Frequentist probability or frequentism is an interpretation of probability; it defines an event's probability as the limit of its relative frequency in many trials. Probabilities can be found by a repeatable objective process. The continued use of frequentist methods in scientific inference, however, has been called into question.
In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, cryptography and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance.
Geostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets. Developed originally to predict probability distributions of ore grades for mining operations, it is currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology, oceanography, geochemistry, geometallurgy, geography, forestry, environmental control, landscape ecology, soil science, and agriculture. Geostatistics is applied in varied branches of geography, particularly those involving the spread of diseases (epidemiology), the practice of commerce and military planning (logistics), and the development of efficient spatial networks. Geostatistical algorithms are incorporated in many places, including geographic information systems (GIS).
In probability theory and statistics, the cumulantsκn of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution. Any two probability distributions whose moments are identical will have identical cumulants as well, and vice versa.
Harald August Bohr was a Danish mathematician and footballer. After receiving his doctorate in 1910, Bohr became an eminent mathematician, founding the field of almost periodic functions. His brother was the Nobel Prize-winning physicist Niels Bohr. He was a member of the Danish national football team for the 1908 Summer Olympics, where he won a silver medal.
The Gram–Charlier A series, and the Edgeworth series are series that approximate a probability distribution in terms of its cumulants. The series are the same; but, the arrangement of terms differ. The key idea of these expansions is to write the characteristic function of the distribution whose probability density function f is to be approximated in terms of the characteristic function of a distribution with known and suitable properties, and to recover f through the inverse Fourier transform.
Jørgen Pedersen Gram was a Danish actuary and mathematician who was born in Nustrup, Duchy of Schleswig, Denmark and died in Copenhagen, Denmark.
Anders Hjorth Hald was a Danish statistician. He was a professor at the University of Copenhagen from 1960 to 1982. While a professor, he did research in industrial quality control and other areas, and also authored textbooks. After retirement, he made important contributions to the history of statistics.
Per Erik Rutger Martin-Löf is a Swedish logician, philosopher, and mathematical statistician. He is internationally renowned for his work on the foundations of probability, statistics, mathematical logic, and computer science. Since the late 1970s, Martin-Löf's publications have been mainly in logic. In philosophical logic, Martin-Löf has wrestled with the philosophy of logical consequence and judgment, partly inspired by the work of Brentano, Frege, and Husserl. In mathematical logic, Martin-Löf has been active in developing intuitionistic type theory as a constructive foundation of mathematics; Martin-Löf's work on type theory has influenced computer science.
William Fleetwood Sheppard FRSE LLM Australian-British civil servant, mathematician and statistician remembered for his work in finite differences, interpolation and statistical theory, known in particular for the eponymous Sheppard's corrections.
In mathematics, in the area of statistical analysis, the bispectrum is a statistic used to search for nonlinear interactions.
Johan Frederik Steffensen was a Danish mathematician, statistician, and actuary who did research in the fields of calculus of finite differences and interpolation. He was professor of actuarial science at the University of Copenhagen from 1923 to 1943. Steffensen's inequality and Steffensen's method are named after him. He was an Invited Speaker at the 1912 International Congress of Mathematicians (ICM) in Cambridge, England and at the 1924 ICM in Toronto.
... His more important works included the theory of statistics (1923), interpolation (1925), insurance mathematics (1934) and the calculation of interest (1936). ... He was President of the Danish Actuarial Society in 1922-24 and 1930-33, and of the Danish Mathematical Society in 1930-36 ...
Sir William Palin Elderton KBE PhD (Oslo) (1877–1962) was a British actuary who served as president of the Institute of Actuaries (1932–1934). Elderton also had a very long association with the statistical journal Biometrika. In its early days he published several articles, and in 1935 he became chairman of the Biometrika Trust.
Statistics, in the modern sense of the word, began evolving in the 18th century in response to the novel needs of industrializing sovereign states. The evolution of statistics was, in particular, intimately connected with the development of European states following the peace of Westphalia (1648), and with the development of probability theory, which put statistics on a firm theoretical basis.
Heinrich Carl Franz Emil Timerding was a German mathematician, professor at the Braunschweig University of Technology, mainly known for his contributions to probability theory. He was awarded the Brunswick and the Prussian War Merit Cross, the Ritterkreuz of the Order of Henry the Lion, and in 1938 the Nazi Civil Service Faithful Service Medal.
The following is a timeline of probability and statistics.
Ludvig Henrik Ferdinand Oppermann was a Danish mathematician and philologist who formulated Oppermann's conjecture on the distribution of prime numbers.
Henry Lewis Rietz was an American mathematician, actuarial scientist, and statistician, who was a leader in the development of statistical theory. He became the first president of the Institute of Mathematical Statistics.
The cluster-expansion approach is a technique in quantum mechanics that systematically truncates the BBGKY hierarchy problem that arises when quantum dynamics of interacting systems is solved. This method is well suited for producing a closed set of numerically computable equations that can be applied to analyze a great variety of many-body and/or quantum-optical problems. For example, it is widely applied in semiconductor quantum optics and it can be applied to generalize the semiconductor Bloch equations and semiconductor luminescence equations.
