**Bayes Theorem**: A theorem in probability theory named for Thomas Bayes (1702-1761). In epidemiology, it is used to obtain the probability of disease in a group of people with some characteristic on the basis of the overall rate of that disease and of the likelihood of that characteristic in healthy and diseased individuals. The most familiar application is in clinical decision analysis where it is used for estimating the probability of a particular diagnosis given the appearance of some symptoms or test result.

**Mathematical Concepts**: Numeric or quantitative entities, descriptions, properties, relationships, operations, and events.

**Algorithms**: A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task.

**Mathematics**: The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)

**Models, Statistical**: Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.

**Information Theory**: An interdisciplinary study dealing with the transmission of messages or signals, or the communication of information. Information theory does not directly deal with meaning or content, but with physical representations that have meaning or content. It overlaps considerably with communication theory and CYBERNETICS.

**Models, Theoretical**: Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.

**Computer Simulation**: Computer-based representation of physical systems and phenomena such as chemical processes.

**Probability**: The study of chance processes or the relative frequency characterizing a chance process.

**Enzymes**: Biological molecules that possess catalytic activity. They may occur naturally or be synthetically created. Enzymes are usually proteins, however CATALYTIC RNA and CATALYTIC DNA molecules have also been identified.

**Models, Genetic**: Theoretical representations that simulate the behavior or activity of genetic processes or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.

**Achillea**: A plant genus of the family ASTERACEAE that has long been used in folk medicine for treating wounds.

**Models, Biological**: Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.

**Likelihood Functions**: Functions constructed from a statistical model and a set of observed data which give the probability of that data for various values of the unknown model parameters. Those parameter values that maximize the probability are the maximum likelihood estimates of the parameters.

**Blogging**: Using an INTERNET based personal journal which may consist of reflections, comments, and often hyperlinks.

**Animal Care Committees**: Institutional committees established to protect the welfare of animals used in research and education. The 1971 NIH Guide for the Care and Use of Laboratory Animals introduced the policy that institutions using warm-blooded animals in projects supported by NIH grants either be accredited by a recognized professional laboratory animal accrediting body or establish its own committee to evaluate animal care; the Public Health Service adopted a policy in 1979 requiring such committees; and the 1985 amendments to the Animal Welfare Act mandate review and approval of federally funded research with animals by a formally designated Institutional Animal Care and Use Committee (IACUC).

**Animals, Laboratory**

**Juvenile Delinquency**: The antisocial acts of children or persons under age which are illegal or lawfully interpreted as constituting delinquency.

**Financing, Construction**: Funding resources and procedures for capital improvement or the construction of facilities.

**Nebraska**

**Basal Metabolism**: Heat production, or its measurement, of an organism at the lowest level of cell chemistry in an inactive, awake, fasting state. It may be determined directly by means of a calorimeter or indirectly by calculating the heat production from an analysis of the end products of oxidation within the organism or from the amount of oxygen utilized.

**Capital Expenditures**: Those funds disbursed for facilities and equipment, particularly those related to the delivery of health care.

**Arnold-Chiari Malformation**: A group of congenital malformations involving the brainstem, cerebellum, upper spinal cord, and surrounding bony structures. Type II is the most common, and features compression of the medulla and cerebellar tonsils into the upper cervical spinal canal and an associated MENINGOMYELOCELE. Type I features similar, but less severe malformations and is without an associated meningomyelocele. Type III has the features of type II with an additional herniation of the entire cerebellum through the bony defect involving the foramen magnum, forming an ENCEPHALOCELE. Type IV is a form a cerebellar hypoplasia. Clinical manifestations of types I-III include TORTICOLLIS; opisthotonus; HEADACHE; VERTIGO; VOCAL CORD PARALYSIS; APNEA; NYSTAGMUS, CONGENITAL; swallowing difficulties; and ATAXIA. (From Menkes, Textbook of Child Neurology, 5th ed, p261; Davis, Textbook of Neuropathology, 2nd ed, pp236-46)

**Science**: The study of natural phenomena by observation, measurement, and experimentation.

**Books**

**Forecasting**: The prediction or projection of the nature of future problems or existing conditions based upon the extrapolation or interpretation of existing scientific data or by the application of scientific methodology.

**Antigens, CD82**: A widely expressed transmembrane glycoprotein that functions as a METASTASIS suppressor protein. It is underexpressed in a variety of human NEOPLASMS.

**Multilingualism**: The ability to speak, read, or write several languages or many languages with some facility. Bilingualism is the most common form. (From Random House Unabridged Dictionary, 2d ed)

**Vocabulary**: The sum or the stock of words used by a language, a group, or an individual. (From Webster, 3d ed)

**Language**: A verbal or nonverbal means of communicating ideas or feelings.

**Rationalization**: A defense mechanism operating unconsciously, in which the individual attempts to justify or make consciously tolerable, by plausible means, feelings, behavior, and motives that would otherwise be intolerable.

**Uncertainty**: The condition in which reasonable knowledge regarding risks, benefits, or the future is not available.

**Cemeteries**: Areas set apart as burial grounds.

**London**

**Graves Disease**: A common form of hyperthyroidism with a diffuse hyperplastic GOITER. It is an autoimmune disorder that produces antibodies against the THYROID STIMULATING HORMONE RECEPTOR. These autoantibodies activate the TSH receptor, thereby stimulating the THYROID GLAND and hypersecretion of THYROID HORMONES. These autoantibodies can also affect the eyes (GRAVES OPHTHALMOPATHY) and the skin (Graves dermopathy).

**Sister Mary Joseph's Nodule**: Metastatic lesion of the UMBILICUS associated with intra-abdominal neoplasms especially of the GASTROINTESTINAL TRACT or OVARY.

