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List Of Unsolved Problems In Statistics
There are many longstanding List of unsolved problems in mathematics, unsolved problems in mathematics for which a solution has still not yet been found. The notable unsolved problems in statistics are generally of a different flavor; according to John Tukey, "difficulties in identifying problems have delayed statistics far more than difficulties in solving problems." A list of "one or two open problems" (in fact 22 of them) was given by David Cox (statistician), David Cox. Inference and testing * How to detect and correct for systematic errors, especially in sciences where random errors are large (a situation Tukey termed uncomfortable science). * The Graybill–Deal estimator is often used to estimate the common mean of two normal populations with unknown and possibly unequal variances. Though this estimator is generally unbiased, its admissible decision rule, admissibility remains to be shown. * Meta-analysis: Though independent p-values can be combined using Fisher's method, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Unsolved Problems In Mathematics
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations. Some problems belong to more than one discipline and are studied using techniques from different areas. Prizes are often awarded for the solution to a long-standing problem, and some lists of unsolved problems, such as the Millennium Prize Problems, receive considerable attention. This list is a composite of notable unsolved problems mentioned in previously published lists, including but not limited to lists considered authoritative. Although this list may never be comprehensive, the problems listed here vary widely in both difficulty and importance. Lists of unsolved problems in math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Significance Level
In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis (simply by chance alone). More precisely, a study's defined significance level, denoted by \alpha, is the probability of the study rejecting the null hypothesis, given that the null hypothesis is true; and the ''p''-value of a result, ''p'', is the probability of obtaining a result at least as extreme, given that the null hypothesis is true. The result is statistically significant, by the standards of the study, when p \le \alpha. The significance level for a study is chosen before data collection, and is typically set to 5% or much lower—depending on the field of study. In any experiment or observation that involves drawing a sample from a population, there is always the possibility that an observed effect would have occurred due to sampling error alone. But if the ''p''-value of an observed effect is less than (or equal to) the significa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Predict
A prediction (Latin ''præ-'', "before," and ''dicere'', "to say"), or forecast, is a statement about a future event or data. They are often, but not always, based upon experience or knowledge. There is no universal agreement about the exact difference from "estimation"; different authors and disciplines ascribe different connotations. Future events are necessarily uncertain, so guaranteed accurate information about the future is impossible. Prediction can be useful to assist in making plans about possible developments. Opinion In a non-statistical sense, the term "prediction" is often used to refer to an informed guess or opinion. A prediction of this kind might be informed by a predicting person's abductive reasoning, inductive reasoning, deductive reasoning, and experience; and may be useful—if the predicting person is a knowledgeable person in the field. The Delphi method is a technique for eliciting such expert-judgement-based predictions in a controlled way. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doomsday Argument
The Doomsday Argument (DA), or Carter catastrophe, is a probabilistic argument that claims to predict the future population of the human species, based on an estimation of the number of humans born to date. The Doomsday argument was originally proposed by the astrophysicist Brandon Carter in 1983 leading to the initial name of the Carter catastrophe. The argument was subsequently championed by the philosopher John A. Leslie and has since been independently discovered by J. Richard Gott, and Holger Bech Nielsen. Similar principles of eschatology were proposed earlier by Heinz von Foerster among others. A more general form was given earlier in the Lindy effect, which proposes that for certain phenomena, the future life expectancy is ''proportional to'' (though not necessarily ''equal to'') the current age and is based on a decreasing mortality rate over time. If the total number of humans who were born or will ever be born is denoted by ''N'', then the Copernican principle sugges ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sampling Of Species Problem
Sampling may refer to: *Sampling (signal processing), converting a continuous signal into a discrete signal * Sampling (graphics), converting continuous colors into discrete color components *Sampling (music), the reuse of a sound recording in another recording **Sampler (musical instrument), an electronic musical instrument used to record and play back samples * Sampling (statistics), selection of observations to acquire some knowledge of a statistical population *Sampling (case studies), selection of cases for single or multiple case studies * Sampling (audit), application of audit procedures to less than 100% of population to be audited * Sampling (medicine), gathering of matter from the body to aid in the process of a medical diagnosis and/or evaluation of an indication for treatment, further medical tests or other procedures. * Sampling (occupational hygiene), detection of hazardous materials in the workplace *Sampling (for testing or analysis), taking a representative portion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Problems In Latin Squares
