All Questions
Tagged with pr.probability st.statistics
1,134 questions
2
votes
1
answer
178
views
Maximal inequality over two indices
In Freedman's series of 3 books on Markov processes, I find that I keep on running into terms like:
P[$\max_{0 \leq s \leq 1, s \leq t \leq rs}$ | B(t) - B(s) | > $\epsilon$]
in the background of ...
6
votes
2
answers
545
views
Extension of copulas
Let $(X,Y)$ be a random vector. Suppose that the marginal distribution functions of $X$ and $Y$ are known (say $F_1$ and $F_2$). Then the joint law of $(X,Y)$ is given by the following formula:
$$F_{...
- 931
3
votes
3
answers
2k
views
Recovering joint distribution from marginals
Suppose we have a Markov Random Field P(X1,...,Xn) on graph G. Suppose we know P(Xi,Xj) for every edge (i,j). Can we recover P(X1,...,Xn)?
If G is a tree, then there's a formula for joint (product of ...
- 233
0
votes
2
answers
595
views
univariate prior corresponding to weighted sum of L1 and L2 penalties?
Is there a univariate probability distribution $p_{\lambda,\alpha}(\beta)$ over the reals, parameterized by $\lambda > 0$ and $1 >= \alpha >= 0$, such that $p_{\lambda,\alpha} \propto \exp(-\...
CommunityBot
- 1
4
votes
3
answers
286
views
Medium-Sized Calculations and Organization
This is not a math question as much as a process question. For the first time in my (very short) career, I find myself doing one of those messy calculations, where each 'line' of the calculation can ...
- 146
4
votes
2
answers
258
views
near independence of markov chain observations at high lags
I have to simulate independent draws from a very complicated distribution. They only feasible way appears to be using MCMC. I was considering running thousands of chains in parallel, but that would ...
- 36
2
votes
2
answers
521
views
A variant of the hypergeometric distribution - in the literature?
I have been working on a problem in combinatorics that makes use of the following discrete distribution.
Let $a_{1}, a_{2},..., a_{N}$ be any binary sequence of of length $N$ with $n$ ones and $m$ ...
- 201
1
vote
1
answer
499
views
A question about Chapter 12 (Vapnik-Chervonenkis Theory) of 'A Probabilistic Theory of Pattern Recognition'
Hi,
Can anyone familiar with the book 'A Probabilistic Theory of Pattern
Recognition' or the theory described help me out?
See quote from chapter 12, 'Vapnik-Chervonenkis Theory', of 'A
...
- 113
6
votes
2
answers
428
views
how to sample a conditioned diffusion
there are several reasons why we could be interested in sampling conditioned diffusions:
if we observed a diffusion at discrete time and want to do some kind of inference on the parameters of the ...
- 1,334
-2
votes
2
answers
2k
views
probability of subset sum after rolling dice 4 times [closed]
If we roll 4 dices (fair), what is the probability of "sum of subset" being 5. e.g. 1432,1121, 2344, 2354 have a subset sum of 5. Can you illustrate how to calculate this.
- 1,743
4
votes
2
answers
714
views
Mathematical means of studying large and complex but finite systems?
I want a list of the sort of mathematics/mathematical tools that are applied to the study of complex and probabilistic systems in order to make quantitative and qualitative observations about their ...
- 2,383
1
vote
1
answer
22k
views
Covariance and standard deviation relationship
I would like to know if an increase in the covariance between two variables would imply that the standard deviation for one of the variables has increased?
This is assuming that the standard ...
- 49
2
votes
1
answer
258
views
How would one extend the Brier score to an infinite number of forecasts?
Is there a neat way to use something like the Brier score to score an infinite set of forecasts/outcomes?
- 66
11
votes
2
answers
819
views
Estimate rate of real correct/wrong from 4 answers quiz.
I recently read that one in ten students think the first man on the moon was Buzz Lightyear, a Toy story cartoon. I'm not here to discuss the data in itself, rather, this reading got me into a problem ...
CommunityBot
- 1
2
votes
1
answer
254
views
Brownian Bridge under observational error
Suppose that $Z_t$ follows a simple discrete random walk $Z_t=Z_{t-1}+e_t$ , where $e_t$ are a bunch of uncorrelated normal variables with arbitrary variance sigma^2, and that there are observations ...
- 2,133
3
votes
1
answer
366
views
Random generation of subsets using conditional probabilities
Edit: Rewritten with motivation, and hopefully more clarity.
I'm building a site for a card game called dominion. In it, people build 'decks' of 10 distinct cards from a set of (currently) ...
- 13k
1
vote
2
answers
1k
views
Can you explain a step in an expectation maximization algorithm in a Nature article?
I am currently going through the following article: http://www.nature.com/nbt/journal/v26/n8/full/nbt1406.html
In this article, how did they arrive at the values in the Estimation step (Figure 1 Step ...
