Notation

The book uses one consistent set of symbols throughout. Local meaning always wins where a chapter says so, but unless noted these conventions hold everywhere.

Linear algebra and matrices.

Symbol	Meaning
X	design / feature matrix (rows are observations, columns are predictors)
y	response vector (e.g. sales)
\beta, \hat\beta	coefficient vector; its estimate
X^\top, A^{-1}	transpose; inverse
X^\top X	Gram matrix (the normal-equations matrix)
I, \mathbf{1}	identity matrix; all-ones vector
\lVert v \rVert	Euclidean (\ell_2) norm of v
\operatorname{diag}(\cdot)	diagonal matrix from a vector
\kappa(A)	condition number of A (with \kappa(X^\top X) \approx \kappa(X)^2)
A \succ 0, A \succeq 0	positive definite; positive semidefinite (Loewner order)
\lambda_i, \sigma_i	eigenvalue; singular value

Probability and statistics.

Symbol	Meaning
\mathbb{E}[\cdot], \operatorname{Var}(\cdot), \operatorname{Cov}(\cdot)	expectation; variance; covariance
\mathcal{N}(\mu, \Sigma)	(multivariate) normal with mean \mu, covariance \Sigma
\Sigma, \sigma^2	covariance matrix; (scalar) variance
X \sim p	X is distributed according to p
\perp	(conditional) independence
p(\cdot), \propto	density / mass function; “proportional to”

Bayesian inference.

Symbol	Meaning
p(\beta), p(\beta \mid y)	prior; posterior over parameters
\mathcal{L}(\beta), \ell(\beta)	likelihood; log-likelihood
\tau	prior scale (standard deviation)
\Lambda	precision (inverse covariance)

Optimization.

Symbol	Meaning
\nabla f, \nabla^2 f	gradient; Hessian
\arg\max, \arg\min	maximizing / minimizing argument
b, B	budget allocation vector; total budget
\lambda^\star	optimal Lagrange multiplier / shadow price
KKT	Karush–Kuhn–Tucker optimality conditions

Marketing-mix-modeling quantities.

Symbol	Meaning
adstock	geometric carryover transform of spend (rate r)
saturation	concave diminishing-returns response transform
EVPI	expected value of perfect information

Logic and proofs.

Symbol	Meaning
:=, \triangleq	“is defined as”
\Rightarrow, \iff	implies; if and only if
\blacksquare	end of proof