6
votes
4answers
432 views

Laplace transform on the cone of positive-definite matrices

The title says most. Let $P_p$ be the cone of positive-definite $p \times p$ matrices. One can define the Laplace transform of (the distribution of) a random matrix with values in $P_p$ by (for ...
1
vote
2answers
1k views

Inversion of Moment-generating functions (aka Laplace transform of prob dist)

I want to embark on a project about inverting a Moment-generating function of a probabilitiy distribution. That is given by \begin{equation} M_X(t) = \text{E} \exp(tX) \end{equation} Since I have ...
0
votes
1answer
126 views

How are epidemic models simulated in case of mobility?

I am not a mathematician but out of curiosity I am trying to implement the SIS epidemic model when the nodes have mobility to understand how it will change the results. I understand how to perform ...
0
votes
1answer
9k views

Difference between Principal Component Analysis(PCA) and Singular Value Decomposition(SVD)?

I am confused between PCA and SVD. The wikipedia page for PCA has this line. "PCA can be done by eigenvalue decomposition of a data covariance matrix or singular value decomposition of a data matrix, ...
7
votes
4answers
1k views

Estimating the probability that one Poisson RV is larger than another

Let $X$ and $Y$ be Poisson random variables with means $\lambda$ and $1$, respectively. The difference of $X$ and $Y$ is a Skellam random variable, with probability density function $$\mathbb P(X - Y ...
1
vote
1answer
327 views

Statistical inequality

Let $X$ be a finite discrete variable and $X\ge0$. Is it true that $$16\operatorname{Var}(X) \le \left[8{\mathbb E}(X) + \operatorname{Range}(X)\right]\operatorname{Range}(X)$$ where ...
17
votes
1answer
1k views

Intuitive Proof of Cramer's Decomposition Theorem

Cramer's decomposition theorem states that if $X$ and $Y$ are independent real random variables and $X+Y$ has normal distribution, then both $X$ and $Y$ are normally distributed. I've seen a few ...
2
votes
7answers
596 views

Splines, harmonic analysis, singular integrals.

Apologies if my question is poorly phrased. I'm a computer scientist trying to teach myself about generalized functions. (Simple explanations are preferred. -- Thanks.) One of the references I'm ...
2
votes
5answers
588 views

Statistical Data Analysis

For personal research, I'm doing some analysis on collected data and trying to develop relationships between two variables where the data is collected through a data logger. I'm hypothesising that a ...
1
vote
2answers
1k views

Multiple outliers for two variable linear regression

Problem Visually, the "extreme" outliers in the following graph are somewhat obvious: http://i.imgur.com/tiSbS.png Question Given: T - Set of all temperatures Y - Set of all years ΣT - Sum of ...
8
votes
4answers
702 views

What m minimizes E(|m-X|^3) for a random variable X?

Let X be a random variable. Then E(|m-X|^1) is minimized when (as a function of m) when m is the median of X, and E(|m-X|^2) is minimized when m is the mean of x. A couple weeks ago in a technical ...