# Questions tagged [multivariate-normal]

The multivariate normal distribution, is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. (Also called, multivariate Gaussian)

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### Efficient sampling from a multivariate Gaussian Mixture distribution for a given CDF level

I have a multivariate Gaussian Mixture (GM) distribution. I am wondering if there is any more efficient way of drawing samples (i.e., identify the iso-surface) from a multivariate Gaussian Mixture ...
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### Degenerate multivariate normal in Maximum Likelihood Estimator (Akaike's Info Criterion, BIC, LR Test usage)

Let's suppose that the considered set of random variable has a covariance matrix which is psd. Therefore the Gaussian pdf must be written in its degenerate form, where the determninat of the ...
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### Fitting a Gaussian to two Gaussians [duplicate]

Let's say I have a dataset set of 2D points. I break the dataset to 2 subsets, equal in number. Then I fit a bivariate (2D) Gaussian to each subset. So I have two bivariate gaussians, each with its ...
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### Problem with two correlated random normals

Imagine you have a two-dimensional multivariate normal random variable with $\mu = [0, 0]$ and $\Sigma\ = \begin{bmatrix}1 & r\\r & 1\end{bmatrix}$. (Conceptually, you have two random normal ...
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### Computing probability density function at a point, given the covariance matrix and mean

(Edited for clarity.) Say I have the variance-covariance matrix $\mathbf{V}$ and mean $\mathbf{\mu}$ of a multivariate normal distribution. Given a sample, $\mathbf{s}$, can I compute/estimate the ...
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### Conjugate prior for DPGMMs using Gibbs sampling

I am using Gibbs sampling to infer DPGMMs. The prior for multivariate Gaussians is Normal-inverse Wishart. But it turns out that the covariances are not estimated accurately. Here is codes and results....
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The question is pretty much in the title, I need to find an approximate distribution of $XY$ when $(X,Y)$ follow a Bivariate Normal Distribution where $X$ and $Y$ are each $N(0,1)$ distributed and $... 0answers 35 views ### Simplification of bivariate normal$\phi_2(x,y,\rho)$at$y=y_F$(i.e. fixing one of the axes) Suppose we start off with the traditional standard bivariate normal distribution:$$\phi_2(x,y|\rho,\mu_x=0,\mu_y=0,\sigma_x=1,\sigma_y=1)=\frac{1}{2\pi\sqrt{1-\rho^2}}\exp \left(-\frac{x^2-2\rho x y ... 0answers 58 views ### Using Hotelling's T-statistic to find an elliptic confidence set The problem: We have samples of sizes${n_1} = 25,{n_2} = 15,{n_3} = 30$drawn independently from$N\left( {{\mu _i},{\sigma ^2}} \right),i = 1,2,3$(normal distributions with same variance). We have$...
Suppose $z$ is a random variable taking values in $\mathbb{C}^n$ and admitting the complex Gaussian density $p(z;W) \propto \exp{(-\frac{1}{2}z^*Wz)}$, where $W$ is Hermitian. Let $r$ be the vector of ...