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Per Martin-Löf
Per Erik Rutger Martin-Löf (/ˈmɑːrtɪn lɒf/;[1] Swedish: [ˈmaʈiːn ˈløːv];[2] born May 8, 1942) 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
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Stockholm University
Stockholm
Stockholm
University
University
(Swedish: Stockholms universitet) is a public university in Stockholm, Sweden, founded as a college in 1878, with university status since 1960. Stockholm
Stockholm
University
University
has two scientific fields: the natural sciences and the humanities/social sciences. With over 70,000 students at four different faculties: law, humanities, the mathematical, and natural sciences, it is one of the largest universities in Scandinavia
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Theory Of Computation
In theoretical computer science and mathematics, the theory of computation is the branch that deals with how efficiently problems can be solved on a model of computation, using an algorithm. The field is divided into three major branches: automata theory and language, computability theory, and computational complexity theory, which are linked by the question: "What are the fundamental capabilities and limitations of computers?".[1] In order to perform a rigorous study of computation, computer scientists work with a mathematical abstraction of computers called a model of computation
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Computer Science
Computer science
Computer science
is the study of the theory, experimentation, and engineering that form the basis for the design and use of computers. It is the scientific and practical approach to computation and its applications and the systematic study of the feasibility, structure, expression, and mechanization of the methodical procedures (or algorithms) that underlie the acquisition, representation, processing, storage, communication of, and access to, information. An alternate, more succinct definition of computer science is the study of automating algorithmic processes that scale. A computer scientist specializes in the theory of computation and the design of computational systems.[1] Its fields can be divided into a variety of theoretical and practical disciplines
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Exponential Families
In probability and statistics, an exponential family is a set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, based on some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural sets of distributions to consider. The concept of exponential families is credited to[1] E. J. G. Pitman,[2] G. Darmois,[3] and B. O. Koopman[4] in 1935–36
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Missing Data
In statistics, missing data, or missing values, occur when no data value is stored for the variable in an observation. Missing data
Missing data
are a common occurrence and can have a significant effect on the conclusions that can be drawn from the data. Missing data
Missing data
can occur because of nonresponse: no information is provided for one or more items or for a whole unit ("subject"). Some items are more likely to generate a nonresponse than others: for example items about private subjects such as income. Attrition ("Dropout") is a type of missingness that can occur in longitudinal studies - for instance studying development where a measurement is repeated after a certain period of time
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Model Selection
Model selection
Model selection
is the task of selecting a statistical model from a set of candidate models, given data. In the simplest cases, a pre-existing set of data is considered. However, the task can also involve the design of experiments such that the data collected is well-suited to the problem of model selection. Given candidate models of similar predictive or explanatory power, the simplest model is most likely to be the best choice (Occam's razor). Konishi & Kitagawa (2008, p. 75) state, "The majority of the problems in statistical inference can be considered to be problems related to statistical modeling"
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Bird-watcher
Birdwatching, or birding, is a form of wildlife observation in which the observation of birds is a recreational activity or citizen science. It can be done with the naked eye, through a visual enhancement device like binoculars and telescopes, by listening for bird sounds,[1][2] or by watching public webcams. Birdwatching often involves a significant auditory component, as many bird species are more easily detected and identified by ear than by eye
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Kolmogorov Complexity
In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity
Kolmogorov complexity
of an object, such as a piece of text, is the length of the shortest computer program (in a predetermined programming language) that produces the object as output. It is a measure of the computational resources needed to specify the object, and is also known as descriptive complexity, Kolmogorov–Chaitin complexity, algorithmic complexity, algorithmic entropy, or program-size complexity. It is named after Andrey Kolmogorov, who first published on the subject in 1963.[1][2] The notion of Kolmogorov complexity
Kolmogorov complexity
can be used to state and prove impossibility results akin to Cantor's diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem
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Richard Von Mises
Richard Edler
Edler
