All Questions
9,497 questions
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Derivative of the most probable value (of a gaussian variable) VS most probable value of the derivative
Let $x$ be a random variable with gaussian probability distribution $P(x)$. We assume that $x$ depends parametrically on a parameter $t$ so that :
$P(x(t))=\frac{1}{\sqrt{2\pi\sigma^2(t)}}\exp(-\frac{(...
- 1
0
votes
0
answers
145
views
Finding expectation of size of a subgraph
I have been trying to implement a algorithm but got stuck in finding expectation of the size of the subgraph.
n - size of the network.
d - at most number of communities a node could participate ...
- 1
0
votes
1
answer
165
views
transition probability convergence for Harris chains - Durrett.
Dear mathoverflow.
This is a question to a proof in a graduate text. I have asked two professors at my university without help, so I hope it suffices in difficulty for this forum otherwise I ...
- 3
0
votes
0
answers
303
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hitting probability for integrated Ornstein-Uhlenbeck process
Consider an Ornstein-Uhlenbeck position process:
$dV_t=dB_t-\lambda V_tdt$
$dX_t=V_tdt$
where $B_t,V_t,X_t$ are all in $R^d$ with $d\geq 3$. Let $X_0\neq0$, $V_0=0$ .
Let $r>0$ and $S_r$ be the ...
0
votes
1
answer
2k
views
Finding linearly independent columns of a large sparse rectangular matrix
I have a problem that necessitates solving a large non-negative least-squares
problem. My matrix A is large, sparse, highly rectangular (num rows >> num cols)
and nearly binary. However, A is not ...
- 103
0
votes
0
answers
104
views
Proving that a property holds for random sequences with given marginal distribution by rearrangement
I am currently investigating the property of random sequences with a special marginal distribution function $F(x)$. Given any random sequence $X_1, X_2, \cdots, X_n$, supposing their joint ...
- 21
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votes
1
answer
107
views
Can one combine (join) probabilities from 2 aspects of a related process?
Consider 2 related aspects of a process for prices in a financial market:
time &
return.
Time
Say I've identified a distribution that reasonably models the occurrence of the lengths of price ...
- 111
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votes
0
answers
135
views
expected number of shared 1s between two binary strings from a given set
Let say, I have two binary strings with length N, chosen from a set where there are $2^N-K,(K \ge 0)$ independent strings. What would be the expected number of Ones at the same index from two randomly ...
- 21
0
votes
1
answer
283
views
Probability and events [closed]
Hi everyone
The question is the following:
A certain event may or may not take place. So we say that if we focus on it one time, it has a probability p of being satisfied (0 <= p < 1)
If we ...
- 3
0
votes
0
answers
111
views
Stationarity of an Integral Process
Let $f$ be a continous deterministic function defined on $\left[0,c\right]$ and $(B_{t}^{H})_{t\geq 0}$ be a fBM with $H\in \left(0,1\right)$. We define a Process $\left(X_{t}\right)_{t\geq 0}$ with
$$...
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votes
0
answers
103
views
Gauss-Newton for quotient functions
I'm optimizing a function of the form
$$
\sum \frac{ \|\mathbf{f_i}(x)\|^2 }{ g_i(x)^2 + h_i(x)^2 }
$$
where $x$ is a real vector, $\mathbf{f}(x)$ is a real vector, and $g(x)$ is a scalar. My first ...
- 561
0
votes
1
answer
182
views
How to Rigorize an inequalities argument
Context
I'm working on a problem involving Lovasz Local Lemma, for proving that there exists a graph with a certain property.
What I need to prove:
There exists some constant $c$, and functions $p,...
- 3
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votes
0
answers
194
views
A linear program related question
Dear all, recently, I encountered the following problem. It is closely related to the order of growth for UMD constants of all $n$-dimensional Banach lattice.
Let $\alpha^k \in (\alpha_1^k, \alpha_2^...
- 769
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0
answers
79
views
Computing maximum point for minimal function of a family of linear functions
Let $x \in S^n $ where $S^n = ${$ [x_1,x_2,...,x_{n+1}]\in \mathbb{R}^{n+1} \mid x \ge 0 , \sum x_i = 1 $} and let $f_i : I^n \to \mathbb{R}$ be a finite $m$-sized family of LINEAR functions such that:...
- 11
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votes
0
answers
783
views
LP relaxation for ILP\IP (integer linear programming)
I am familiar with LP relaxation for ILP (or IP). Assume we concern with integer minimization problem, which we formalize using ILP; we then relax the ILP into LP and we say that the LP provides a ...
0
votes
0
answers
352
views
prewhitening (whitening transform) in terms of expected-value-wr-sigma-algebra
I'm trying to understand the mathematics of prewhitening a little better. (See http://en.wikipedia.org/wiki/Whitening_transformation, e.g.)
Taking the conditional expectation of an RV with respect to ...
0
votes
0
answers
161
views
T. Lyons Criterion
Hello all,
I want to prove that any flow on the following tree must have an infinite energy.
