Bioinformatics now entails the creation and advancement of databases, algorithms, computational and statistical techniques and theory to solve formal and practical problems arising from the management and analysis of biological data.

The importance of the theory lay in the fact that it confirmed the kinetic theory's account of the second law of thermodynamics as being an essentially statistical law.

Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, and combinatorics also has many applications in optimization, computer science, ergodic theory and statistical physics.

It incorporates the bijective approach and various tools in analysis, analytic number theory, and has connections with statistical mechanics.

* Conjugate pairing of probability distributions, in the Fourier-analytic theory of characteristic functions and statistical mechanics

A theory of statistical inference was developed by Charles S. Peirce in " Illustrations of the Logic of Science " ( 1877 – 1878 ) and " A Theory of Probable Inference " ( 1883 ), two publications that emphasized the importance of randomization-based inference in statistics.

However, in robust statistics, statistical theory goes on to consider the balance between having good properties, if tightly defined assumptions hold, and having less good properties that hold under wider conditions.

Enrico Fermi (; 29 September 1901 – 28 November 1954 ) was an Italian physicist, naturalized American later in his life, particularly known for his work on the development of the first nuclear reactor, Chicago Pile-1, and for his contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics.

In other words, there is some yet undiscovered theory of nature to which quantum mechanics acts as a kind of statistical approximation ( albeit an exceedingly successful one ).

Econometric theory uses statistical theory to evaluate and develop econometric methods.

More precisely, and technically, a Feynman diagram is a graphical representation of a perturbative contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory.

In Shannon's revolutionary and groundbreaking paper, the work for which had been substantially completed at Bell Labs by the end of 1944, Shannon for the first time introduced the qualitative and quantitative model of communication as a statistical process underlying information theory, opening with the assertion that

Using a statistical description for data, information theory quantifies the number of bits needed to describe the data, which is the information entropy of the source.

Some statistical evidence for the theory has also been advanced by Anwar Shaikh.

In each case, the designation " linear " is used to identify a subclass of models for which substantial reduction in the complexity of the related statistical theory is possible.

This statistical theory, proposed by Alfred Saupe and Wilhelm Maier, includes contributions from an attractive intermolecular potential from an induced dipole moment between adjacent liquid crystal molecules.

Some Empiricist theories of language acquisition include the statistical learning theory Charles F. Hockett of language acquisition, Relational Frame Theory, functionalist linguistics, social interactionist theory, and usage-based language acquisition.

In the 1940s, Patrick Blackett combined these statistical theories with microeconomic theory and gave birth to the science of operations research.

Probability theory was used in statistical mechanics.

There are numerous algorithms available for training neural network models ; most of them can be viewed as a straightforward application of optimization theory and statistical estimation.

To gain this understanding, neuroscientists strive to make a link between observed biological processes ( data ), biologically plausible mechanisms for neural processing and learning ( biological neural network models ) and theory ( statistical learning theory and information theory ).

A statistical copolymer in which the probability of finding a particular type of monomer residue at a particular point in the chain is independent of the types of surrounding monomer residue may be referred to as a truly random copolymer ( 3 ).

The Municipality of Bucharest, along with the surrounding Ilfov County, forms the Bucharest development region, which is equivalent to NUTS-II regions in the European Union and is used by the European Union and the Romanian Government for statistical analysis and regional development.

The Bureau of Economic Analysis combines the city of Bedford with surrounding Bedford county for statistical purposes.

Because of the fluidity of the term " metropolitan statistical area ," the term used colloquially is more often " metro service area ," " metro area ," or " MSA " taken to include not only a city, but also surrounding suburban, exurban and sometimes rural areas, all which it is presumed to influence.

The Bureau of Economic Analysis combines the city of Winchester with surrounding Frederick County for statistical purposes.

The Bureau of Economic Analysis combines the city of Poquoson with surrounding York county for statistical purposes.

The Bureau of Economic Analysis combines the city of Norton with surrounding Wise County for statistical purposes.

The Bureau of Economic Analysis combines the city of Emporia with surrounding Greensville county for statistical purposes.

* Hubbard Lake is the name of a statistical area applied by the U. S. Census Bureau to the populated area surrounding the Hubbard Lake body of water and includes portions of three townships.

The statistical area " Sas van Gent ", which also can include the surrounding countryside, has a population of around 3, 920 inhabitants.

The statistical area " De Lier ", which also can include the peripheral parts of the village, as well as the surrounding countryside, has a population of around 11, 470.

The statistical area "' s-Gravenzande ", which also can include the peripheral parts of the village, as well as the surrounding countryside, has a population of around 19, 750.

The statistical area " Naaldwijk ", which also can include the surrounding countryside, has a population of around 17, 370.

The statistical area " Wateringen ", which also can include the surrounding countryside, has a population of around 13, 880.

The statistical area " Monster ", which also can include the surrounding countryside, has a population of around 14, 540.

The statistical area " Duivendrecht ", which also can include the surrounding countryside, has a population of around 4880.

The statistical area " Eelde ", which also can include the surrounding countryside, has a population of around 7110.

* the statistical New York metropolitan area consisting of New York City and surrounding counties of New York, New Jersey, Connecticut and Pennsylvania

The statistical area " Bourtange ", which also can include the surrounding countryside, has a population of around 530.

The statistical district " Assendelft ", which covers the village and the surrounding countryside, has a population of around 21, 000.

The statistical district " Krommenie ", which covers the village and the surrounding countryside, has a population of around 17, 330.

The statistical district " Westzaan ", which covers the village and the surrounding countryside, has a population of around 4580.

The statistical area " Nieuwpoort ", which also can include the surrounding countryside, has a population of around 1370 ( 2006 ).

The aire urbaine ( French for " urban area ") is a statistical region created by the INSEE ( National statistics bureau of France ) that comprises a commuter belt ( couronne périurbaine ) surrounding a contiguous urban core ( pôle urbain ).