All Questions
Tagged with pr.probability gaussian
220 questions
3
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Equivalence of Gaussian measures on Hilbert space
Suppose we have 2 nondegenerate Gaussian measures given by N(0,T) and N(0,S) supported on a separable Hilbert space H. T and S are such that eigenbasis of S lies in the cameron martin space of N(0,T)....
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Efficient evaluation of multidimensional kernel density estimate
Edit I have copied this discussion to the stats community site here, since I feel it is more relevant. Please feel free to close this in due course.
I've seen a reasonable amount of literature about ...
CommunityBot
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4
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2
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2k
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Distribution of a product of two discrete i.i.d. variables
The problem is to estimate the distribution of product of two $\textit{discretized Gaussian}$ random variables with zero means. The discretized Gaussian means that the p.m.f. looks like
$D_s(x)=\...
CommunityBot
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1
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3
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Lipschitz continuous maps from $\mathbb R^n$ to $\mathbb R^n$ that preserve Gaussian measure?
The only ones I can think of are linear maps like rotations and permutations. Is there a more general characterization?
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1
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Variance of maximum of mixture of gaussians
Let $\{X_i\}$ be an iid collection of standard normal $(N(0,1))$ random variables . Let $X = (X_1,\ldots,X_n)$, and consider a function of the form $f(X) = \max(A\cdot X)$, where $A$ is some symmetric,...
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2
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If Gaussian measures on a Hilbert space converge weakly to 0, how do their covariance operators converge?
Suppose we have a sequence of Gaussian measures $N(0, S(n))$ supported on a Hilbert space $H$ and we know that the sequence converges weakly to the delta measure at $0$, what are the necessary and ...
- 4,010
3
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1
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Computation complexity of calculating the cdf of an n-th dimensional gaussian random vector
Suppose you have a general $n$-th dimensional random Gaussian vector with probability distribution function $\mathcal{N}\left(\mathbf{x}|\boldsymbol{\mu},\boldsymbol{\Sigma}\right)$.
What is the ...
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Gaussian measure on Banach spaces
Given any separable Banach space $B$ and a centered Gaussian measure $Q$ on it with Cameron-Martin space $H$, does there exist a Hilbert space $G$ and a Gaussian measure $W$ on it such that following ...
- 3,958
4
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1
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Number of times a Gaussian process crosses zero in an interval
Using a probabilistic method for number theoretic purposes, I have encountered the following question (it may be very standard):
Let $X_t$ be a Gaussian process $(t>0)$ such that $X_0=0$. What ...
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1
answer
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Variance of euclidean norm of Gaussian vectors
Let $X$ be a Gaussian vector in dimension $n$, with $0$ mean and covariance identity. Let $A$ be a square matrix of size $n$, and $Y = A X$. Let $N$ be the square of $Y$ euclidean norm: $N = \sum Y_i^...
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1
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482
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Continuous dependence of the expectation of a r.v. on the probability measure
$\newcommand{\bsV}{\boldsymbol{V}}$ $\newcommand{\bsE}{\boldsymbol{E}}$ $\newcommand{\bR}{\mathbb{R}}$ Suppose that $\bsV$ is an $N$-dimensional real Euclidean space. Denote by $\newcommand{\eA}{\...
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1
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752
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transform a polynomial into another one upto a constant
I have a polynomial $p(x)=a_Nx^N+a_{N-1}x^{N-1}+\dots+a_0$. I want to convert this into another polynomial of same order, say $b_Ny^N+b_{N-1}y^{N-1}+\dots+b_0$. Is it possible to find a transformation ...
- 1,302
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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{(...
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5
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3
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898
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Lower bound for Gaussian random vector with negative correlation
Let $X = (X_1,\ldots,X_n) \in \mathbb{R}^n$ be jointly Gaussian with mean $0$, covariance matrix: $Var(X_i) = 1$, $Cov(X_i, X_{i+1}) = -1/2$, and $Cov(X_i, X_j) = 0$ else.
Let $\zeta \in \mathbb{R}^...
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2
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Are Gaussian Processes more important than other stochastic processes?
I am doing a course at university and it deals with Gaussian Processes mainly. We use them for fitting data and prediction, machine learning, regression, classification. Is there any particular reason ...
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1
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A uniqueness proposition involving Erf, the error function
This is a generalization of a previous MO question, "Reducing system of equations involving Erf, Error Function".
Consider the system of equations:
$$1/2 + {\rm Erf}(x) - \alpha {\rm Erf}(\frac{x+y}{...
CommunityBot
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4
votes
2
answers
1k
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Reducing system of equations involving Erf, Error Function
I have a system of equations:
$$1/2 + {\rm Erf}(x) - {\rm Erf}(\frac{x+y}{2})=0$$
$$-1/2 + {\rm Erf}(y) - {\rm Erf}(\frac{x+y}{2})=0,$$
Where $x \le y$ and ${\rm Erf}$ is the Error Function.
By ...
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3
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1
answer
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Divergence between two random variables
I have two Gaussian random variables $X$ and $Y$, each of which is an estimator of an underlying quantity. I need to measure whether $Y$ is estimating something different than $X$. So if the mean of $...
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2
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1
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Overall covariance of Mixture of Gaussian
I have a Mixture of Gaussians to model an arbitrary distribution. I would like to model a distribution derived from this GMM with:
Mean = Weighted average mean of GMM means.
I am not sure about how ...
CommunityBot
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1
answer
377
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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 ...
CommunityBot
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