# Questions tagged [gaussian]

The tag has no usage guidance.

231 questions
Filter by
Sorted by
Tagged with
8 views

114 views

### Relation satisfied by a Gaussian random variable

I want to prove the following relation for $X\sim \mathcal{N}(0,1)$, $x\in \mathbb{R}$ and $f(x)=\mathbb{E}[\max(X,x)]$: $$f(\frac{f(x+1)+f(x-1)}{2})\leq \frac{f(f(x)-1)+f(f(x)+1)}{2}$$ It seems that ...
53 views

### Gaussian process kernel parameter tuning

I am reading on gaussian processes and there are multiple resources that say how the parameters of the prior (kernel, mean) can be fitted based on data,specifically by choosing those that maximize the ...
35 views

124 views

### measure of a degenerate Gaussian distribution

I want to do computations with a degenerate Gaussian measure, but I do not know how to represent it in a close form. After starting with a Gaussian random variable and restricting it to a condition, I ...
112 views

64 views

### Algorithm for economically sampling method for Gaussian matrix product

Let $A$ be an $n\times n$ random matrix with i.i.d. $N(0,\sigma)$ entries, for some $\sigma>0$ and let $x\in \mathbb{R}^n$. A direct computation shows that $Ax \sim N(0,\sigma x^{\top}x)$. I would ...
22 views

### Computating the expectation of a functional applied to a Gaussian Process

First, a definition : a process $Z$ over $\mathbb R^n$ is said to be a Gaussian Process on $\mathbb R^n$ with mean function $m(\cdot)$ and covariance function $k(\cdot, \cdot)$ if for any integer $k$ ...
300 views

145 views

74 views

### Hermite polynomial after rotation

When we consider the $n$-dimensional standard normal distribution, the orthogonal basis is $\{H_S(x)\}_{S}$ where $H_S(x) = \prod_{k=1}^n H_{s_k}(x_k)$. Here $H_*(x)$ is the normalized probabilist's ...
100 views

### Gaussian integral $\int_X \|x\|_X^2 \mu(dx)$ in Banach space

For a centered Gaussian measure $\mu$ on a Hilbert space $X$, it is known that $$\int_X \|x\|^2 \mu(dx) = tr(Q)$$ where $Q$ is the covariance operator. Is there a similar version for Gaussian measures ...
259 views

### Invariance of Gaussian under rotation

I am reading a paper, it stated the following lemma and the proof. Lemma Let $z \in R^{n}$ be a random vector with i.i.d, $\mathcal{N}(0,v^2)$ entries and let $D \in \mathbb{R}^{m \times n}$ be a ...