MDM Reference • Glossary & notation
Glossary and Notation
The symbols below carry the same meaning on every page of this reference. The list is short by design, and it holds only the signs that recur.
Symbols
| Symbol | Reading |
|---|---|
| E[X] | the expectation of the random variable X |
| Var(X) | the variance, the expected squared departure from the mean |
| s | the standard deviation, the square root of the variance |
| Cov(X,Y) | the covariance of two variables |
| r | the correlation, a standardised covariance |
| S | the square arrangement of covariances |
| n | the number of readings in a sample |
| L | the likelihood of a sample under a stated parameter |
| f | a frequency, the rate of repetition of a component |
| phi | a phase, the starting point of a repeating form |
Terms
- Population the whole collection about which a statement is wanted.
- Sample the finite part of a population that is observed.
- Estimator a rule that turns a sample into a proposed value.
- Bias the expected departure of an estimator from its target.
- Likelihood the density of the sample read as a function of the parameter.
- Spectrum the distribution of variation across rates.
- Coherence the rate-by-rate tendency of two series to keep a fixed phase relation.
- Stationarity a constant mean and a covariance depending only on separation.
- Autocovariance the covariance of a series with itself at a stated lag.
- Ergodicity the agreement of a long-path average with a whole-collection average.
Conventions
Time is written in the lower case. Columns of readings are written as bold letters where a scalar might otherwise be confused with a list. Estimates are marked when an exact relation is not meant. A bar over a letter marks a sample average, and a hat over a letter marks an estimate.
Use of the glossary
Where a term is defined in an essay, the essay gives the fuller treatment and the glossary gives only the sign and the short reading. A reader who meets an unfamiliar symbol should turn here first and then to the relevant cell. The glossary is revised whenever an essay introduces a new sign, so that the two stay in step.
Reading a symbol in context
A symbol is a promise that a meaning will be held steady, and the promise is kept only within a stated setting. The same letter may carry a different sense in a different branch of the literature, and a reader who arrives with an outside habit should check the table above rather than assume. Where a clash is possible, the essays spell the sense in words beside the symbol.
On lowered marks and raised marks
A small mark set low beside a letter usually names the unit to which a quantity belongs, while a small mark set high usually names a power or a transpose. The two are kept apart in the printing, and a reader should keep them apart in reading. Where a raised mark might bear either sense, the essay says which is meant rather than leaving the reader to judge.
Extending the list
The table grows with the reference. When an essay needs a sign that is not yet listed, the sign is added here in the same revision, so that the glossary and the essays never drift apart. A reader who finds a symbol that is missing from the table is asked to report it to the desk, and the omission will be repaired.