Mean percentage errorIn statistics, the mean percentage error (MPE) is the computed average of percentage errors by which forecasts of a model differ from actual values of the quantity being forecast. The formula for the mean percentage error is: where at is the actual value of the quantity being forecast, ft is the forecast, and n is the number of different times for which the variable is forecast. Because actual rather than absolute values of the forecast errors are used in the formula, positive and negative forecast errors can offset each other; as a result the formula can be used as a measure of the bias in the forecasts.
Errors and residualsIn statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "true value" (not necessarily observable). The error of an observation is the deviation of the observed value from the true value of a quantity of interest (for example, a population mean). The residual is the difference between the observed value and the estimated value of the quantity of interest (for example, a sample mean).
Average absolute deviationThe average absolute deviation (AAD) of a data set is the average of the absolute deviations from a central point. It is a summary statistic of statistical dispersion or variability. In the general form, the central point can be a mean, median, mode, or the result of any other measure of central tendency or any reference value related to the given data set. AAD includes the mean absolute deviation and the median absolute deviation (both abbreviated as MAD). Several measures of statistical dispersion are defined in terms of the absolute deviation.
Rydberg constantIn spectroscopy, the Rydberg constant, symbol for heavy atoms or for hydrogen, named after the Swedish physicist Johannes Rydberg, is a physical constant relating to the electromagnetic spectra of an atom. The constant first arose as an empirical fitting parameter in the Rydberg formula for the hydrogen spectral series, but Niels Bohr later showed that its value could be calculated from more fundamental constants according to his model of the atom.
Predictive modellingPredictive modelling uses statistics to predict outcomes. Most often the event one wants to predict is in the future, but predictive modelling can be applied to any type of unknown event, regardless of when it occurred. For example, predictive models are often used to detect crimes and identify suspects, after the crime has taken place. In many cases, the model is chosen on the basis of detection theory to try to guess the probability of an outcome given a set amount of input data, for example given an email determining how likely that it is spam.
Planck constantThe Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalence, the relationship between mass and frequency. Specifically, a photon's energy is equal to its frequency multiplied by the Planck constant. The constant is generally denoted by . The reduced Planck constant, or Dirac constant, equal to divided by , is denoted by .
Phase transitionIn chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure.
Frequency modulationFrequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. The technology is used in telecommunications, radio broadcasting, signal processing, and computing. In analog frequency modulation, such as radio broadcasting, of an audio signal representing voice or music, the instantaneous frequency deviation, i.e. the difference between the frequency of the carrier and its center frequency, has a functional relation to the modulating signal amplitude.
Fixed-point iterationIn numerical analysis, fixed-point iteration is a method of computing fixed points of a function. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is which gives rise to the sequence of iterated function applications which is hoped to converge to a point . If is continuous, then one can prove that the obtained is a fixed point of , i.e., More generally, the function can be defined on any metric space with values in that same space.
Predictive analyticsPredictive analytics is a form of business analytics applying machine learning to generate a predictive model for certain business applications. As such, it encompasses a variety of statistical techniques from predictive modeling and machine learning that analyze current and historical facts to make predictions about future or otherwise unknown events. It represents a major subset of machine learning applications; in some contexts, it is synonymous with machine learning.
