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How Not To Be Wrong
''How Not to Be Wrong: The Power of Mathematical Thinking'', written by Jordan Ellenberg, is a ''New York Times Best Selling'' book that connects various economic and societal philosophies with basic mathematics and statistical principles. Summary ''How Not to Be Wrong'' explains the mathematics behind some of simplest day-to-day thinking. It then goes into more complex decisions people make. For example, Ellenberg explains many misconceptions about lotteries and whether or not they can be mathematically beaten. Ellenberg uses mathematics to examine real-world issues ranging from the loving of straight lines in the reporting of obesity to the game theory of missing flights, from the relevance to digestion of regression to the mean to the counter-intuitive Berkson's paradox. Chapter summaries Part 1: Linearity Chapter 1, Less Like Sweden: Ellenberg encourages his readers to think nonlinearly, and know that "where you should go depends on where you are". To develop his th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jordan Ellenberg
Jordan Stuart Ellenberg (born October 30, 1971) is an American mathematician who is a professor of mathematics at the University of Wisconsin–Madison. His research involves arithmetic geometry. He is also an author of both fiction and non-fiction writing. Early life Ellenberg was born in Potomac, Maryland. He was a child prodigy who taught himself to read at the age of two by watching ''Sesame Street''. His mother discovered his ability one day while she was driving on the Capital Beltway when her toddler informed her: "The sign says ' Bethesda is to the right.'" In second grade, he helped his teenage babysitter with her math homework. By fourth grade, he was participating in high school competitions (such as the American Regions Mathematics League) as a member of the Montgomery County math team. And by eighth grade, he had started college-level work. He was part of the Johns Hopkins University Study of Mathematically Precocious Youth longitudinal cohort. He scored a perfect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical Greece, Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of philosophy within the Lyceum (classical), Lyceum and the wider Aristotelianism, Aristotelian tradition. His writings cover many subjects including Physics (Aristotle), physics, biology, zoology, metaphysics, logic, ethics, aesthetics, Poetics (Aristotle), poetry, theatre, music, rhetoric, psychology, linguistics, economics, politics, meteorology, History of geology, geology, and government. Aristotle provided a complex synthesis of the various philosophies existing prior to him. It was above all from his teachings that Western culture, the West inherited its intellectual lexicon, as well as problems and methods of inquiry. As a result, his philosophy has exerted a unique influence on almost every form of knowledge in the West a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Massachusetts Institute Of Technology
The Massachusetts Institute of Technology (MIT) is a Private university, private Land-grant university, land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the most prestigious and highly ranked academic institutions in the world. Founded in response to the increasing Technological and industrial history of the United States, industrialization of the United States, MIT adopted a European History of European universities, polytechnic university model and stressed laboratory instruction in applied science and engineering. MIT is one of three private land grant universities in the United States, the others being Cornell University and Tuskegee University. The institute has an Campus of the Massachusetts Institute of Technology, urban campus that extends more than a mile (1.6 km) alongside the Charles River, and encompasses a number of major off-campus fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Punnett Square
The Punnett square is a square diagram that is used to predict the genotypes of a particular cross or breeding experiment. It is named after Reginald C. Punnett, who devised the approach in 1905. The diagram is used by biologists to determine the probability of an offspring having a particular genotype. The Punnett square is a tabular summary of possible combinations of maternal alleles with paternal alleles. These tables can be used to examine the genotypical outcome probabilities of the offspring of a single trait (allele), or when crossing multiple traits from the parents. The Punnett square is a visual representation of Mendelian inheritance. It is important to understand the terms "heterozygous", "homozygous", "double heterozygote" (or homozygote), "dominant allele" and "recessive allele" when using the Punnett square method. For multiple traits, using the "forked-line method" is typically much easier than the Punnett square. Phenotypes may be predicted with at least better ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayes' Theorem
In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to an individual of a known age to be assessed more accurately (by conditioning it on their age) than simply assuming that the individual is typical of the population as a whole. One of the many applications of Bayes' theorem is Bayesian inference, a particular approach to statistical inference. When applied, the probabilities involved in the theorem may have different probability interpretations. With Bayesian probability interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence. Bayesian inference is fundamental to Baye ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Inference
Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the Sequential analysis, dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability". Introduction to Bayes' rule Formal explanation Bayesian inference derives the posterior probability as a consequence relation, consequence of two Antecedent (logic), antecedents: a prior probability and a "likelihood function" derived from a statistical model for the observed data. Bayesian inference computes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Facebook
Facebook is an online social media and social networking service owned by American company Meta Platforms. Founded in 2004 by Mark Zuckerberg with fellow Harvard College students and roommates Eduardo Saverin, Andrew McCollum, Dustin Moskovitz, and Chris Hughes, its name comes from the face book directories often given to American university students. Membership was initially limited to Harvard students, gradually expanding to other North American universities and, since 2006, anyone over 13 years old. As of July 2022, Facebook claimed 2.93 billion monthly active users, and ranked third worldwide among the most visited websites as of July 2022. It was the most downloaded mobile app of the 2010s. Facebook can be accessed from devices with Internet connectivity, such as personal computers, tablets and smartphones. After registering, users can create a profile revealing information about themselves. They can post text, photos and multimedia which are shared w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Netflix Prize
The Netflix Prize was an open competition for the best collaborative filtering algorithm to predict user ratings for films, based on previous ratings without any other information about the users or films, i.e. without the users being identified except by numbers assigned for the contest. The competition was held by Netflix, an online DVD-rental and video streaming service, and was open to anyone who is neither connected with Netflix (current and former employees, agents, close relatives of Netflix employees, etc.) nor a resident of certain blocked countries (such as Cuba or North Korea). On September 21, 2009, the grand prize of was given to the BellKor's Pragmatic Chaos team which bested Netflix's own algorithm for predicting ratings by 10.06%. Problem and data sets Netflix provided a ''training'' data set of 100,480,507 ratings that 480,189 users gave to 17,770 movies. Each training rating is a quadruplet of the form . The user and movie fields are integer IDs, while grades ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Inference
Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the Sequential analysis, dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability". Introduction to Bayes' rule Formal explanation Bayesian inference derives the posterior probability as a consequence relation, consequence of two Antecedent (logic), antecedents: a prior probability and a "likelihood function" derived from a statistical model for the observed data. Bayesian inference computes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Egon Pearson
Egon Sharpe Pearson (11 August 1895 – 12 June 1980) was one of three children of Karl Pearson and Maria, née Sharpe, and, like his father, a leading British statistician. Career He was educated at Winchester College and Trinity College, Cambridge, and succeeded his father as professor of statistics at University College London and as editor of the journal ''Biometrika''. Pearson is best known for development of the Neyman–Pearson lemma of statistical hypothesis testing. He was elected a Fellow of the Econometric Society in 1948. He was President of the Royal Statistical Society in 1955–56, and was awarded its Guy Medal in gold in 1955. He was appointed a CBE in 1946. He was elected a Fellow of the Royal Society in March 1966. His candidacy citation read: Family life Pearson married Eileen Jolly in 1934 and the couple had two daughters, Judith and Sarah. Eileen died of pneumonia in 1949. Pearson subsequently married Margaret Theodosia Scott in 1967 and the coupl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jerzy Neyman
Jerzy Neyman (April 16, 1894 – August 5, 1981; born Jerzy Spława-Neyman; ) was a Polish mathematician and statistician who spent the first part of his professional career at various institutions in Warsaw, Poland and then at University College London, and the second part at the University of California, Berkeley. Neyman first introduced the modern concept of a confidence interval into statistical hypothesis testing and co-revised Ronald Fisher's null hypothesis testing (in collaboration with Egon Pearson). Life and career He was born into a Polish family in Bendery, in the Bessarabia Governorate of the Russian Empire, the fourth of four children of Czesław Spława-Neyman and Kazimiera Lutosławska. His family was Roman Catholic and Neyman served as an altar boy during his early childhood. Later, Neyman would become an agnostic. Neyman's family descended from a long line of Polish nobles and military heroes. He graduated from the Kamieniec Podolski gubernial gymnasium for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
P-value
In null-hypothesis significance testing, the ''p''-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. A very small ''p''-value means that such an extreme observed outcome would be very unlikely under the null hypothesis. Reporting ''p''-values of statistical tests is common practice in academic publications of many quantitative fields. Since the precise meaning of ''p''-value is hard to grasp, misuse is widespread and has been a major topic in metascience. Basic concepts In statistics, every conjecture concerning the unknown probability distribution of a collection of random variables representing the observed data X in some study is called a ''statistical hypothesis''. If we state one hypothesis only and the aim of the statistical test is to see whether this hypothesis is tenable, but not to investigate other specific hypotheses, then such a test is called a null ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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