**Umbilicus**: The pit in the center of the ABDOMINAL WALL marking the point where the UMBILICAL CORD entered in the FETUS.

**Phylogeny**: The relationships of groups of organisms as reflected by their genetic makeup.

**Mind-Body Relations, Metaphysical**: The relation between the mind and the body in a religious, social, spiritual, behavioral, and metaphysical context. This concept is significant in the field of alternative medicine. It differs from the relationship between physiologic processes and behavior where the emphasis is on the body's physiology ( = PSYCHOPHYSIOLOGY).

**Humanism**: An ethical system which emphasizes human values and the personal worth of each individual, as well as concern for the dignity and freedom of humankind.

**Asteraceae**: A large plant family of the order Asterales, subclass Asteridae, class Magnoliopsida. The family is also known as Compositae. Flower petals are joined near the base and stamens alternate with the corolla lobes. The common name of "daisy" refers to several genera of this family including Aster; CHRYSANTHEMUM; RUDBECKIA; TANACETUM.

**Weightlessness**: Condition in which no acceleration, whether due to gravity or any other force, can be detected by an observer within a system. It also means the absence of weight or the absence of the force of gravity acting on a body. Microgravity, gravitational force between 0 and 10 -6 g, is included here. (From NASA Thesaurus, 1988)

**Contracts**: Agreements between two or more parties, especially those that are written and enforceable by law (American Heritage Dictionary of the English Language, 4th ed). It is sometimes used to characterize the nature of the professional-patient relationship.

**Superstitions**: A belief or practice which lacks adequate basis for proof; an embodiment of fear of the unknown, magic, and ignorance.

**Religion**: A set of beliefs concerning the nature, cause, and purpose of the universe, especially when considered as the creation of a superhuman agency. It usually involves devotional and ritual observances and often a moral code for the conduct of human affairs. (Random House Collegiate Dictionary, rev. ed.)

**Christianity**: The religion stemming from the life, teachings, and death of Jesus Christ: the religion that believes in God as the Father Almighty who works redemptively through the Holy Spirit for men's salvation and that affirms Jesus Christ as Lord and Savior who proclaimed to man the gospel of salvation. (From Webster, 3d ed)

**Religion and Medicine**: The interrelationship of medicine and religion.

**Church of Jesus Christ of Latter-day Saints**: A group of religious bodies tracing their origin to Joseph Smith in 1830 and accepting the Book of Mormon as divine revelation. (from Merriam-Webster's Collegiate Dictionary, 10th ed)

**Floods**: Sudden onset water phenomena with different speed of occurrence. These include flash floods, seasonal river floods, and coastal floods, associated with CYCLONIC STORMS; TIDALWAVES; and storm surges.

**Forensic Genetics**: The application of genetic analyses and MOLECULAR DIAGNOSTIC TECHNIQUES to legal matters and crime analysis.

**Orthoptera**: An order of insects comprising two suborders: Caelifera and Ensifera. They consist of GRASSHOPPERS, locusts, and crickets (GRYLLIDAE).

## Bayesian inference on biopolymer models. (1/6254)

MOTIVATION: Most existing bioinformatics methods are limited to making point estimates of one variable, e.g. the optimal alignment, with fixed input values for all other variables, e.g. gap penalties and scoring matrices. While the requirement to specify parameters remains one of the more vexing issues in bioinformatics, it is a reflection of a larger issue: the need to broaden the view on statistical inference in bioinformatics. RESULTS: The assignment of probabilities for all possible values of all unknown variables in a problem in the form of a posterior distribution is the goal of Bayesian inference. Here we show how this goal can be achieved for most bioinformatics methods that use dynamic programming. Specifically, a tutorial style description of a Bayesian inference procedure for segmentation of a sequence based on the heterogeneity in its composition is given. In addition, full Bayesian inference algorithms for sequence alignment are described. AVAILABILITY: Software and a set of transparencies for a tutorial describing these ideas are available at http://www.wadsworth.org/res&res/bioinfo/ (+info)## Genetic determination of individual birth weight and its association with sow productivity traits using Bayesian analyses. (2/6254)

Genetic association between individual birth weight (IBW) and litter birth weight (LBW) was analyzed on records of 14,950 individual pigs born alive between 1988 and 1994 at the pig breeding farm of the University of Kiel. Dams were from three purebred lines (German Landrace, German Edelschwein, and Large White) and their crosses. Phenotypically, preweaning mortality of pigs decreased substantially from 40% for pigs with < or = 1 kg weight to less than 7% for pigs with > 1.6 kg. For these low to high birth weight categories, preweaning growth (d 21 of age) and early postweaning growth (weaning to 25 kg) increased by more than 28 and 8% per day, respectively. Bayesian analysis was performed based on direct-maternal effects models for IBW and multiple-trait direct effects models for number of pigs born in total (NOBT) and alive (NOBA) and LBW. Bayesian posterior means for direct and maternal heritability and litter proportion of variance in IBW were .09, .26, and .18, respectively. After adjustment for NOBT, these changed to .08, .22, and .09, respectively. Adjustment for NOBT reduced the direct and maternal genetic correlation from -.41 to -.22. For these direct-maternal correlations, the 95% highest posterior density intervals were -.75 to -.07, and -.58 to .17 before and after adjustment for NOBT. Adjustment for NOBT was found to be necessary to obtain unbiased estimates of genetic effects for IBW. The relationship between IBW and NOBT, and thus the adjustment, was linear with a decrease in IBW of 44 g per additionally born pig. For litter traits, direct heritabilities were .10, .08, and .08 for NOBT, NOBA, and LBW, respectively. After adjustment of LBW for NOBA the heritability changed to .43. Expected variance components for LBW derived from estimates of IBW revealed that genetic and environmental covariances between full-sibs and variation in litter size resulted in the large deviation of maternal heritability for IBW and its equivalent estimate for LBW. These covariances among full-sibs could not be estimated if only LBW were recorded. Therefore, selection for increased IBW is recommended, with the opportunity to improve both direct and maternal genetic effects of birth weight of pigs and, thus, their vitality and pre- and postnatal growth. (+info)## Bayesian mapping of multiple quantitative trait loci from incomplete outbred offspring data. (3/6254)

