For questions about the Gaussian probability distribution, its definition, properties and use.
Questions tagged [gaussian]
493 questions
2
votes
0 answers
Are folded normal variables subgaussian?
Suppose that $X \sim N(\mu, \sigma^2)$ is Gaussian. Then $Y := |X|$ is a Folded normal random variable.
$X$ is clearly Subgaussian i.e. $M_{X}(\lambda) := E\left(e^{\lambda(X - \mu)}\right) \leq e^{\sigma^{2} \lambda^{2} / 2}, \; \forall \lambda \in…
user4687531
- 249
1
vote
1 answer
Why is the covariance matrix inverted in the multivariate Gaussian distribution?
The multivariate gaussian distribution has probability density function:
$$
\frac{1}{\sqrt{(2\pi)^k|\mathbf{\Sigma}|}}
\exp\left(-\frac12(\mathbf{x}-\boldsymbol{\mu})^\text{T}\mathbf{\Sigma}^{-1}(\mathbf{x}-\boldsymbol{\mu})\right)
$$
(Original at…
Edmondo
- 119
1
vote
1 answer
Find probability for a sub-set of in multiple objects following gaussian distr
I have a problem to solve.
A factory makes bolds (following the normal distribution) with an average weight= $\mu$ gr and s.d =$\sigma$ gr. A bold is considered faulty if it weights less than $z$ gr. A store buys $100$ of these bolds, what is the…
Just_Newbie
- 149
1
vote
0 answers
Bayes’ theorem for Gaussians (Multivariate-Gaussian)
I have a question regarding the Bayes'theorem of Gaussians.
Assume we have the multivariate gaussian density function:
$$x=(X1, X2)$$
$X1$ and $X2$ are random variables
$$\Sigma = \begin{bmatrix}\sigma^2 & \alpha * \sigma^2 \\
\alpha * \sigma^2 &…
TecK97
- 23
1
vote
0 answers
"A sum of gaussian RVs is another gaussian"
In my machine learning notes for Gaussian Mixture Models, I see the following statement:
It is common to confuse a mixture of Gaussian with a sum of Gaussians. Note that, a sum of Gaussian RVs is another Gaussian, and therefore unimodel.
This is…
roulette01
- 403
1
vote
1 answer
Derivation of the product of Gaussian functions
I am trying to derive the form of the product of two Gaussian functions of the form $\chi = e^{-\alpha|r - A|^2}$, where $\alpha$ is a positive constant and $A$ is a 3D vector. These are used in computational chemistry to represent the orbitals, so…
Raphaël
- 121
0
votes
0 answers
What is the probability of multiple Gaussian distribution measurements to be in agreement.
I have N measurements, each reports a Gaussian distribution of the scalar value (i.e. each reports mean and variance of it: $(\mu_i, \sigma_i^2)$).
What is the probability that these measurements are "correct"? Or, to phrase it differently, what is…
0
votes
0 answers
Gaussian Kernel Expectation
Let $\kappa(x, x')=\exp(-\frac{1}{2\sigma^2}||x-x'||)$ be the Gaussian kernel with the multivariate random variable $x, x' \in \mathbb{R}^D$ and scalar parameter $\sigma \in \mathbb{R}_+$. I am interested in the expectation $\mathbb{E}_{x,x'}…
Andreas Look
- 115
0
votes
1 answer
Proof of joint Gaussian distribution in a linear equation
Let $X = AY + Z$ where $A$ is constant, $Y$ and $Z$ are independent gaussian rvs. How do you prove that $X$ and $Y$ are jointly gaussian? I know that the sum of two independent gaussians gives a gaussian distribution. But I have no idea where to…
eet
- 393
0
votes
1 answer
Predictive distribution of SPGP
Eq(8) in Sparse Gaussian Processes using Pseudo-inputs states that
\begin{align*}
"p(y^*|x^*,D,\bar{X})=\int{p(y^*|x^*,\bar{X},\bar{f})p(\bar{f}|D,\bar{X})d\bar{f}}"
\end{align*}
which can be derived…
DfKe
- 1