1
vote
2answers
68 views
Incremental entropy computation
After a quick internet search I found no method for incremental entropy computation.
Question 1
Let $\{x_i\}_{i=1}^n$ and $\{x_i\}_{i=1+n}^{n+m}$ be two samples and let $S_i^j:= …
0
votes
0answers
54 views
random walks with small increments and time intervals [closed]
Imagine you have $\$50$ and every $2$ minutes you either gain or lose $33$ cents. How would you model the evolution of the hypothetical bankroll for the next hour?
My approach bas …
0
votes
3answers
212 views
Random infinite sequence : Can machines generate truly random sequences. [closed]
Test : "A True Random Sequence Source and a computer producing a certain sequence of numbers are kept in separate rooms and judges try to tell them apart by conducting a serie …
0
votes
0answers
14 views
Marginalizing multivariate normal over defined interval
Hello everyone,
I am trying to obtain an analytic expression for the following Gaussian integral
$$\frac{1}{\sqrt{(2 \pi)^n |\Sigma|}} \int \kern-0.2em \cdots \kern-0.2em \int d\ …
0
votes
1answer
48 views
Sampling a hemisphere using an arbitary distribtuion
I am writing a ray tracer and I wish to fire rays from a point p into a hemisphere above that point according to some distribution.
1) I have derived a method to uniformly sample …
0
votes
0answers
23 views
Testing to see if a time series has reached a constant value
I have a noisy time series, (representing the measured mass of antibody bound to a chip covered in antigen). The values of the series seems to settle at a specific value (presumabl …
-1
votes
0answers
51 views
expectation of inner product of two normalized vectors
Hi all,
Say we have $\tilde{\bf{h}}$=$\bf{h}$+$\bf{e}$ where $\bf{h}$ is a given complex vector and $\tilde{\bf{h}}$ is the estimate.
$\bf{e}$ is the error vector where each ent …
7
votes
0answers
125 views
Testing contrasts in statistics: Is this provably a hard problem, or not?
Scheffé's method for identifying statistically significant contrasts is widely known. A contrast among the means $\mu_i$, $i=1,\ldots,r$ of $r$ populations is a linear combination …
0
votes
0answers
30 views
Chi-square approximations for censored data
If you are working with censored data (that is, you only know a lower bound for the value of some observations), can you still use the Chi-square approximation for the statistic $D …
1
vote
1answer
43 views
How to simulate random paths of a non-homogeneous continuous-time Markov process with discrete state space for a given infinitesimal generator matrix?
Let $X=(X_{t},t \in T)$ be a non-homogeneous, continuous time Markov process with a finite state space S={1,...,K}.
Let $\alpha_{i,j}(t)$ be the hazard rates of some $\varGamma$- …
0
votes
0answers
17 views
Statistics applied in A/B Testing and calculating ideal test duration for statistical significance
I'm trying to get my head around the maths used here:
http://visualwebsiteoptimizer.com/ab-split-test-duration/
Can someone point me in the right direction in terms of what algor …
0
votes
0answers
65 views
Orthogonal transformation on random matrices
Let $A$ and $B$ be two random matrices such that $A = U^T B V$. Here $U$ and $V$ are deterministic and orthogonal matrices. The random matrices $A$ and $B$ have the same distributi …
1
vote
2answers
200 views
A machine learning application question
I am familiar with basic probabilities, random processes but not so much of machine learning methods. This is the problem I am trying to solve.
I want to predict the nature of use …
0
votes
1answer
79 views
What is the Bahadur-Anderson Algorithm?
What is the Bahadur-Anderson Algorithm, and which book could one read to learn it?
2
votes
0answers
29 views
Importance sampling of finite path of stochastic difference equation
Before passing to question, let me briefly recap what's importance sampling of random variables is about. Suppose $\xi$ is a real-valued random variable with density $f$, and let $ …

