Step 05 · Reference
Terms and Notation
Notation is a promise that a symbol means the same thing on every page. This reference gathers the promises the compendium makes, in one place, so that a reader may return to them without searching.
Symbols of the distribution
- mu
- the centre of a distribution, where its mass balances.
- sigma
- the spread of a distribution, in the original units.
- sigma squared
- the variance, the average squared distance from the centre.
- z
- a standard score, a distance from the centre measured in units of sigma.
- p
- a share of the area under a density, read as a probability.
Symbols of dependence
- cov
- the covariance of two quantities, a measure of shared movement.
- rho
- the correlation, a covariance rescaled to lie between minus and plus one.
- C
- a covariance matrix, with variances on the diagonal and covariances beside them.
- conditional mean
- the centre of a slice through a joint density.
- marginal
- the shadow a joint density casts on one axis alone.
Symbols of the series
- t
- a time index, evenly spaced and arranged in sequence.
- lag
- a displacement between two moments of a record.
- autocorrelation
- the resemblance between a record and a shifted copy of itself.
- spectral density
- the share of variance attached to each frequency.
- ergodic
- describing a record whose time averages settle to process values.
Terms that recur
Stationary
A record is stationary when shifting its clock changes nothing about the joint behaviour of its values. Weak stationarity fixes the mean, the variance and the dependence on lag; strict stationarity fixes the whole joint density.
Density
A density assigns a height to each value, and probability is the area beneath it. Densities are read as areas, never as single points.
Estimator
An estimator is a rule for producing a number from a record. The same word names both the rule and the number it produces, which is a small harm the compendium accepts for brevity.
Quantile
A quantile is a cut point that leaves a chosen share of the record below it. The median, the quartiles and the deciles are all quantiles.
Likelihood
The likelihood reads a density as a statement about which parameter values make the observed record plausible. It is a function of the parameter, not of the record, and this reversal is worth holding firmly in mind.
How to read the rail
The rail above groups the papers into five steps. Step one treats a single distribution; step two treats two quantities and their matrix; step three treats a record through time; step four treats frequency and simple recipes for memory; step five gathers reference material. A reader may enter at any tile and follow the links within its panel.
A note on rounding
Shares quoted in the papers are rounded to three places and standard-score cut points to two. The rounding is a courtesy to the reader and never carries more meaning than the method behind it. Where a figure is approximate, the compendium says so in the sentence beside it.
Using this reference well
Keep this page open beside any paper that gives trouble. The symbols are listed in the sequence they first appear, so a reader who meets an unfamiliar mark can find it without searching. Where a word names both a rule and the number the rule produces, the entry says so, because that double duty is a frequent source of confusion for a reader working alone.
The reference is also the place to check the compendium's own choices. Where the conventions could reasonably differ, the desk has chosen one and holds to it, and the choice is recorded here rather than left to be inferred. A reader who notices an inconsistency between a paper and this page should treat it as an error and report it, because the reference is meant to be the single place where the notation is settled.