The structure of the graph is (taken from R.Lyons and Y.Peres book)
"We’ll construct a tree $T$ embedded ...
- 1
0
votes
0
answers
130
views
span of symmetrically truncated symmetric random variables
If $X_i$ are symmetric independent random variables, is $\vert \sum X_i I_{\vert X_i \vert < N_i}\vert $ stochastically smaller than $\vert \sum X_i \vert$ ? Is it comparable in any way which ...
- 90
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votes
0
answers
321
views
Expected value of a logarithm of a Levy process
I have a strictly positive Levy process $(L_t)$ with no Brownian part, drift $\gamma$ and jump measure $\nu$. Is it possible to calculate the expected value of the logarithm of this process, so $\...
- 667
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votes
0
answers
226
views
Branching process question
(Cross-posted to math stackexchange question 130154)
I am trying to analyze the following branching process. We start with a root (level 0) node. Each surviving node has two children, each of which ...
- 3,475
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votes
0
answers
187
views
Sampling when given a set of marginal distributions
There is an unknown joint multivariate distribution P(A_1, A_2, A_3, ..., A_n) (in my scenario, it's a n-dimensional contingency table), which we need to sample from.
Given an arbitrary set of ...
0
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0
answers
127
views
A problem about partial sum of random number composition
Consider the strong random number composition,
$x_1 + x_2 + \cdots + x_n = m$, with $x_i > 0$ and all possible compositions have the same probability.
Let random variable $S_i = \sum_{j=1}^i x_j$...
- 177
0
votes
1
answer
207
views
Copulas and marginals thereof
Hello everyone,
I recently became aware of the existence of the copula concept.
So, I have been reading a few things about copulas lately, but
I cannot seem to find information on the following ...
- 103
0
votes
0
answers
165
views
Joint Probability that contains a variable and its Fourier Transform
Given the vector $\mathbf{d}$, where $\mathbf{d}\in\mathbb{C}^{N\times 1}$, we have two variables
$X = \mid\mathrm{F}[d]\mid^2,\quad\quad X\ge 0$
$Y = a+b (\mathrm{d}^H\mathrm{d})\quad Y\ge 0$
...
- 447
0
votes
0
answers
493
views
Simulating conditional expectations
There is a multidimensional process X defined via its SDE (we can assume that its a diffusion type process), and lets define another process by $g_t = E[G(X_T)|X_t]$ for $t\leq T$.
I would like to ...
- 667
0
votes
0
answers
118
views
sparsest cut always has solution
Hi!
How to prove that sparsest cut always has an optimal solution which is the cut for some vertex-subset.
Looks like it's should be a kind of fundamental theorem for sparsest cut. But I didn't ...
- 1
0
votes
0
answers
337
views
What is the mean-value of a particular exponential sum related to the non-trivial zeros of Riemann's zeta function?
This question arose from an earlier one and the MO user's useful answers there: What are the values of the derivative of Riemann's zeta function at the known non-trivial zeros? (which is not a ...
- 2,480
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votes
0
answers
479
views
Passage Time Distributions for Poisson processes.
Let $(X_t)_{t \geq 0}$ be a standard Poisson process with intensity $\mu$. Let $\tau_b = \inf ( t>0 : X_t= at + b)$, where $a>0$ and $b<0$, and let $\sigma = \inf (t>0 : X_t \geq at)$. ...
- 943
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votes
0
answers
184
views
Integration of discounted normal distribution
Hi
I want to find expectation of integration of normal distribution $\varphi(t)\sim N(0,\sigma\sqrt t)$
but i also want to discount it continuously with parameter $\alpha$.I mean i need to ...
- 1
0
votes
0
answers
458
views
Bounding mutual information given bounds on pointwise mutual information
Suppose I have two sets $X$ and $Y$ and a joint probability distribution over these sets $p(x,y)$. Let $p(x)$ and $p(y)$ denote the marginal distributions over $X$ and $Y$ respectively.
The mutual ...
- 1
0
votes
0
answers
163
views
"Reverse" stochastic dominance
Let $\mu$ and $\mu'$ be probability measures on $\lbrace0,1\rbrace^\Lambda,\:\: \Lambda:= {\lbrace 0,1,\ldots,n\rbrace}$. Assume that
$\mu(X_i=1|X = \zeta \text{ on } \Lambda \setminus \lbrace i\...
- 1,491
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votes
2
answers
383
views
"X \in \cdot" in Probability Measure [closed]
My question is quite simple, but I was unable to find an answer by googling, since you can't exactly google syntax. What does the $\in \cdot$ mean in:
$$\lim_{n\to\inf}||P(S_n\in\cdot)-P(S_n+k\in\cdot)...
- 3
0
votes
0
answers
293
views
Open Jackson network with deterministic arrivals.
Dear Friends,
Is there any known Jackson-like theorem for an open Jackson network with deterministic arrivals?
Thanks,
Michael.