A general fine-scale Bayesian quantitative trait locus (QTL) mapping method for outcrossing species is presented. It is suitable for an analysis of complete and incomplete data from experimental designs of F2 families or backcrosses. The amount of genotyping of parents and grandparents is optional, as well as the assumption that the QTL alleles in the crossed lines are fixed. Grandparental origin indicators are used, but without forgetting the original genotype or allelic origin information. The method treats the number of QTL in the analyzed chromosome as a random variable and allows some QTL effects from other chromosomes to be taken into account in a composite interval mapping manner. A block-update of ordered genotypes (haplotypes) of the whole family is sampled once in each marker locus during every round of the Markov Chain Monte Carlo algorithm used in the numerical estimation. As a byproduct, the method gives the posterior distributions for linkage phases in the family and therefore it can also be used as a haplotyping algorithm. The Bayesian method is tested and compared with two frequentist methods using simulated data sets, considering two different parental crosses and three different levels of available parental information. The method is implemented as a software package and is freely available under the name Multimapper/outbred at URL http://www.rni.helsinki.fi/mjs/. (+info)## The validation of interviews for estimating morbidity. (4/6254)

Health interview surveys have been widely used to measure morbidity in developing countries, particularly for infectious diseases. Structured questionnaires using algorithms which derive sign/symptom-based diagnoses seem to be the most reliable but there have been few studies to validate them. The purpose of validation is to evaluate the sensitivity and specificity of brief algorithms (combinations of signs/symptoms) which can then be used for the rapid assessment of community health problems. Validation requires a comparison with an external standard such as physician or serological diagnoses. There are several potential pitfalls in assessing validity, such as selection bias, differences in populations and the pattern of diseases in study populations compared to the community. Validation studies conducted in the community may overcome bias caused by case selection. Health centre derived estimates can be adjusted and applied to the community with caution. Further study is needed to validate algorithms for important diseases in different cultural settings. Community-based studies need to be conducted, and the utility of derived algorithms for tracking disease frequency explored further. (+info)## Bayesian analysis of birth weight and litter size in Baluchi sheep using Gibbs sampling. (5/6254)

Variance and covariance components for birth weight (BWT), as a lamb trait, and litter size measured on ewes in the first, second, and third parities (LS1 through LS3) were estimated using a Bayesian application of the Gibbs sampler. Data came from Baluchi sheep born between 1966 and 1989 at the Abbasabad sheep breeding station, located northeast of Mashhad, Iran. There were 10,406 records of BWT recorded for all ewe lambs and for ram lambs that later became sires or maternal grandsires. All lambs that later became dams had records of LS1 through LS3. Separate bivariate analyses were done for each combination of BWT and one of the three variables LS1 through LS3. The Gibbs sampler with data augmentation was used to draw samples from the marginal posterior distribution for sire, maternal grandsire, and residual variances and the covariance between the sire and maternal grandsire for BWT, variances for the sire and residual variances for the litter size traits, and the covariances between sire effects for different trait combinations, sire and maternal grandsire effects for different combinations of BWT and LS1 through LS3, and the residual covariations between traits. Although most of the densities of estimates were slightly skewed, they seemed to fit the normal distribution well, because the mean, mode, and median were similar. Direct and maternal heritabilities for BWT were relatively high with marginal posterior modes of .14 and .13, respectively. The average of the three direct-maternal genetic correlation estimates for BWT was low, .10, but had a high standard deviation. Heritability increased from LS1 to LS3 and was relatively high, .29 to .37. Direct genetic correlations between BWT and LS1 and between BWT and LS3 were negative, -.32 and -.43, respectively. Otherwise, the same correlation between BWT and LS2 was positive and low, .06. Genetic correlations between maternal effects for BWT and direct effects for LS1 through LS3 were all highly negative and consistent for all parities, circa -.75. Environmental correlations between BWT and LS1 through LS3 were relatively low and ranged from .18 to .29 and had high standard errors. (+info)## Thermodynamics and kinetics of a folded-folded' transition at valine-9 of a GCN4-like leucine zipper. (6/6254)

Spin inversion transfer (SIT) NMR experiments are reported probing the thermodynamics and kinetics of interconversion of two folded forms of a GCN4-like leucine zipper near room temperature. The peptide is 13Calpha-labeled at position V9(a) and results are compared with prior findings for position L13(e). The SIT data are interpreted via a Bayesian analysis, yielding local values of T1a, T1b, kab, kba, and Keq as functions of temperature for the transition FaV9 right arrow over left arrow FbV9 between locally folded dimeric forms. Equilibrium constants, determined from relative spin counts at spin equilibrium, agree well with the ratios kab/kba from the dynamic SIT experiments. Thermodynamic and kinetic parameters are similar for V9(a) and L13(e), but not the same, confirming that the molecular conformational population is not two-state. The energetic parameters determined for both sites are examined, yielding conclusions that apply to both and are robust to uncertainties in the preexponential factor (kT/h) of the Eyring equation. These conclusions are 1) the activation free energy is substantial, requiring a sparsely populated transition state; 2) the transition state's enthalpy far exceeds that of either Fa or Fb; 3) the transition state's entropy far exceeds that of Fa, but is comparable to that of Fb; 4) "Arrhenius kinetics" characterize the temperature dependence of both kab and kba, indicating that the temperatures of slow interconversion are not below that of the glass transition. Any postulated free energy surface for these coiled coils must satisfy these constraints. (+info)## Iterative reconstruction based on median root prior in quantification of myocardial blood flow and oxygen metabolism. (7/6254)

