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Probability Kinematics
Radical probabilism is a hypothesis in philosophy, in particular epistemology, and probability theory that holds that no facts are known for certain. That view holds profound implications for statistical inference. The philosophy is particularly associated with Richard Jeffrey who wittily characterised it with the ''dictum'' "It's probabilities all the way down." Background Bayes' theorem states a rule for updating a probability conditioned on other information. In 1967, Ian Hacking argued that in a static form, Bayes' theorem only connects probabilities that are held simultaneously; it does not tell the learner how to update probabilities when new evidence becomes available over time, contrary to what contemporary Bayesians suggested. According to Hacking, adopting Bayes' theorem is a temptation. Suppose that a learner forms probabilities ''P''old(''A'' & ''B'') = ''p'' and ''P''old(''B'') = ''q''. If the learner subsequently learns that ''B'' is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some sources claim the term was coined by Pythagoras ( BCE), although this theory is disputed by some. Philosophical methods include questioning, critical discussion, rational argument, and systematic presentation. in . Historically, ''philosophy'' encompassed all bodies of knowledge and a practitioner was known as a ''philosopher''."The English word "philosophy" is first attested to , meaning "knowledge, body of knowledge." "natural philosophy," which began as a discipline in ancient India and Ancient Greece, encompasses astronomy, medicine, and physics. For example, Newton's 1687 ''Mathematical Principles of Natural Philosophy'' later became classified as a book of physics. In the 19th century, the growth of modern research universiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brian Skyrms
Brian Skyrms (born 1938) is an American philosopher, Distinguished Professor of Logic and Philosophy of Science and Economics at the University of California, Irvine, and a professor of philosophy at Stanford University. He has worked on problems in the philosophy of science, causation, decision theory, game theory, and the foundations of probability. Education and career Skyrms graduated from Lehigh University in 1960 and earned his Ph.D. in philosophy from the University of Pittsburgh in 1964. He taught at several different universities, before teaching at the University of Illinois, Chicago from 1968 until 1980, when he moved to the University of California, Irvine. Skyrms is a Fellow of the American Academy of Arts & Sciences and one of two living philosophers (along with Allan Gibbard) to be elected a Fellow of the National Academy of Sciences. Philosophical work Most recently, his work has focused on the evolution of social norms using evolutionary game theory. His ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Statistics
Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a ''degree of belief'' in an event. The degree of belief may be based on prior knowledge about the event, such as the results of previous experiments, or on personal beliefs about the event. This differs from a number of other interpretations of probability, such as the frequentist interpretation that views probability as the limit of the relative frequency of an event after many trials. Bayesian statistical methods use Bayes' theorem to compute and update probabilities after obtaining new data. Bayes' theorem describes the conditional probability of an event based on data as well as prior information or beliefs about the event or conditions related to the event. For example, in Bayesian inference, Bayes' theorem can be used to estimate the parameters of a probability distribution or statistical model. Since Bayesian statistics treats probabi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principle Of Reflection
A principle is a proposition or value that is a guide for behavior or evaluation. In law, it is a rule that has to be or usually is to be followed. It can be desirably followed, or it can be an inevitable consequence of something, such as the laws observed in nature or the way that a system is constructed. The principles of such a system are understood by its users as the essential characteristics of the system, or reflecting system's designed purpose, and the effective operation or use of which would be impossible if any one of the principles was to be ignored. A system may be explicitly based on and implemented from a document of principles as was done in IBM's 360/370 ''Principles of Operation''. Examples of principles are, entropy in a number of fields, least action in physics, those in descriptive comprehensive and fundamental law: doctrines or assumptions forming normative rules of conduct, separation of church and state in statecraft, the central dogma of molecular biology ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Entropy Principle
The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge about a system is the one with largest entropy, in the context of precisely stated prior data (such as a proposition that expresses testable information). Another way of stating this: Take precisely stated prior data or testable information about a probability distribution function. Consider the set of all trial probability distributions that would encode the prior data. According to this principle, the distribution with maximal information entropy is the best choice. History The principle was first expounded by E. T. Jaynes in two papers in 1957 where he emphasized a natural correspondence between statistical mechanics and information theory. In particular, Jaynes offered a new and very general rationale why the Gibbsian method of statistical mechanics works. He argued that the entropy of statistical mechanics and the information entropy of informatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Law Of Total Probability
