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.

*  The effect of prior assumptions over the weights in BayesPI with application to study protein-DNA interactions from ChIP-based...
Bayes Theorem*. Chromatin Immunoprecipitation*. DNA / metabolism*. DNA-Binding Proteins / metabolism*. Monte Carlo Method. ... Based on Bayes' theorem, a posterior distribution of the model parameters, can be given as ... and then infer the hyperparameters through Bayes' rule ...
*  Structure learning in a sensorimotor association task. - CUED Publications database
Bayes Theorem Humans Learning Motor Cortex. Subjects:. UNSPECIFIED. Divisions:. Div F , Computational and Biological Learning. ...
*  Atheism: Proving The Negative: Proving Atheism and Bayes' Theorem
Proving Atheism and Bayes' Theorem There's a significant difference between the actual probability that some event will or has ... The incredible thing about Bayes' theorem is that it allows us to account for the two different starting points in ... then as we saw with Bayes' Theorem, whatever prior probabilities you have concerning some issue, you should continuously fold ...
*  Internet Archive Search: mediatype:texts AND subject:"BAYES THEOREM"
Donor challenge: A generous supporter will match your donation 3 to 1 right now. Triple your impact! Dear Internet Archive Supporter,. I ask only once a year: please help the Internet Archive today. We're an independent, non-profit website that the entire world depends on. Most can't afford to donate, but we hope you can. If everyone chips in $5, we can keep this going for free. For a fraction of the cost of a book, we can share that book online forever. When I started this, people called me crazy ...
*  What Is Bayes Theorem? | NeuroLogica Blog
I have written a little about Bayes Theorem, mainly on Science-Based Medicine, which is a statistical method for analyzing data ... That is really the basic concept of Bayes Theorem. However, there are some statistical nuances when applying Bayes to specific ... Bayes Theorem is just one of the plethora of tools in the toolbox, but the only tools that apply to the whole toolbox are the ... I think Bayes' theorem is a vital part of understanding the process of Science. Not because people need to be able to do the ...
*  Bayes Theorem-Probabilty Question
From Bayes' Theorem we have:. p(p , c) = p(c , p) * p(p) / p(c) (1). p(ph , c) = p(c , ph) * p(ph) / p(c) (2). p(l , c) = p(c ... From Bayes' Theorem we have:. p(p , c) = p(c , p) * p(c) / p(p) (1). p(ph , c) = p(c , ph) * p(c) / p(ph) (2). p(l , c) = p(c ... Bayes Theorem-Probabilty Question. Hello Hi everybody!. Here is a new thread I faced difficult in solving please give me the ... Bayes' theorem is:. {vertical-align:15%;} which is not what you have here.. CB. ...
*  Bayes Theorem - Who Posted?
Math Help Forum is a free math help forum for Calculus, Algebra, LaTeX, Geometry, Trigonometry, Statistics and Probability, Differential Equations, Discrete Math
*  Bayes theorem (disambiguation) - Wikipedia
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 ...
*  Bayes' theorem |
Bayes Theorem by apollos ✓. Bayes Theorem by apollos ✓. all events must have nonzero probability (+ other suggestions) by yark ... Bayes' theorem. Let (. A. n. ). subscript. A. n. (A_{n}). be a sequence of mutually exclusive events whose union is the sample ... Bayes' Theorem states. P. (. A. j. ,. E. ). =. P. (. A. j. ). P. (. E. ,. A. j. ). ∑. i. P. (. A. i. ). P. (. E. ,. A. i. ). ...
*  Evidence under Bayes theorem - Wikipedia
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 ...
*  Decision Under Uncertainty - Bayes' Theorem
Use probability concepts found in Bayes' Theorem to formulate a decision. Address the following: - Include how you applied. ... Decision Under Uncertainty - Bayes' Theorem Add. Remove. Need help with the following:. Research statistical data in a business ... Use probability concepts found in Bayes' Theorem to formulate a decision.. Address the following:. - Include how you applied ... In probability theory and statistics, Bayes' theorem is a concept where there are two distinct interpretations. These are ...
*  Bayes' theorem - Wikipedia
"Bayes Factor." Weisstein, Eric W. "Bayes' Theorem". MathWorld. Bayes' theorem at Bayes Theorem and the Folly of ... the subjective Bayes' theorem represents a generalization of Bayes' theorem. Bayes' theorem was named after Thomas Bayes (1701- ... Jeffreys wrote that Bayes' theorem "is to the theory of probability what the Pythagorean theorem is to geometry". Bayes' ... Laplace refined Bayes' theorem over a period of decades: Laplace announced his independent discovery of Bayes' theorem in: ...'_theorem
*  Using Naive Bayes Theorem to label data
... 11 March 2017. on Naive Bayes, Machine Learning, Supervised Learning, Data Mining, ... Today I am going to write off-topic about using Naive Bayes algorithm for record classification. This is a supervised category ... Suppose you're given following dataset which has unknown label and your task is to use training dataset and Naive Bayes ... To make sure you understood the Naive Bayes explanation correctly, here's another test dataset with unknown label. Can you ...