The aim of this study was to compare reproducibility and accuracy of two reconstruction methods in quantification of myocardial blood flow and oxygen metabolism with 15O-labeled tracers and PET. A new iterative Bayesian reconstruction method based on median root prior (MRP) was compared with filtered backprojection (FBP) reconstruction method, which is traditionally used for image reconstruction in PET studies. METHODS: Regional myocardial blood flow (rMBF), oxygen extraction fraction (rOEF) and myocardial metabolic rate of oxygen consumption (rMMRO2) were quantified from images reconstructed in 27 subjects using both MRP and FBP methods. For each subject, regions of interest (ROIs) were drawn on the lateral, anterior and septal regions on four planes. To test reproducibility, the ROI drawing procedure was repeated. By using two sets of ROIs, variability was evaluated from images reconstructed with the MRP and the FBP methods. RESULTS: Correlation coefficients of mean values of rMBF, rOEF and rMMRO2 were significantly higher in the images reconstructed with the MRP reconstruction method compared with the images reconstructed with the FBP method (rMBF: MRP r = 0.896 versus FBP r = 0.737, P < 0.001; rOEF: 0.915 versus 0.855, P < 0.001; rMMRO2: 0.954 versus 0.885, P < 0.001). Coefficient of variation for each parameter was significantly lower in MRP images than in FBP images (rMBF: MRP 23.5% +/- 11.3% versus FBP 30.1% +/- 14.7%, P < 0.001; rOEF: 21.0% +/- 11.1% versus 32.1% +/- 19.8%, P < 0.001; rMMRO2: 23.1% +/- 13.2% versus 30.3% +/- 19.1%, P < 0.001). CONCLUSION: The MRP reconstruction method provides higher reproducibility and lower variability in the quantitative myocardial parameters when compared with the FBP method. This study shows that the new MRP reconstruction method improves accuracy and stability of clinical quantification of myocardial blood flow and oxygen metabolism with 15O and PET. (+info)## Taking account of between-patient variability when modeling decline in Alzheimer's disease. (8/6254)

The pattern of deterioration in patients with Alzheimer's disease is highly variable within a given population. With recent speculation that the apolipoprotein E allele may influence rate of decline and claims that certain drugs may slow the course of the disease, there is a compelling need for sound statistical methodology to address these questions. Current statistical methods for describing decline do not adequately take into account between-patient variability and possible floor and/or ceiling effects in the scale measuring decline, and they fail to allow for uncertainty in disease onset. In this paper, the authors analyze longitudinal Mini-Mental State Examination scores from two groups of Alzheimer's disease subjects from Palo Alto, California, and Minneapolis, Minnesota, in 1981-1993 and 1986-1988, respectively. A Bayesian hierarchical model is introduced as an elegant means of simultaneously overcoming all of the difficulties referred to above. (+info)**Bayes** **theorem** (disambiguation)

**Bayes**

**theorem**may refer to:

**Bayes**'

**theorem**- a

**theorem**which expresses how a subjective degree of belief should rationally ... Bayesian theory in E-discovery - the application of

**Bayes**'

**theorem**in legal evidence diagnostics and E-discovery, where it ... Bayesian theory in marketing - the application of

**Bayes**'

**theorem**in marketing, where it allows for decision making and market ...

## Evidence under **Bayes** **theorem**

R v Adams - court case about

**Bayes**'**Theorem**with DNA "**Bayes**'**Theorem**in the Court of Appeal , Law Articles", Bernard Robertson ... One area of particular interest and controversy has been**Bayes**'**theorem**.**Bayes**'**theorem**is an elementary proposition of ... The use of evidence under**Bayes**'**theorem**relates to the likelihood of finding evidence in relation to the accused, where**Bayes**... If she used**Bayes**'**theorem**, she could multiply those prior odds by a "likelihood ratio" in order to update her odds after ...## Thomas **Bayes**

The use of the

**Bayes****theorem**has been extended in science and in other fields.**Bayes**himself might not have embraced the broad ... "Who Discovered**Bayes's****Theorem**?" The American Statistician, 37(4):290-296, 1983. Biographical sketch of Thomas**Bayes**An ...**Bayes**'**theorem**.**Bayes**never published what would eventually become his most famous accomplishment; his notes were edited and ... This essay contains a statement of a special case of**Bayes**'**theorem**. In the first decades of the eighteenth century, many ...## Stigler's law of eponymy

"Who discovered

**Bayes's****theorem**?". The American Statistician. 37 (4): 290-6. doi:10.2307/2682766. Kern, Scott E (September- ... Eponym List of examples of Stigler's law List of misnamed**theorems**List of persons considered father or mother of a scientific ... It says, "Mathematical formulas and**theorems**are usually not named after their original discoverers" and was named after Carl ... Examples include Hubble's law which was derived by Georges Lemaître two years before Edwin Hubble, the Pythagorean**theorem**...## Pediatric Attention Disorders Diagnostic Screener

Fagan, T. J. (1975). "Nomogram for

**Bayes****theorem**". New England Journal of Medicine. 293 (5): 257. doi:10.1056/ ...## Nicholas Saunderson

The discovery of

**Bayes**'**theorem**remains a controversial topic in the history of mathematics. While it is certain to have been ... Who discovered**Bayes's****Theorem**? Stephen M. Stigler The American Statistician vol 37 (4) 1983 290-296 [1] lucasianchair.org ... According to one historian of statistics, he may have been the earliest discoverer of**Bayes****theorem**. He worked as Lucasian ... Stephen M. Stigler, Who Discovered**Bayes's****Theorem**?, The American Statistician, Vol. 37, No. 4, Part 1 (November 1983), pp. 290 ...## Stephen Stigler

"Who discovered

**Bayes's****theorem**?". The American Statistician. 37 (4): 290-96. doi:10.2307/2682766. JSTOR 2682766. MR 1712969. ...## Pattern theory

**Bayes**

**theorem**gives p (s , i ) p(i) = p (s, i ) = p (i,s ) p(s) To analyze the signal (recognition): fix i, maximize p, infer s ...