In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It expresses the total probability of an outcome which can be realized via several distinct events, hence the name. Statement The law of total probability isZwillinger, D., Kokoska, S. (2000) ''CRC Standard Probability and Statistics Tables and Formulae'', CRC Press. page 31. a theorem that states, in its discrete case, if \left\ is a finite or countably infinite partition of a sample space (in other words, a set of pairwise disjoint events whose union is the entire sample space) and each event B_n is measurable, then for any event A of the same probability space: :P(A)=\sum_n P(A\cap B_n) or, alternatively, :P(A)=\sum_n P(A\mid B_n)P(B_n), where, for any n for which P(B_n) = 0 these terms are simply omitted from the summation, because P(A\mid B_n) is finite. The summation can be interpreted as a weighted average, and consequ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinite Regress
An infinite regress is an infinite series of entities governed by a recursive principle that determines how each entity in the series depends on or is produced by its predecessor. In the epistemic regress, for example, a belief is justified because it is based on another belief that is justified. But this other belief is itself in need of one more justified belief for itself to be justified and so on. An infinite regress argument is an argument against a theory based on the fact that this theory leads to an infinite regress. For such an argument to be successful, it has to demonstrate not just that the theory in question entails an infinite regress but also that this regress is ''vicious''. There are different ways in which a regress can be vicious. The most serious form of viciousness involves a contradiction in the form of ''metaphysical impossibility''. Other forms occur when the infinite regress is responsible for the theory in question being implausible or for its failure to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cromwell's Rule
Cromwell's rule, named by statistician Dennis Lindley, states that the use of prior probabilities of 1 ("the event will definitely occur") or 0 ("the event will definitely not occur") should be avoided, except when applied to statements that are logically true or false, such as 2+2 equaling 4 or 5. The reference is to Oliver Cromwell, who wrote to the General Assembly of the Church of Scotland on 3 August 1650, shortly before the Battle of Dunbar, including a phrase that has become well known and frequently quoted: As Lindley puts it, assigning a probability should "leave a little probability for the moon being made of green cheese; it can be as small as 1 in a million, but have it there since otherwise an army of astronauts returning with samples of the said cheese will leave you unmoved." Similarly, in assessing the likelihood that tossing a coin will result in either a head or a tail facing upwards, there is a possibility, albeit remote, that the coin will land on its edge a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional Probability
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is and the event is known or assumed to have occurred, "the conditional probability of given ", or "the probability of under the condition ", is usually written as or occasionally . This can also be understood as the fraction of probability B that intersects with A: P(A \mid B) = \frac. For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person is sick, then they are much more likely to be coughing. For example, the conditional probability that someone unwell (sick) is coughing might be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Lewis (philosopher)
David Kellogg Lewis (September 28, 1941 – October 14, 2001) was an American philosopher who is widely regarded as one of the most important philosophers of the 20th century. Lewis taught briefly at UCLA and then at Princeton University from 1970 until his death. He is closely associated with Australia, whose philosophical community he visited almost annually for more than 30 years. Lewis made significant contributions in philosophy of mind, philosophy of probability, epistemology, philosophical logic, aesthetics, philosophy of mathematics, philosophy of time and philosophy of science. In most of these fields he is considered among the most important figures of recent decades. But Lewis is most famous for his work in metaphysics, philosophy of language and semantics, in which his books ''On the Plurality of Worlds'' (1986) and ''Counterfactuals'' (1973) are considered classics. His works on the logic and semantics of counterfactual conditionals are broadly used by philosop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epistemology
Epistemology (; ), or the theory of knowledge, is the branch of philosophy concerned with knowledge. Epistemology is considered a major subfield of philosophy, along with other major subfields such as ethics, logic, and metaphysics. Epistemologists study the nature, origin, and scope of knowledge, epistemic justification, the rationality of belief, and various related issues. Debates in epistemology are generally clustered around four core areas: # The philosophical analysis of the nature of knowledge and the conditions required for a belief to constitute knowledge, such as truth and justification # Potential sources of knowledge and justified belief, such as perception, reason, memory, and testimony # The structure of a body of knowledge or justified belief, including whether all justified beliefs must be derived from justified foundational beliefs or whether justification requires only a coherent set of beliefs # Philosophical skepticism, which questions the possibili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
