Linked Questions

1
vote
0answers
594 views

Conditional distribution for 3 variables [duplicate]

Everywhere it is done for bivariate or given a hints. But Not in details for trivariate.
0
votes
0answers
236 views

Probability density of conditional multivariate distribution [duplicate]

We have a multivariate normal vector ${\boldsymbol Y} \sim \mathcal{N}(\boldsymbol\mu, \Sigma)$. Consider partitioning ${\boldsymbol Y}$ into $${\boldsymbol Y}=\begin{bmatrix}{\boldsymbol y}_1 \\ {...
1
vote
0answers
232 views

Deriving the conditional distributions of a multivariate normal distribution (more than 2) [duplicate]

(This is a follow up on another question Deriving the conditional distributions of a multivariate normal distribution.) I struggle when I condition several variables on another. My question is how to ...
0
votes
0answers
85 views

Epsilon from Bivariate Normal Distribution [duplicate]

I came across the following example from a book. I am given a dataset generated from a bivariate normal distribution: Among the data, there are missing values for the last 20 of x2i (but not for x1i)....
0
votes
1answer
41 views

How to calculate univariate conditional distribution of a trivariate gaussian [duplicate]

I am trying to find the conditional distribution of a trivariate gaussian. So here is a hypothetical trivariate gaussian: $$\mathcal{N}(\mu_{ABC},\Sigma_{ABC}),\;\mu_{ABC}=\begin{bmatrix}\mu_A \\ \...
0
votes
0answers
51 views

Composite Likelihood in the multivariate gaussian distribution [duplicate]

Given a multivariate gaussian distribution of the form $$\begin{pmatrix} y_{1}\\y_{2} \\y_{3}\end{pmatrix} \sim N\begin{pmatrix} \begin{pmatrix} 0\\0 \\0 \end{pmatrix}, &\begin{pmatrix} \sigma_{...
0
votes
0answers
35 views

Conditional Expectation of a normal distribution [duplicate]

say we have a multivariate normal distribution with ${\boldsymbol Y} \sim \mathcal{N}(\boldsymbol\mu, \Sigma)$ The conditional expection is $\overline{\boldsymbol\mu}=\boldsymbol\mu_1+\Sigma_{12}{\...
1
vote
0answers
23 views

Normal random vector with some known values [duplicate]

I need help with some questions regarding the normal random vector. Suppose that I have a random vector that follows a multivariate normal distribution $$ \boldsymbol{X} = \begin{bmatrix} X_1 \\ X_2 \\...
0
votes
0answers
19 views

How to find mean of multivariate normal distribution when holding a variable constant? [duplicate]

I wanted to know if there is a way to calculate the mean of a multivariate normal distribution when a certain variable is held constant. For example, if I had a continuous bivariate normal ...
10
votes
2answers
14k views

Conditional mean independence implies unbiasedness and consistency of the OLS estimator

Consider the following multiple regression model: $$Y=X\beta+Z\delta+U.\tag{1}$$ Here $Y$ is a $n\times 1$ column vector; $X$ a $n\times (k+1)$ matrix; $\beta$ a $(k+1)\times 1$ column vector; $Z$ a ...
7
votes
2answers
4k views

Conceptual proof that conditional of a multivariate Gaussian is multivariate Gaussian

I understand the arithmetic derivation of the PDF of a conditional distribution of a multivariate Gaussian, as explained here, for example. Does anyone know of a more conceptual (perhaps, co-ordinate ...
9
votes
1answer
5k views

Expressing conditional covariance matrix in terms of covariance matrix

Suppose we have two multivariate random variables $\mathbf{X}$ (of dimension $n_x$) and $\mathbf{Y}$ (of dimension $n_y$). The covariance matrix $C_{X,Y}$ can be written as the following block-matrix ...
10
votes
2answers
549 views

What is the probability that $X<Y$ given $\min(X,Y)$?

Suppose $X$ and $Y$ are bivariate normal with mean $\mu=(\mu_1,\mu_2)$ and covariance $\Sigma = \begin{bmatrix} \sigma_{11} & \sigma_{12} \\ \sigma_{12} & \sigma_{22} \\ \...
3
votes
1answer
2k views

Generating normal random samples given covariance matrix and observations on some components?

Suppose we have n by n covariance matrix of n normal random variables. Is there program where we plug in sample values for k of the n variables and the program, by using the covariance matrix and ...
8
votes
1answer
4k views

Simulating the posterior of a Gaussian process

For the first time (excuse imprecission / mistakes) I took a look at Gaussian processes, and more specifically, watched this video by Nando de Freitas. The notes are available online here. At some ...

15 30 50 per page