**Bayes**

**theorem**gives p(e,f)p(f) = p(e, f) = p(f,e)p(e) and reduces to the fundamental equation of machine translation: maximize ... Statistical PT makes ubiquitous use of conditional probability in the form of

**Bayes**

**theorem**and Markov Models. Both these ... Validate by sampling from the derived models by and infer hidden states with

**Bayes**' rule. Across all modalities, a limited ...

## Bayesian inference in marketing

Lastly

**Bayes****theorem**is coherent. It is considered the most appropriate way to update beliefs by welcoming the incorporation of ...**Bayes**'**theorem**is fundamental to Bayesian inference. It is a subset of statistics, providing a mathematical framework for ... The three principle strengths of**Bayes**'**theorem**that have been identified by scholars are that it is prescriptive, complete and ... The fundamental ideas and concepts behind**Bayes**'**theorem**, and its use within Bayesian inference, have been developed and added ...## Minimum mean square error

This can be directly shown using the

**Bayes****theorem**. As a consequence, to find the MMSE estimator, it is sufficient to find the ... and based directly on**Bayes****theorem**, it allows us to make better posterior estimates as more observations become available. ...## 1763 in Great Britain

24 November - Thomas

**Bayes's****theorem**is first announced (posthumously). Josiah Wedgwood receives orders for his pottery from ... Thomas**Bayes**, F.R.S. to John Canton, M.A. and F.R.S. (PDF) "Icons, a portrait of England 1750-1800". Archived from the original ...## Inductive probability

**Bayes's**

**theorem**is named after Rev. Thomas

**Bayes**1701-1761. Bayesian inference broadened the application of probability to many ... The basis of inference is

**Bayes**'

**theorem**. But this

**theorem**is sometimes hard to apply and understand. The simpler method to ...

**Bayes**'

**theorem**is about conditional probabilities. What is the probability that event B happens if firstly event A happens? P ... But

**Bayes**'

**theorem**always depended on prior probabilities, to generate new probabilities. It was unclear where these prior ...

## Christ myth theory

ISBN 978-1-4520-5926-6. Carrier, Richard (2012). Proving History:

**Bayes's****Theorem**and the Quest for the Historical Jesus. ... Chapter 2. Carrier (2014a) Tucker, Aviezer (February 2016). "The Reverend**Bayes**vs Jesus Christ". History and Theory. 55:1: 129 ...## Base rate fallacy

**Bayes's**

**theorem**tells us that p ( d r u n k , D ) = p ( D , d r u n k ) p ( d r u n k ) p ( D ) {\displaystyle p(\mathrm {drunk ... More formally, the same probability of roughly 0.02 can be established using

**Bayes's**

**theorem**. The goal is to find the ... Formally, this probability can be calculated using

**Bayes**'

**theorem**, as shown above. However, there are different ways of ... for

**Bayes**'

**theorem**, which one can compute from the preceding values using p ( D ) = p ( D , d r u n k ) p ( d r u n k ) + p ( D ...

## John Edmund Kerrich

In addition, the pair used ping-pong balls to demonstrate

**Bayes's****theorem**.[how?] Until the advent of computer simulations, ...## Bayesian probability

The term Bayesian refers to Thomas

**Bayes**(1702-1761), who proved a special case of what is now called**Bayes**'**theorem**in a paper ... "**Bayes**'**Theorem**". stanford.edu. Retrieved 2016-03-21. Fuchs, Christopher A.; Schack, Rüdiger (2012-01-01). Ben-Menahem, Yemima; ... The sequential use of**Bayes**' formula: when more data become available, calculate the posterior distribution using**Bayes**' ... It was Pierre-Simon Laplace (1749-1827) who introduced a general version of the**theorem**and used it to approach problems in ...## R v Adams

The judge told the jury they could use

**Bayes's****theorem**if they wished. Adams was convicted and the case went to appeal. The ... At the retrial the defence team again wanted to instruct the new jury in the use of**Bayes's****theorem**(though Prof. Donnelly had ... The appeal was unsuccessful and the Appeal Court ruling was highly critical of the appropriateness of**Bayes's****theorem**in the ... The jury was instructed in the use of**Bayes's****theorem**by Professor Peter Donnelly of Oxford University. ...## Radical probabilism

He might be tempted to adopt

**Bayes**'**theorem**by analogy and set his Pnew(A) = Pold(A , B) = p/q. In fact, that step,**Bayes**' rule ... In Bayesian statistics, the**theorem**itself plays a more limited role.**Bayes**'**theorem**connects probabilities that are held ... However, adopting**Bayes**'**theorem**is a temptation. Suppose that a learner forms probabilities Pold(A & B) = p and Pold(B) = q. ... to adopt the law of total probability and extend it to updating in much the same way as was**Bayes**'**theorem**. Pnew(A) = Pold(A , ...## Edward M. Miller

The Relevance of Group Membership for Personnel Selection: A Demonstration Using

**Bayes****Theorem**. Journal of Social, Political, ...## Comparison of different machine translation approaches

The initial model of SMT, based on

**Bayes****Theorem**, proposed by Brown et al. takes the view that every sentence in one language ...## Edward Epstein (meteorologist)

