Lexicon of mathematical symbols

DRAFT

Latin symbols
\(a\) estimated value of a coefficient in a predictive model
\(A\) area of a sampling plot
\(\mathcal{A}\) area of a stand
\(b\) estimated value of a coefficient in a predictive model
\(B\) biomass of an aliquot, a compartment (trunk, branches, leaves \(\ldots\)), of a tree or stand
\(\mathrm{CV}_X\) coefficient of variation of a variable \(X\)
\(c\) exponent of a power expression
\(C\) definition 1: circumference of a tree; definition 2: cost of sampling; definition 3: model validation criterion
\(D\) diameter of a tree at breast height (dbh)
\(D_0\) dbh of the dominant tree in a stand
\(E\) precision of the estimation of a variable
\(f\) a function linking a response variable to one or more effect variables
\(F\) Furnival’s index
\(g\) a function
\(G\) basal area of a tree or a stand
\(h\) a height between zero (the ground) and the height \(H\) of the tree
\(H\) height of a tree
\(H_0\) height of the dominant tree in the stand
\(\mathbf{I}_n\) Fisher’s information matrix for a sample of size \(n\)
\(k\) multiplier of a power expression
\(K\) number of subsets in a cross validation
\(\ell\) likelihood of a sample
\(\mathcal{L}\) log-likelihood of a sample
\(L\) length of a log
\(M\) definition 1: number of biomass compartments in a tree; definition 2: number of competitor models for predicting the same response variable
\(n\) sample size
\(N\) definition 1: total number of sampling units (tree or plot) in a stand; definition 2: stand density (number of stems per hectare)
\(\mathcal{N}\) the normal distribution (also called a Gaussian or Laplace-Gauss distribution)
\(p\) number of effect variables in a model (not including the y-intercept)
\(P\) stem profile (plot giving the area of a cross-cut through the trunk at different heights)
\(q\) definition 1: number of estimated parameters in a model; definition 2: quantile of the standard normal distribution
\(Q\) number of Monte Carlo iterations
\(R\) definition 1: a model’s determination coefficient; definition 2 (in the model selection theory): a risk; definition 3: radius of a log
\(S\) number of strata in a stratification
\(S_X\) empirical standard deviation of a variable \(X\)
\(\mathcal{S}_n\) dataset containing \(n\) observations
\(t_{n}\) quantile of a Student’s distribution with \(n\) degrees of freedom
\(T\) age of a plantation
\(V\) volume of a log, tree or stand
\(w\) definition 1: weight of an observation in a weighted regression; definition 2: weight of a model in a mixture of models
\(X\) a variable (generally the effect variable of a model)
\(\mathbf{x}\) a vector of effect variables
\(\mathbf{X}\) design matrix for a linear model
\(Y\) a variable (generally the response variable of a model)
\(\mathbf{Y}\) response vector of a multivariate model
\(z\) a latent variable for the EM algorithm
\(Z\) a variable (generally a covariable defining the stratification of a dataset)

Greek symbols
\(\alpha\) definition 1: (unknown) “true” value of a coefficient in a predictive model; definition 2: confidence threshold for a confidence interval (generally 5 %)
\(\beta\) (unknown) true'' value of a coefficient in a predictive model </td> </tr> <tr> <td style="text-align:right;"> $\gamma$ </td> <td style="text-align:left;width: 20cm; "> loss function (in the model selection theory) </td> </tr> <tr> <td style="text-align:right;"> $\delta$ </td> <td style="text-align:left;width: 20cm; "> Dirac's function </td> </tr> <tr> <td style="text-align:right;"> $\Delta$ </td> <td style="text-align:left;width: 20cm; "> a difference in value for a given variable </td> </tr> <tr> <td style="text-align:right;"> $\varepsilon$ </td> <td style="text-align:left;width: 20cm; "> residual error of a predictive model </td> </tr> <tr> <td style="text-align:right;"> $\boldsymbol{\varepsilon}$ </td> <td style="text-align:left;width: 20cm; "> vector of the residual errors of a multivariate model </td> </tr> <tr> <td style="text-align:right;"> $\zeta$ </td> <td style="text-align:left;width: 20cm; "> residual covariance between two compartments </td> </tr> <tr> <td style="text-align:right;"> $\eta$ </td> <td style="text-align:left;width: 20cm; "> volumetric shrinkage coefficient </td> </tr> <tr> <td style="text-align:right;"> $\theta$ </td> <td style="text-align:left;width: 20cm; "> a set of model parameters </td> </tr> <tr> <td style="text-align:right;"> $\boldsymbol{\theta}$ </td> <td style="text-align:left;width: 20cm; "> a vector of parameters in a multivariate model </td> </tr> <tr> <td style="text-align:right;"> $\vartheta$ </td> <td style="text-align:left;width: 20cm; "> a set of parameters </td> </tr> <tr> <td style="text-align:right;"> $\mu$ </td> <td style="text-align:left;width: 20cm; "> expectation of a random variable = (unknown) "true" mean of a variable to be estimated </td> </tr> <tr> <td style="text-align:right;"> $\xi$ </td> <td style="text-align:left;width: 20cm; "> Box-Cox transformation parameter </td> </tr> <tr> <td style="text-align:right;"> $\rho$ </td> <td style="text-align:left;width: 20cm; "> wood density </td> </tr> <tr> <td style="text-align:right;"> $\sigma$ </td> <td style="text-align:left;width: 20cm; "> standard deviation of the residual error of a predictive model </td> </tr> <tr> <td style="text-align:right;"> $\boldsymbol{\Sigma}$ </td> <td style="text-align:left;width: 20cm; "> variance-covariance matrix of a multinormal distribution </td> </tr> <tr> <td style="text-align:right;"> $\tau$ </td> <td style="text-align:left;width: 20cm; "> (unknown)true’’ standard deviation of a variable to be estimated
\(\phi\) probability density of a normal distribution
\(\psi\) function defining a variable transformation
\(\chi\) water content
\(\chi_0\) fiber saturation point
\(\omega\) a proportion (for example, the proportion of fresh biomass in a log)

Non-alphabetical symbols
\(\varnothing\) diameter of a tree, a log, a branch or a root