# Questions tagged [gaussian]

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### Derivative of an integral of a Gaussian

I'd like to compute the derivative of an expected value w.r.t one of the parameters that define the mean of a Gaussian: $Z=\int \mathcal{N}(x;\mu,\Sigma)f(x) \, dx$, then $\frac{dZ}{dK}=\text{??}$ ...
58 views

### How to calculate $\int_{\mathbb{R}^n_{\geq0}} d\mathbf{w} e^{-\frac{1}{2}\|\mathbf{w}\|^2} [\mathbf{w\cdot x}]_+$

I am trying to evaluate $$\int_{\mathbb{R}^n_{\geq0}} d\mathbf{w} e^{-\frac{1}{2}\|\mathbf{w}\|^2} [\mathbf{w\cdot x}]_+$$ where $\mathbf{w} \in \mathbb{R}^n_{\geq0}$ (a real vector in the positive ...
59 views

### Why is squared exponential kernel often used in Gaussian Process regression when the most standard case is time-like X?

I might be confused about something. Consider doing inference on $Y'\mid X',Y,X$ using standard Gaussian Process Regression with 1d $Y$ and 1d $X$. Suppose $X$ is time-like (target is stationary or ...
70 views

### Estimating the average of two gaussians' mean with minimal squared error

This is a follow-up to my previous question. Assume that $X\sim \mathcal N(\mu_1,\sigma_1^2)$ and $Y\sim \mathcal N(\mu_2,\sigma_2^2)$. I want to estimate $\frac{\mu_1+\mu_2}{2}$ after observing $X,Y$....
52 views

### Estimating the average of two gaussians' mean

Assume that $X\sim \mathcal N(\sigma_1,\mu_1)$ and $Y\sim \mathcal N(\sigma_2,\mu_2)$. I want to estimate $\frac{\mu_1+\mu_2}{2}$ after observing $X,Y$. In my setting, $\sigma_1,\sigma_2$ are known ...
316 views

### Explicit constant for Carbery–Wright inequality

The Carbery-Wright is a seminal result about the anti-concentration of polynomials of Gaussian random variables. See e.g. Meka, Nguyen, and Vu - Anti-concentration for polynomials of independent ...
36 views