In mathematics, the theory of Latin squares is an active research area with many open problems. As in other areas of mathematics, such problems are often made public at professional conferences and meetings. Problems posed here appeared in, for instance, the ''Loops (Prague)'' conferences and the ''Milehigh (Denver)'' conferences. Open problems Bounds on maximal number of transversals in a Latin square A ''transversal'' in a Latin square of order ''n'' is a set ''S'' of ''n'' cells such that every row and every column contains exactly one cell of ''S'', and such that the symbols in ''S'' form . Let ''T''(''n'') be the maximum number of transversals in a Latin square of order ''n''. Estimate ''T''(''n''). *''Proposed:'' by Ian Wanless at Loops '03, Prague 2003 *''Comments:'' Wanless, McKay and McLeod have bounds of the form ''c''''n'' exp(''c'' ''n'' log ''n''). A related question is to estimate the number of transversals in the Cayley tables of cyclic groups of odd order. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Design Of Experiments
The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated with experiments in which the design introduces conditions that directly affect the variation, but may also refer to the design of quasi-experiments, in which natural conditions that influence the variation are selected for observation. In its simplest form, an experiment aims at predicting the outcome by introducing a change of the preconditions, which is represented by one or more independent variables, also referred to as "input variables" or "predictor variables." The change in one or more independent variables is generally hypothesized to result in a change in one or more dependent variables, also referred to as "output variables" or "response variables." The experimental design may also identify control variables that must be h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latin Square
In combinatorics and in experimental design, a Latin square is an ''n'' × ''n'' array filled with ''n'' different symbols, each occurring exactly once in each row and exactly once in each column. An example of a 3×3 Latin square is The name "Latin square" was inspired by mathematical papers by Leonhard Euler (1707–1783), who used Latin characters as symbols, but any set of symbols can be used: in the above example, the alphabetic sequence A, B, C can be replaced by the integer sequence 1, 2, 3. Euler began the general theory of Latin squares. History The Korean mathematician Choi Seok-jeong was the first to publish an example of Latin squares of order nine, in order to construct a magic square in 1700, predating Leonhard Euler by 67 years. Reduced form A Latin square is said to be ''reduced'' (also, ''normalized'' or ''in standard form'') if both its first row and its first column are in their natural order. For example, the La ... [...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] |
DNA Microarray
A DNA microarray (also commonly known as DNA chip or biochip) is a collection of microscopic DNA spots attached to a solid surface. Scientists use DNA microarrays to measure the expression levels of large numbers of genes simultaneously or to genotype multiple regions of a genome. Each DNA spot contains picomoles (10−12 moles) of a specific DNA sequence, known as '' probes'' (or ''reporters'' or '' oligos''). These can be a short section of a gene or other DNA element that are used to hybridize a cDNA or cRNA (also called anti-sense RNA) sample (called ''target'') under high-stringency conditions. Probe-target hybridization is usually detected and quantified by detection of fluorophore-, silver-, or chemiluminescence-labeled targets to determine relative abundance of nucleic acid sequences in the target. The original nucleic acid arrays were macro arrays approximately 9 cm × 12 cm and the first computerized image based analysis was published in 1981. It was inv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequential Testing
In statistics, sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data are evaluated as they are collected, and further sampling is stopped in accordance with a pre-defined stopping rule as soon as significant results are observed. Thus a conclusion may sometimes be reached at a much earlier stage than would be possible with more classical hypothesis testing or estimation, at consequently lower financial and/or human cost. History The method of sequential analysis is first attributed to Abraham Wald with Jacob Wolfowitz, W. Allen Wallis, and Milton Friedman while at Columbia University's Statistical Research Group as a tool for more efficient industrial quality control during World War II. Its value to the war effort was immediately recognised, and led to its receiving a "restricted" classification. At the same time, George Barnard led a group working on optimal stopping in Great Britain. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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