# Questions tagged [multivariate-distribution]

Probability distribution over vectors (as opposed to univariate distributions that are over numbers).

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### How to determine quantiles (isolines?) of a multivariate normal distribution

I'm interested in how one can calculate a quantile of a multivariate distribution. In the figures, I have drawn the 5% and 95% quantiles of a given univariate normal distribution (left). For the right ...
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### Derive multivariate from bivariate normal distribution

Could anyone help me on the following. Let $K$ and $M$ be integers so that $K\geq3$ and $2\leq M < K$. Let $\boldsymbol{X}=(X_1, ..., X_K)^T$ be a random vector, $\boldsymbol{\mu}$ be a $K\times 1$...
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### Multivariate conditional entropy

I would like to take data columns and compute the multivariate conditional entropy. For instance, suppose I have columns $A, B, C D, E$ and I want to compute the conditional entropy $H(E | A,B,C,D)$. ...
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### Ornstein-Uhlenbeck process

Given a multivariate Ornstein-Uhlenbeck process that is a stochastic process, is it correct that each component of this process is a univariate Ornstein-Uhlenbeck process?
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### Joint distribution of independent t-distributed random variables

The multivariate t distribution seems to be defined as a "ratio" of a vector of normal random variables and a single gamma (or chi-squared) random variable (independent from the vector of normal). ...
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### The mode of multivariate Gamma distribution

Let X, Y, Z be i.i.d. distributed Gamma random variables. What could the mode of the vector $(X, X+Y, X+Y+Z)$ be? Does the mode of a random vector equal the combination of the marginal modes?
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### Can a random variable be uncorrelated with its product with a correlated random variable?

I have a random variable $X.$ I want to find a random variable $Y$ such that $Y$ is correlated with $X,$ but $Y$ is not correlated with the product of $X$ and $Y.$ Is it always possible?
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### Why is conditional independence more important than marginal independence?

Graphical models are based on the idea of representing certain types of conditional independences in a (joint) distribution via a graph, and are an active research area. As argued (correctly I believe ...
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### Swiss Cheese Distributions

I am curious about a normal distribution with no probability mass in certain regions, sort of like the complement of the truncated normal. In particular, it will have zero mass in a circular region. ...
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### GLM in Matrix Notation

I would like to verify my thoughts here concerning matrix notation of generalized linear models (i.e. generalized general linear models). A classical generalized linear model is given by  Y_i = h(\...
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### What graphical model formalism should I use to model state-space model?

I have a state-space model of a greenhouse control model that I'd like to transform into a probabilistic graphical model (to make it easier for non-technical managers to understand relationships among ...
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### Probability distribution transformation of variables question

Problem: Hi there, I'm stuck trying to derive an equation stated in a research paper relating to Bayesian statistics in Cosmology (the paper is: http://mnras.oxfordjournals.org/content/398/4/2049....
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### How does Gibbs sampling produce values for a variable using the univariate conditional probability?

I have a question about Gibbs sampling for generating samples. The Gibbs sampling algorithm is often stated. $x^0 = (x_1^0, x_2^0, \ldots, x_n^0)$ //initialize random values for $t=1$ in $T$ //...
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### Inner Product for Geometric Interpretation of Multivariate Random Vectors

I was looking into the geometric interpretation of random variables as random vectors in a vector space. The textbook I'm referring to defined $\operatorname {Cov}(X,Y)$ as the inner product for any ...
Background You may find the definition of the non-paranormal distribution at the 2nd paragraph in p.2296 of this paper. In short, $(X_1, \ldots, X_p)$ is non-paranormal if there exists a set of ...