6
votes
1
answer
836
views
Peakedness of multimodal distributions
In Probability theory, does there exist some measures of peaked-ness for multi-modal distributions. I guess kurtosis as such would not be a good measure of peaked-ness for multimodal distributions. ...
- 598
3
votes
3
answers
316
views
Finding a distribution family that is preserved under mixture.
Consider the following
$f_{t+1}(z)=p_{12} f_{t}(z/A)+ p_{21} f_{t}(z/B)+p_{22} f_{t}(z/(A+B))$, where $A$, $B$, and the $p$'s are constants and $f_t$ is a probability distribution. Are there any nice ...
2
votes
1
answer
2k
views
Statistical test comparing two relative frequencies
I'm working with four populations consisting of true/false events. They each have a different mean and variance. I have samples from each, with different sample sizes. Call the percentage of observed ...
- 44.4k
2
votes
3
answers
2k
views
Distribution of the sum of the $m$ smallest values in a sample of size $n$
Let $\mathbf X = [X_1, X_2, \ldots, X_n]^\mbox{T}$ be a vector random variable drawn from a known distribution with CDF $F(x)$. The CDF for the minimum value in $\mathbf X$ is clearly $P[\min_{i=1\...
- 10.4k
8
votes
3
answers
511
views
MicroArray, tesing if a sample is the same with high variance data.
I'll explain the problem but what I am looking for is a few suggested methods to approach this problem.
You don't need to know what a microarray but if you are interested look here link text
The info ...
CommunityBot
- 1
10
votes
4
answers
966
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 ...
- 3
9
votes
0
answers
2k
views
Has the Lie group preserving a probability distribution been used in Bayesian statistics?
For a (possibly signed) nondegenerate probability measure $\pi$ on $\{1,\dots,n\}$ define
$$\langle \pi \rangle := \{R \in \operatorname{STO}(n): \pi R = \pi \}.$$
Here $\operatorname{STO}(n)$ denotes ...
- 15.4k
3
votes
1
answer
320
views
Joint Law with 2 marginals and marginal of the spread
I have a question for you and thank you in advance for your answers and ideas.
Let us suppose that we have the marginal distributions of two r.v X and Y, and also the law of X-Y (or any linear ...
- 498
8
votes
3
answers
2k
views
randomness in nature [closed]
What is the explanation of the apparent randomness of high-level phenomena in nature?
For example the distribution of females vs. males in a population (I am referring to randomness in terms of the ...
- 24.7k
2
votes
2
answers
956
views
An Easy Sanov-Type Theorem for Markov Chains?
First, the (simple!) setup:
I have a Markov chain X t on some finite state space Ω with stationary distribution π, and a function f from Ω to R. I'd like to estimate the integral of ...
- 263
2
votes
0
answers
1k
views
Problem with Pearson correlation coefficient. [closed]
I have two random variables X and Y. X follows a power law distribution. I know its generating function G(x). I also know the Pearson correlation coefficient of X and Y. How do I find the generating ...
- 25.8k
0
votes
1
answer
207
views
Correlation of Statistical Tests
Suppose I have a sequence $\{x_i\}_{i=1}^\infty$ of zeros and ones. I want to test if they are randomly generated according to a conjectured scheme (the example to keep in mind is that they are ...
- 498
2
votes
3
answers
571
views
How does the Dirichlet process work?
Hi, i'm looking to get into nonparametric bayesian techniques but I'm having problem understanding what's going on in the definition of the Dirichlet process or how it works. So what does P ~ DP(&...
CommunityBot
- 1
5
votes
2
answers
6k
views
Difference between Beta Process and Dirichlet process
I'm trying to understand the definition of a Beta process, as given in the paper:
www.ece.duke.edu/~lcarin/Paisley_BP-FA_ICML.pdf
The problem is that from the definition it follows that every ...
- 85.6k
1
vote
1
answer
340
views
for a natural exponential family, A is the cumulant function of h?
Reading "Monte Carlo Statistical Methods" by Robert and Casella, they mention that if
$f(x) = h(x) \exp(\langle \theta, x \rangle - A(\theta))$
defines a family of distributions for $X$, parametrized ...
- 263
4
votes
0
answers
497
views
A Local CLT with large variance
For n an even integer, $0 \leq i \leq$ ${n} \choose{j}$, $1 \leq j \leq n$ let $X_{i,j}$ be a
random variable taking values $\frac{n}{2}-j,0,j - \frac{n}{2}$ with equal probability. Let $S_{n}$ be ...
- 263
2
votes
1
answer
380
views
Parity, Balls and Boxes
Start with a distribution $\mu$ on [n], and drop m balls into these n+1 slots independently and according to the distribution &mu. That is, we have iid random variables x 1 through x m ...
- 2,133