, and the inequality you need is for $x > 0 , 1 - \Phi(x) < \frac {\phi(x)} x$, which follows from $1 - \Phi(x) = \int_x^{\infty} \phi(y) dy < \int_x^{\infty} \frac yx \phi(y) dy$ |
|
May 6 |
comment |
Product of predictable process and a characteristic function is integrable Isn't $\int \theta_u 1_A dS_u = 1_A \int \theta_u dS_u $ ? So inequality only depends on $a > 0$ ? |
|
May 5 |
comment |
Submartingale bounds no, consider $Z_1, Z_1 + Z_2$ where they are independent mean zero and Z_2 is wildly asymmetric. You can make that prob as close to 0 or 1 as you like |
|
May 5 |
comment |
Posterior density and posterior moments I think your range of integration in last integral should be $\int_{-\infty}^{\infty}$, just on grounds that log($\theta$) is normal, and if that's true, yo can do the integral. |
|
May 2 |
comment |
Monotone increasing sequence of random variable that converge in probability implies convergence almost surely try truncating, as truncated r.v.s converge in prob. and pt-wise. |
|
May 2 |
comment |
Simple symmetric random walk - is my assumption correct? do you mean that $\vee$ to be a $\wedge$ ? |
|
Apr 29 |
comment |
Generalized Likelihood Ratio Test and Hypothesis Testing what part are you having trouble with, the form of the test or the significance level calculation ? |
