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Bonferroni
Carlo Emilio Bonferroni (28 January 1892 – 18 August 1960) was an Italian mathematician who worked on probability theory. Biography Bonferroni studied piano and conducting in Turin Conservatory and at University of Turin under Giuseppe Peano and Corrado Segre, where he obtained his laurea. During this time he also studied at University of Vienna and ETH Zurich. During World War I, he was an officer among the engineers. Bonferroni held a position as assistant professor at the Polytechnic University of Turin, and in 1923 took up the chair of financial mathematics at the Economics Institute of the University of Bari. In 1933 he transferred to University of Florence, where he held his chair until his death. Bonferroni is best known for the Bonferroni inequalities (a generalization of the union bound), and for the Bonferroni correction in statistics (which he did not invent, but which is related to the Bonferroni inequalities). See also * Bonferroni inequalities * Bonferroni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bonferroni Correction
In statistics, the Bonferroni correction is a method to counteract the multiple comparisons problem. Background The method is named for its use of the Bonferroni inequalities. An extension of the method to confidence intervals was proposed by Olive Jean Dunn. Statistical hypothesis testing is based on rejecting the null hypothesis if the likelihood of the observed data under the null hypotheses is low. If multiple hypotheses are tested, the probability of observing a rare event increases, and therefore, the likelihood of incorrectly rejecting a null hypothesis (i.e., making a Type I error) increases. The Bonferroni correction compensates for that increase by testing each individual hypothesis at a significance level of \alpha/m, where \alpha is the desired overall alpha level and m is the number of hypotheses. For example, if a trial is testing m = 20 hypotheses with a desired \alpha = 0.05, then the Bonferroni correction would test each individual hypothesis at \alpha = 0.05/20 = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bonferroni Inequalities
In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events. This inequality provides an upper bound on the probability of occurrence of at least one of a countable number of events in terms of the individual probabilities of the events. Boole's inequality is named for its discoverer George Boole. Formally, for a countable set of events ''A''1, ''A''2, ''A''3, ..., we have :\left(\bigcup_^ A_i \right) \le \sum_^ (A_i). In measure-theoretic terms, Boole's inequality follows from the fact that a measure (and certainly any probability measure) is ''σ''- sub-additive. Proof Proof using induction Boole's inequality may be proved for finite collections of n events using the method of induction. For the n=1 case, it follows that :\mathbb P(A_1) \le \mathbb P(A_1). For the case n, we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boole's Inequality
In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events. This inequality provides an upper bound on the probability of occurrence of at least one of a countable number of events in terms of the individual probabilities of the events. Boole's inequality is named for its discoverer George Boole. Formally, for a countable set of events ''A''1, ''A''2, ''A''3, ..., we have :\left(\bigcup_^ A_i \right) \le \sum_^ (A_i). In measure-theoretic terms, Boole's inequality follows from the fact that a measure (and certainly any probability measure) is ''σ''- sub-additive. Proof Proof using induction Boole's inequality may be proved for finite collections of n events using the method of induction. For the n=1 case, it follows that :\mathbb P(A_1) \le \mathbb P(A_1). For the case n, we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Florence
The University of Florence (Italian: ''Università degli Studi di Firenze'', UniFI) is an Italian public research university located in Florence, Italy. It comprises 12 schools and has around 50,000 students enrolled. History The first university in Florence was the Studium Generale, which was established by the Florentine Republic in 1321. The Studium was recognized by Pope Clement VI in 1349, and authorized to grant regular degrees. The Pope also established that the first Italian faculty of theology would be in Florence. The Studium became an imperial university in 1364, but was moved to Pisa in 1473 when Lorenzo the Magnificent gained control of Florence. Charles VIII moved it back from 1497 to 1515, but it was moved to Pisa again when the Medici family returned to power. The modern university dates from 1859, when a group of disparate higher-studies institutions grouped together in the Istituto di Studi Pratici e di Perfezionamento, which a year later was recognized as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bergamo