... "the first formal treatment of

**Bayes's****theorem**in meteorology," according to BAMS. Another paper that involved**Bayes's****theorem**... was "Quality Control for Probability Forecasts," in which, as Epstein explained in the abstract, he used**Bayes**'**theorem**to ...## Evidence-based medicine

Odds can be calculated from, and then converted to, the [more familiar] probability.) This reflects

**Bayes**'**theorem**. The ...## Optimal estimation

In applied statistics, optimal estimation is a regularized matrix inverse method based on

**Bayes****theorem**. It is used very ...## Prosecutor's fallacy

... using

**Bayes**'**theorem**: P ( I , E ) = P ( E , I ) ⋅ P ( I ) P ( E ) {\displaystyle P(I,E)=P(E,I)\cdot {\frac {P(I)}{P(E)}}} Where ...## Representativeness heuristic

The use of the representativeness heuristic will likely lead to violations of

**Bayes**'**Theorem**.**Bayes**'**Theorem**states: P ( H , D ... found using**Bayes**'**theorem**, is lower than these estimates: There is a 12% chance (15% times 80%) of the witness correctly ...## Baum-Welch algorithm

... according to

**Bayes**'**theorem**: γ i ( t ) = P ( X t = i , Y , θ ) = P ( X t = i , Y , θ ) P ( Y , θ ) = α i ( t ) β i ( t ) ∑ j = ...**Bayes** **Theorem** Nate Silver - Business Insider

**Bayes**

**theorem**computes the posterior probability, or the probability that, given you found the underwear, your spouse is ... One of the most important notions in probability and statistics is

**Bayes**

**Theorem**, and it can be a little difficult to ... The book goes back to

**Bayes**

**theorem**constantly, and for excellent reasons - its an exceptionally powerful way to honestly ... FiveThirtyEights founder Nate Silver gives the single most coherent explanation of

**Bayes**

**Theorem**out there. ...

**BAYES** **THEOREM** AND LEGAL FACT-FINDING

According to them (p462), it should be decided by application of

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Probability:

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... Let ($\displaystyle A_n$) and ($\displaystyle B_n$) be in A with $\displaystyle A_n$--,A and $\ ...

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I have written a little about

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Luckily

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From

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James Rock explains how hes using

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One of the most distressing aspects of Alzheimers disease is the difficulty in determining whether mild memory problems are the beginning of an inevitable mental decline. Researchers at the Stanford University School of Medicine have developed a blood test that is a step toward giving people an answer two to six years in advance of the onset of the disease. The test identifies changes in a handful of proteins in blood plasma that cells use to convey messages to one another. The research team discovered a connection between shifts in the cells dialog and the changes in the brain accompanying Alzheimers. They found that the blood test could indicate who had Alzheimers with 90 percent agreement with clinical diagnoses, and could predict the onset of Alzheimers two to six years before symptoms appeared. "Just as a psychiatrist can conclude a lot of things by listening to the words of a patient, so by listening to different proteins we are measuring whether something is going wrong in the ...

https://blog.diegovalle.net/2007/10/bayes-theorem-and-alzheimers.html## Category:**Bayes**' **theorem** - Wikimedia Commons

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## Composite Service Recommendation Based on **Bayes** **Theorem**: Computer Science & IT Journal Article | IGI Global

Composite Service Recommendation Based on

https://www.igi-global.com/article/composite-service-recommendation-based-bayes/70390**Bayes****Theorem**: 10.4018/jwsr.2012040104: The number of web services increased ... "Composite Service Recommendation Based on**Bayes****Theorem**," International Journal of Web Services Research (IJWSR) 9 (2012): 2, ... Wu, J., Chen, L., Jian, H., & Wu, Z. (2012). Composite Service Recommendation Based on**Bayes****Theorem**. International Journal of ... "Composite Service Recommendation Based on**Bayes****Theorem**." IJWSR 9.2 (2012): 69-93. Web. 24 Sep. 2018. doi:10.4018/jwsr. ...## probability - Questioning on **bayes's** **theorem** - Mathematics Stack Exchange

Not the answer youre looking for? Browse other questions tagged probability

https://math.stackexchange.com/questions/1563240/questioning-on-bayess-theorem**bayes**-**theorem**or ask your own question. ... What does**Bayes****Theorem**tell you that the definition of conditional probability doesnt? ... begingroup$**Bayes**is OK, but in my experience students do better concentrating on the definition of conditional probability. $\ ... begingroup$ @AndréNicolas**bayes**formula is not right? $\endgroup$ - Allie Dec 6 15 at 22:39 ...## Using **bayes's** **theorem** for probability - Mathematics Stack Exchange

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## Evidence under **Bayes** **theorem** - Wikipedia

R v Adams - court case about

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**Theorem**is to take a set of prior beliefs and see how they change in the face of given evidence ... Using

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## The Converse of **Bayes** **Theorem** with Applications by Kai Wang Ng - 9781118349472

**Theorem**and demonstrates its unexpected applications and points to possible future applications, such as, solving the Bayesian ... This book introduces Converse of

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http://stattrek.com/probability/bayes-theorem.aspx?Tutorial=Stat**theorem**. Shows how to use**Bayes**rule to solve conditional probability problems. Includes sample problem with step-by-step ...**Bayes****Theorem**(aka,**Bayes**Rule).**Bayes****theorem**(also known as**Bayes**rule) is a useful tool for calculating conditional ...**Bayes****theorem**can be stated as follows:.**Bayes****theorem**.. Let A1, A2, ... , An be a set of mutually exclusive events that ... When to Apply**Bayes****Theorem**. Part of the challenge in applying**Bayes****theorem**involves recognizing the types of problems that ...## bayesian - XKCD's modified **Bayes** **theorem**: actually kinda reasonable? - Cross Validated