- 85
0
votes
0
answers
319
views
Estimating a multinomial sum
I have the following sum
\begin{equation}
\sum_{r_1=q+1}^{\tau}\dots\sum_{r_\lambda=q+1}^{\tau}{\tau\choose r_1,\dots,r_\lambda,\tau-r_1-\dots -r_\lambda} (\Lambda-\lambda)^{\tau-r_1-\dots-r_\lambda}
\...
0
votes
1
answer
578
views
One-Variable Optimization Problem
$W_{opt}=\arg \{\max(\pi_0 F_{L_0}(W)-\frac{\pi_1}{W}\int_0^W F_{L_1}( \alpha )d \alpha )\}$
subject to $\quad \int_0^W F_{L_0} (\alpha)d\alpha <\xi$
We should find analytically the optimal $...
- 23
0
votes
0
answers
343
views
Can KL divergence go to 0, but $E[\log(p/q)^2]$ diverge in certain cases?
Let $p(x)$ be a fixed distribution over a discrete space.
Let $A, C > 0$ be constants.
Let $\epsilon > 0$. Can we find an example of a distribution
$q_{\epsilon}$ such that $\mathrm{KL}(p||q_{\...
- 1
0
votes
0
answers
138
views
Why do I not use post hoc tests with a 2 x 2 factorial?
I know this is an obvious answer. I am probably over thinking what I'm doing, but I cannot recall. Does it have to do with not having enough variables to compare the various means?
0
votes
3
answers
164
views
Transforming to uniform numbers
Hi
I have a time series of probabilites, vector X
I need to convert the probabilites to uniform numbers.
As I understand it if I put the series into the cdf the output is thus uniform.
The problem ...
- 3
0
votes
0
answers
574
views
What's the expected number of iterations for this process?
Each step of the process consists of choosing a random integer between 1 and the last number chosen this way. On average, how long does it take to obtain "1" as a result of this process for any given ...
- 25
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votes
2
answers
102
views
Does Max Flow produce uniform results? [closed]
I am interested in using Max Flow algorithm. I want to simulate transfer of quantity. Anyway, I am unsure of some thing.
Does Max Flow algorithm produce uniformly distributed max flow?
I have ...
- 11
0
votes
1
answer
377
views
Robust entropy-like measure for analyzing uncertainity
I'm looking for a measure to analysis the uncertainty observed in a set of variables (with multivariate Gaussian distribution). So, I've tried conventional Shanon entropy (differential entropy) which ...
- 5
-1
votes
6
answers
2k
views
Chances to win an election
Let's say that tomorrow national president election is held. A poll asks 1100 persons which of the two candidates, A or B, will he or she will vote. 750 say will vote A, and 250 say will vote B. What ...
- 330
-1
votes
2
answers
409
views
$X$ is Polish and $N$ is countable. Is $N^X$ Polish? [closed]
$X$ is a separable, completely metrizable topological space equipped with its sigma algebra of Borel sets. $N$ is a countable space.
$X^N$ is the collection of all mappings from $N$ to $X$. It is ...
- 263
-1
votes
3
answers
3k
views
Monte Carlo method and possible applications to computer poker?
I want to do something about ”games of incomplete information“，like "Computer poker program".I know,Albert university(in canada) have do a lot of things to that field,they write a program called: "...
- 11
-1
votes
3
answers
215
views
Proving the uniform distribution maximizes the expected value of the product of a random draw of $m$ elements from discrete distribution
Say I have a discrete probability distribution $p_i$, so $0 \le p_i \le 1$ and $\sum_i{p_i}=1$. We sample $m > 1$ draws $D$ from this distribution proportional to $p_i$ with replacement, and ...
- 109
-1
votes
2
answers
249
views
$p$-norm of random variables and weighted $L^p$ space resemblance
I noticed a very similar relationship between weighted $L^p$ space (denoted $L_w^p$) and normed vector space of random variables. I want to unify these two spaces but there always seems to be a ...
- 1
-1
votes
2
answers
217
views
Expected number of balls left out when choosing $n$ times from $n$ balls
I am given $n$ balls. For $n$ times, I pick one of them with uniform probability and put it back after picking it.
Let $U$ be the number of balls I have never picked, so $U\in \{0,\ldots,n-1\}$. We ...
- 48.8k
-1
votes
2
answers
868
views
How can I calculate the expected ranking of a competitor from the probabilities of each competitor reaching first place?
Say I have several competitors contending over some prize. I know the probabilities that any particular one of them will win the prize. It is assumed that the competitors all want to achieve the ...
-1
votes
2
answers
440
views
$\langle X\rangle_t = t$
Suppose $B_t$ is a standard Brownian motion in $\mathbb{R}^d$ and $X_t = |B_t|$. What is the easiest way to see that$$\langle X\rangle_t = t?$$I need this result for a simulation I am running...
- 93
-1
votes
2
answers
405
views
Conditional expectation: commuting integration and supremum
Let $X$ and $A$ be compact Polish spaces endowed with Borel $\sigma$-algebras. Let $\mathcal{A} = X\times \mathcal{B}(A)$ be the $\sigma$-algebra consisting of cylinders whose projections on $A$ are ...
- 109