Bergamo (; lmo, Bèrghem ; from the proto- Germanic elements *''berg +*heim'', the "mountain home") is a city in the alpine Lombardy region of northern Italy, approximately northeast of Milan, and about from Switzerland, the alpine lakes Como and Iseo and 70 km (43 mi) from Garda and Maggiore. The Bergamo Alps (''Alpi Orobie'') begin immediately north of the city. With a population of around 120,000, Bergamo is the fourth-largest city in Lombardy. Bergamo is the seat of the Province of Bergamo, which counts over 1,103,000 residents (2020). The metropolitan area of Bergamo extends beyond the administrative city limits, spanning over a densely urbanized area with slightly less than 500,000 inhabitants. The Bergamo metropolitan area is itself part of the broader Milan metropolitan area, home to over 8 million people. The city of Bergamo is composed of an old walled core, known as ''Città Alta'' ("Upper Town"), nestled within a system of hills, and the modern expan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Florence Faculty
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the designation is reserved for colleges that have a graduate school. The word ''university'' is derived from the Latin ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". The first universities were created in Europe by Catholic Church monks. The University of Bologna (''Università di Bologna''), founded in 1088, is the first university in the sense of: *Being a high degree-awarding institute. *Having independence from the ecclesiastic schools, although conducted by both clergy and non-clergy. *Using the word ''universitas'' (which was coined at its foundation). *Issuing secular and non-secular degrees: grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Bari Faculty
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the designation is reserved for colleges that have a graduate school. The word ''university'' is derived from the Latin ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". The first universities were created in Europe by Catholic Church monks. The University of Bologna (''Università di Bologna''), founded in 1088, is the first university in the sense of: *Being a high degree-awarding institute. *Having independence from the ecclesiastic schools, although conducted by both clergy and non-clergy. *Using the word ''universitas'' (which was coined at its foundation). *Issuing secular and non-secular degrees: grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polytechnic University Of Turin Faculty
Polytechnic is most commonly used to refer to schools, colleges, or universities that qualify as an institute of technology or vocational university also sometimes called universities of applied sciences. Polytechnic may also refer to: Education Tertiary education * Bahrain Polytechnic, in Isa Town * Polytechnic (Greece), schools that teach engineering * Polytechnic (Portugal), schools that offer practical training, profession-oriented * École polytechnique, Polytechnic School (France), Paris * Polytechnic University (New York), New York University Tandon School of Engineering * Polytechnic (United Kingdom), a type of tertiary education teaching institution in the UK between 1965 and 1992 * Polytechnic (Singapore), tertiary institutions in Singapore * Jakarta State Polytechnic, Indonesia * Tokyo Polytechnic University, Japan * Hong Kong Polytechnic University (may be abbreviated as PolyU) * Polytechnic University of Catalonia, or BarcelonaTech, Spain * Rensselaer Polytechnic I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Turin Alumni
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the designation is reserved for colleges that have a graduate school. The word ''university'' is derived from the Latin ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". The first universities were created in Europe by Catholic Church monks. The University of Bologna (''Università di Bologna''), founded in 1088, is the first university in the sense of: *Being a high degree-awarding institute. *Having independence from the ecclesiastic schools, although conducted by both clergy and non-clergy. *Using the word ''universitas'' (which was coined at its foundation). *Issuing secular and non-secular degrees: grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Italian Statisticians
Italian(s) may refer to: * Anything of, from, or related to the people of Italy over the centuries ** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom ** Italian language, a Romance language *** Regional Italian, regional variants of the Italian language ** Languages of Italy, languages and dialects spoken in Italy ** Italian culture, cultural features of Italy ** Italian cuisine, traditional foods ** Folklore of Italy, the folklore and urban legends of Italy ** Mythology of Italy, traditional religion and beliefs Other uses * Italian dressing, a vinaigrette-type salad dressing or marinade * Italian or Italian-A, alternative names for the Ping-Pong virus, an extinct computer virus See also * * * Italia (other) * Italic (other) * Italo (other) * The Italian (other) * Italian people (other) Italian people may refer to: * in terms of ethnicity: all ethnic Italians, in and outside of Italy * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theorists
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These conce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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