von Mises[1] (/ˈmiːziːz/;[2] German: [fɔn ˈmiːzəs]; 19 April 1883 – 14 July 1953) was a scientist and mathematician who worked on solid mechanics, fluid mechanics, aerodynamics, aeronautics, statistics and probability theory. He held the position of Gordon-McKay Professor of Aerodynamics
Aerodynamics
and Applied Mathematics at Harvard University. He described his work in his own words shortly before his death as being on"... practical analysis, integral and differential equations, mechanics, hydrodynamics and aerodynamics, constructive geometry, probability calculus, statistics and philosophy."[3]Although best known for his mathematical work, Mises also contributed to the philosophy of science as a neo-positivist, following the line of Ernst Mach
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Randomness Test
Randomness tests (or tests for randomness), in data evaluation, are used to analyze the distribution of a set of data to see if it is random (patternless). In stochastic modeling, as in some computer simulations, the hoped-for randomness of potential input data can be verified, by a formal test for randomness, to show that the data are valid for use in simulation runs. In some cases, data reveals an obvious non-random pattern, as with so-called "runs in the data" (such as expecting random 0–9 but finding "4 3 2 1 0 4 3 2 1..." and rarely going above 4). If a selected set of data fails the tests, then parameters can be changed or other randomized data can be used which does pass the tests for randomness. There are many practical measures of randomness for a binary sequence. These include measures based on statistical tests, transforms, and complexity or a mixture of these
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Probability
Related concepts and fundamentals:Agnosticism Epistemology Presupposition Probabilityv t e Probability
Probability
is the measure of the likelihood that an event will occur.[1] See glossary of probability and statistics. Probability
Probability
is quantified as a number between 0 and 1, where, loosely speaking,[2] 0 indicates impossibility and 1 indicates certainty.[3][4] The higher the probability of an event, the more likely it is that the event will occur
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Edmund Husserl
Edmund Gustav Albrecht Husserl
Husserl
(/ˈhʊsərl/;[14] German: [ˈhʊsɐl]; 8 April 1859 – 27 April 1938)[15] was a German[16][17] philosopher who established the school of phenomenology. In his early work, he elaborated critiques of historicism and of psychologism in logic based on analyses of intentionality. In his mature work, he sought to develop a systematic foundational science based on the so-called phenomenological reduction. Arguing that transcendental consciousness sets the limits of all possible knowledge, Husserl
Husserl
re-defined phenomenology as a transcendental-idealist philosophy
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Data Compression
In signal processing, data compression, source coding,[1] or bit-rate reduction involves encoding information using fewer bits than the original representation.[2] Compression can be either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in lossless compression. Lossy compression reduces bits by removing unnecessary or less important information.[3] The process of reducing the size of a data file is often referred to as data compression. In the context of data transmission, it is called source coding; encoding done at the source of the data before it is stored or transmitted.[4] Source coding should not be confused with channel coding, for error detection and correction or line coding, the means for mapping data onto a signal. Compression is useful because it reduces resources required to store and transmit data
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Gambling
Gambling
Gambling
is the wagering of money or something of value (referred to as "the stakes") on an event with an uncertain outcome with the primary intent of winning money or material goods. Gambling
Gambling
thus requires three elements be present: consideration, chance and prize.[1] The outcome of the wager is often immediate, such as a single roll of dice, a spin of a roulette wheel, or a horse crossing the finish line, but longer time frames are also common, allowing wagers on the outcome of a future sports contest or even an entire sports season. The term "gaming"[2] in this context typically refers to instances in which the activity has been specifically permitted by law. The two words are not mutually exclusive; i.e., a "gaming" company offers (legal) "gambling" activities to the public[3] and may be regulated by one of many gaming control boards, for example, the Nevada Gaming Control Board
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Betting
Gambling
Gambling
is the wagering of money or something of value (referred to as "the stakes") on an event with an uncertain outcome with the primary intent of winning money or material goods. Gambling
Gambling
thus requires three elements be present: consideration, chance and prize.[1] The outcome of the wager is often immediate, such as a single roll of dice, a spin of a roulette wheel, or a horse crossing the finish line, but longer time frames are also common, allowing wagers on the outcome of a future sports contest or even an entire sports season. The term "gaming"[2] in this context typically refers to instances in which the activity has been specifically permitted by law. The two words are not mutually exclusive; i.e., a "gaming" company offers (legal) "gambling" activities to the public[3] and may be regulated by one of many gaming control boards, for example, the Nevada Gaming Control Board
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