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... he describes a translation algorithm based on

https://www.johndcook.com/blog/2012/03/09/monkeying-with-bayes-theorem/**Bayes****theorem**. Pick the English word that has the highest posterior probability ... And I explain why**Bayes****Theorem**is important in almost every field.**Bayes**sets the limit for how much we can learn from ... Monkeying with**Bayes****theorem**. Posted on 9 March 2012. by John. In Peter Norvigs talk The Unreasonable Effectiveness of Data, ...**Bayes****theorem**is a remarkable thinking tool that has become sort of a revolution. And I think that this tribute is justified. ...**Bayes**' **Theorem** | Examples, Tables, and Proof Sketches (Stanford Encyclopedia of Philosophy)

Supplement to

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"

https://cy.wikipedia.org/wiki/Theorem_Bayes**Bayes****theorem**"is to the theory of probability what the Pythagorean**theorem**is to geometry". ... O fewn damcaniaeth tebygolrwydd ac o fewn ystadegau, mae**theorem****Bayes**(a elwir hefyd yn gyfraith**Bayes**) yn disgrifio ... Gellir datgan y**theorem**Bayesaidd, mewn hafaliad, fel:[3] P. (. A. ∣. B. ). =. P. (. B. ∣. A. ). P. (. A. ). P. (. B. ). ,. {\ ... "fod**theorem****Bayes**i theori tebygolrwydd yr hyn yw**theorem**Pythagoras i geometreg".[2] ...## Lesson 2.2 **Bayes**' **theorem** - Probability and **Bayes**' **Theorem** | Coursera

... we review the basics of probability and

https://www.coursera.org/lecture/bayesian-statistics/lesson-2-2-bayes-theorem-oANY8**Bayes****theorem**. In Lesson 1, we introduce the different paradigms ... ... Probability and**Bayes****Theorem**. In this module, we review the basics of probability and**Bayes****theorem**. In Lesson 1, we ... Lesson 2.2**Bayes****theorem**. To view this video please enable JavaScript, and consider upgrading to a web browser that supports ... In Lesson 2, we review the rules of conditional probability and introduce**Bayes****theorem**. Lesson 3 reviews common probability ...## Applying **Bayes**' **Theorem** to clinical trials. - Free Online Library

Applying

https://www.thefreelibrary.com/Applying+Bayes%27+Theorem+to+clinical+trials-a0404446690**Bayes****Theorem**to clinical trials.(MEDICAL TEST) by EE-Evaluation Engineering; Business Engineering and ... manufacturing Electronics**Bayes****theorem**Analysis Clinical trials Forecasts and trends Medical equipment Testing Physiological ... Pastor Thomas**Bayes**(1702-1761) appears to have had little influence on mathematics outside of statistics where**Bayes****Theorem**...**Theorem**+to+clinical+trials.-a0404446690. *APA style: Applying**Bayes****Theorem**to clinical trials.. (n.d.) >The Free Library. ( ...- This statistical method is named for Thomas Bayes who first formulated the basic process, which is this: begin with an estimate of the probability that any claim, belief, hypothesis is true, then look at any new data and update the probability given the new data. (theness.com)
- Galwyd y theorem ar ôl y Parchedig Thomas Bayes (1701-1761), y gŵr cyntaf i ddarparu hafaliad sy'n caniatáu tystiolaeth newydd i ddiweddaru credoau. (wikipedia.org)
- Pastor Thomas Bayes (1702-1761) appears to have had little influence on mathematics outside of statistics where Bayes' Theorem has found wide application. (thefreelibrary.com)
- Sometime during the 1740s, the Reverend Thomas Bayes made the ingenious discovery that bears his name but then mysteriously abandoned it. (lesswrong.com)
- In the 1700s, when probability theory was just a whiff in the air, the English Reverend Thomas Bayes wanted to know how to infer causes from effects. (lesswrong.com)
- The Reverend Thomas Bayes died 250 years ago this month. (r-bloggers.com)
- The series kicks off with the tribute to Thomas Bayes below. (r-bloggers.com)

- Not so fast, for Bayes Theorem is one of 'conditional probabilities' and we need to know the 'prior beliefs' before we make our decision. (livemint.com)
- Having observed the scoring pattern in the first three overs, Ramu 'updates' the probability of it being a batting pitch as 50% x 0.61% / (50% x 0.61% + 50% x 0.11%) = 85% (this is the all-important Bayes' formula for conditional probabilities). (livemint.com)
- Bayes' theorem (also known as Bayes' rule) is a useful tool for calculating conditional probabilities . (stattrek.com)

- Use the Bayes Rule Calculator to compute conditional probability, when Bayes' theorem can be applied. (stattrek.com)
- Reminds me of something I saw a few years ago: a student came to a meeting with pretty bad translation results when correctly using Bayes' rule. (johndcook.com)
- formulating it in terms of likelihoods and Bayes' rule is really less of a formalism and more of a framework that provides some constraints that are useful for limiting the search space. (johndcook.com)
- Although Bayes' rule drew the attention of the greatest statisticians of the twentieth century, some of them vilified both the method and its adherents, crushed it, and declared it dead. (lesswrong.com)
- In discovering its value for science, many supporters underwent a near-religious conversion yet had to conceal their use of Bayes' rule and pretend they employed something else. (lesswrong.com)
- Bayes' theorem is a rule in probability and statistical theory that calculates an event's probability based on related conditions or events. (decodedscience.org)

