E[X]

Expected value of the random variable X

I(A)

Indicator function on the set A: I(x) = 1 if x ∈ A and I(x) = 0 if x ∉ A

Id

The d × d identity matrix

log x

Natural logarithm of x

ℙ

Transition matrix of a Markov chain

ℝ

The one dimensional field of real numbers

ℝd

The d-dimensional real coordinate space

Γ(·)

Complete gamma function

Φ(·)

cdf of the standard normal distribution

Φ−1

Inverse cdf of the standard normal distribution:${\text{Φ}}^{-1}\left(\alpha \right)=z\Rightarrow \text{Φ}\left(z\right)=\alpha$

$\underset{=}{{\displaystyle \text{D}}}$

equal in distribution

$\stackrel{.}{=}$

is approximately equal to

X ~

X has the distribution named on right of ~.

$\underset{~}{iid}$

Variables on the left are iid from distribution named on the right.

$||x||$

Euclidean norm of x

$\left|A\right|$

Determinant of matrix A

AT

Transpose of A

$\overline{X}$

Sample mean or vector of sample means

ASL

achieved significance level

ASH

average shifted histogram (density estimate)

BVN

bivariate normal

cdf

cumulative distribution function

dCor

distance correlation

dCov

distance covariance

ecdf, edf

empirical cumulative distribution function

GUI

graphical user interface

iid

independent and identically distributed

IMSE

integrated mean squared error

LRT

likelihood ratio test

M-H

Metropolis-Hastings

MC

Monte Carlo

MCMC

Markov Chain Monte Carlo

MISE

mean integrated squared error

MLE

maximum likelihood estimator or estimate

MSE

mean squared error

MVN

multivariate normal

$N\left(\mu ,{\text{σ}}^2\right)$

Normal distribution with mean µ and variance σ2

$N_d\left(\mu ,\Sigma \right)$

d-dimensional multivariate normal distribution with mean vector μ and variance-covariance matrix Σ

${\chi }^2\left(v\right)$

Chi-squared distribution with ν degrees of freedom

$W_d\left(\Sigma ,n\right)$

Wishart distribution with parameters (Σ, n, d)

se

standard error

svd

singular value decomposition