**2. Models**

Habitual models of the measurement experiment are constructed from the principal *f* and stochastic *η* components, formally *M* (*f*, *η*). The principal component is a mathematical description of the physical principle of the experiment. Usually, this is an arithmetic formula, but sometimes the algorithm decides equation or even numerical simulation.

The stochastic component is a description of the random (or considered to be) influence on the result of the experiment. Often, this description consists of a system of equivalent noise sources with some specified characteristics.

The components of the model are formalized as headings of procedures whose variables are divided into two parts—the variable values of which must be determined quite accurately by the time of the working experiment, and the variable *X* whose values are estimated from the data *D* is obtained as a result of the experiment (*M*, *D*) → *X*, where both the experimental data and the evaluated variables can be either simple or complex data structures.

The main purpose of the model is to formulate a prediction. For metrological tasks, we set the value of the controlled parameters of the model, and from it we obtain a data structure modeling experimental data. Two modeling methods that can be compared with the definitions of probability have been distributed. The Monte Carlo method (MCM) is comparable to a countable probability, and the method of converting the densities (MCD) is comparable with the axiomatic probability.

In metrological statistics the most widespread one is the simple additive noise model (additive random error model) *di* <sup>=</sup> *<sup>x</sup>* <sup>+</sup> *<sup>η</sup><sup>i</sup>* , where *di* is the observed process; *x* is the value under measurement (measurand) (is constant throughout the experiment); and *η<sup>i</sup>* is a random impurity, at each time of measurement *i* having a different value. It is the simplest model of a direct measurement experiment. It is also called the trivial model.

It is important that it is a priori known about a random component. It is usually assumed that only the form of distribution of probability of the source of chance is known. It is necessary to estimate the value of the constant component (as a shift parameter of a known distribution) over a small number of data affected by a random error with zero shift (for simplicity of interpretation) but with a scattering magnitude of unknown magnitude. It is also assumed that the time between measurements is so large that the data sampling elements are statistically independent.