- begingroup$ @AndréNicolas bayes formula is not right? (stackexchange.com)
- begingroup$ Bayes is OK, but in my experience students do better concentrating on the definition of conditional probability. (stackexchange.com)
- begingroup$ explainxkcd.com/wiki/index.php/2059:_Modified_Bayes%27_Theorem the explanation from the author. (stackexchange.com)
- begingroup$ But shouldn't you apply Bayes theorem to P(C) to update its value in face of more evidence? (stackexchange.com)

- Bayes theorem computes the posterior probability, or the probability that, given you found the underwear, your spouse is cheating. (businessinsider.com)
- 2) While Bayes' theorem describes a way of obtaining the actual posterior probability, maximizing that is only loosely related to any downstream loss function you actually care about, and there are decision-theoretic reasons to add extra parameters (a temperature in this case) to your model to improve a downstream loss. (johndcook.com)

- James Rock explains how he's using Bayes's Theorem to fit data to a parametric distribution with Mathematica in this talk from the Wolfram Technology Conference. (wolfram.com)
- I think 'Bayes' Theorem' (but perhaps not Bayes's Theorem ) is catchier than the latter two suggestions. (lesswrong.com)

- In Peter Norvig's talk The Unreasonable Effectiveness of Data, starting at 37:42, he describes a translation algorithm based on Bayes' theorem. (johndcook.com)
- Rhoddodd Syr Harold Jeffreys algorithm Bayes a gwaith Laplace ar ffurf wirebol (acsiomatig). (wikipedia.org)

- This section presents an example that demonstrates how Bayes' theorem can be applied effectively to solve statistical problems. (stattrek.com)

- My most memorable encounter with the Reverend Bayes came one Friday afternoon in 1989, when my doctor told me by telephone that the chances were 999 out of 1,000 that I'd be dead within a decade. (lesswrong.com)

- In his new book, The Signal and the Noise , FiveThirtyEight 's founder Nate Silver gives the single most coherent explanation of Bayes' Theorem out there. (businessinsider.com)

- I have written a little about Bayes Theorem, mainly on Science-Based Medicine, which is a statistical method for analyzing data. (theness.com)
- However, there are some statistical nuances when applying Bayes to specific scientific situations. (theness.com)

- Part of the challenge in applying Bayes' theorem involves recognizing the types of problems that warrant its use. (stattrek.com)

- If she used Bayes' theorem, she could multiply those prior odds by a "likelihood ratio" in order to update her odds after learning that the hair matched the defendant's hair. (wikipedia.org)

- This month, Revolution Analytics' partner IBM Netezza commemorates Bayes' contributions to Statistics with a series of videos on Bayes Theorem, its applications, and the implications for Big Data and predictive analytics. (r-bloggers.com)

- Later on, it turned out to have been a simple mistake -- the test was a false positive, and the 999 out of 1,000 figure had been based on a lack of understanding about Bayes' Theorem. (lesswrong.com)

- Power point presentation, 15 slides explaining the Bayes' theorem in a way that can be understood by the students, using examples to make it more clear. (payhip.com)

- The assumption of equivalent confidence is necessary to justify application of Bayes' theorem to any finite sample. (johndcook.com)

- Bayes' theorem can be best understood through an example. (stattrek.com)

- As explained in the FDA's Guidance document, prior information about a topic that you wish to investigate in more detail can be combined with new data using Bayes' Theorem. (thefreelibrary.com)

- We then give the definitions of probability and the laws governing it and apply Bayes theorem. (coursera.org)
- We define and apply the central limit theorem to sampling problems and brieflyt- and c2. (coursera.org)
- The remainder of this lesson covers material that can help you understand when and how to apply Bayes' theorem effectively. (stattrek.com)

- Analysing murder cases is but one use of this legendary theorem-it has applications in pretty much every aspect of human life. (livemint.com)
- You will never be able to fit all of the applications of Bayes Theorem in one hour so pick one or two and make it look awesome. (lesswrong.com)
- Because since then, Bayes Theorem has been the underpinning of predictive analytics applications from spam detection to medical alerts. (r-bloggers.com)

- That is really the basic concept of Bayes Theorem. (theness.com)

- So, this is a problem that we'll utilize Bayes Theorem that we've already given. (coursera.org)

- So we experimented some, and we found out that when you raise that first factor [in Bayes' theorem] to the 1.5 power, you get a better result. (johndcook.com)

- Browse other questions tagged probability bayes-theorem or ask your own question . (stackexchange.com)

- The book goes back to Bayes' theorem constantly, and for excellent reasons - it's an exceptionally powerful way to honestly gauge a complex reality based on estimable probabilities, and is perhaps the most important theory in modern probability. (businessinsider.com)
- This book introduces Converse of Bayes? (qbd.com.au)

- At the moment, I'm thinking about how to design the class, so I'd appreciate any suggestions as to what content I should cover, the best format, clear ways to explain it, cool things related to Bayes' Theorem, good links, and so forth. (lesswrong.com)

- Bayes also shows mathematically why confirmatory tests are so powerful. (theness.com)
- Luckily Bayes' theorem shows us how to take it in into account. (maths.org)

- Imagine that Bayes has his back turned to a table, and he asks his assistant to drop a ball on the table. (lesswrong.com)

- In Lesson 2, we review the rules of conditional probability and introduce Bayes' theorem. (coursera.org)

- Some observers believe that in recent years (i) the debate about probabilities has become stagnant, (ii) the protagonists in the probabilities debate have been talking past each other, (iii) not much is happening at the high-theory level, and (iv) the most interesting work is in the empirical study of the efficacy of instructions on Bayes' theorem in improving jury accuracy. (wikipedia.org)

- In this piece, we will use Bayes' Theorem to analyse why people continue to hold extreme opinions. (livemint.com)
- If you want people to sign up for your class, don't call it Bayes Theorem, or anything equally boring (not many people can even pronounce 'representativeness heuristic' on the first try). (lesswrong.com)