*  Specialized computer support systems for medical diagnosis. Relationship with the Bayes' theorem and with logical diagnostic...
Nomogram for Bayes's theorem. N Eng J Med 1975; 243: 57. [ Links ]. 32. Brito AHX. Análise bayesiana do teste ergométrico. Arq ... Bayes' theorem Although the concepts of sensitivity and specificity are well understood, the same does not apply to the ... One way to minimize them would be the use of the Bayes' theorem converted into a system of scores, as proposed by Rembold and ... Other forms of utilization of the Bayes' theorem have been proposed, for example the use of nomograms 31 , and the 2 x 2 table ...
*  Probably Overthinking It: Bayes's Theorem is not optional
2) There is nothing especially Bayesian about Bayes's Theorem! Bayes's Theorem is an uncontroversial law of probability that is ... I agree there's no Bayes-vs-frequentist difference there. And I agree it's very important to distinguish Bayes' theorem from ... rather than Bayes's Rule (based on odds). To apply Bayes's Theorem, you might find it helpful to use my "Bayesian update ... my test blog has left a new comment on your post 'Bayes's Theorem is not optional': If you look at the answer linked to in the ...
*  Define bayes theorem. describe hypothesis testing, Ask an Expert
problem 11)a) (i) Define Bayes theorem.. (ii) In a bolt factory, machines A,B and C manufacture respectively 32%, 58% and 10% ...
*  The Emirates Economist: Now apply Bayes theorem :: Greg Mankiw's Blog
Now apply Bayes theorem :: Greg Mankiw's Blog Mankiw:. Note the relative performance of Hillary Clinton and John Edwards. ...
*  Carrier, Bayes Theorem, and Jesus' Existence - The Bart Ehrman Blog
Bayes' theorem was logically proven by Rev. Thomas Bayes, and so I don't think it can be disputed. The real trouble with ... Carrier, Bayes Theorem, and Jesus' Existence. As most of you know, I'm pretty much staying out of the mythicist debates. That ... Bayes' theorem then allows us to move to a final probability P(H1,O), which is the probability that a hypothesis is true given ... To apply Bayes' Theorem, we will need to know P(O,H1), i.e. the probability of the manuscript having been produced given that ...
*  Speaking of Science: Bayes Theorem and Its Relevance to Skepticism |
... containing what is now known as Bayes' theorem. Bayes' theorem remained relatively obscure for two centuries, but has since ... Bayes' simple but powerful theorem is notable for its subjectivist interpretation of probability, providing a mathematically ... Chris Everett will present a simple derivation of this important theorem and discuss some of its implications for everyday ... In 1763, the Reverend Thomas Bayes published "An Essay towards solving a Problem in the Doctrine of Chances," ...
*  Veritasium: Bayes' Theorem explained -
... and recently they recorded one offering an intuitive explanation of Bayes' Theorem. They guide the viewer through Bayes' ... The thing we forget in Bayes' Theorem is… ... "The thing we forget in Bayes' Theorem is that our actions play ... and recently they recorded one offering an intuitive explanation of Bayes' Theorem. They guide the viewer through Bayes' ... Veritasium: Bayes' Theorem explained. Date: 6 April 2017Author: Paul van der Laken 0 Comments ...
*  SAGE Reference - Bayes' Theorem, Bayes' Rule
Jackman, S. (2004). Bayes' theorem, bayes' rule. In M. S. Lewis-BeckA. Bryman & T. F. Liao (Eds.), The SAGE encyclopedia of ... Jackman, S 2004, 'Bayes' theorem, bayes' rule', in Lewis-Beck, MS, Bryman, A & Liao, TF (eds), The sage encyclopedia of social ... Jackman, S. (2004). Bayes' theorem, bayes' rule. In M. S. Lewis-BeckA. Bryman & T. F. Liao (Eds.), The SAGE encyclopedia of ... Jackman, S 2004, 'Bayes' theorem, bayes' rule', in Lewis-Beck, MS, Bryman, A & Liao, TF (eds), The sage encyclopedia of social ...
*  Atheism: Proving The Negative: Proving Atheism and Bayes' Theorem
Proving Atheism and Bayes' Theorem There's a significant difference between the actual probability that some event will or has ... The incredible thing about Bayes' theorem is that it allows us to account for the two different starting points in ... then as we saw with Bayes' Theorem, whatever prior probabilities you have concerning some issue, you should continuously fold ...
*  Applied Abstractions: Creating an activity about Bayes' Theorem from a blog post
Theorem. While the questions aren't directly about Bayes' Theorem, it gets students more familiar with conditional ... In my statistics class we were to cover Bayes' Theorem, a topic I have always enjoyed presenting, but never felt that I got ... To address this I wanted to create an activity where students were to apply Bayes' Theorem in a relatively simple way. ... Searching the internet I found the article (an essay really) An Intuitive Explanation of Bayes' Theorem by Eliezer S. Yudkowsky ...
*  Discrete Mathematics Problem on Bayes' Theorem: 10 Boxes - Geoff Pilling | Brilliant
The number of red balls in the \(n^\text{th}\) box is given by \(R(n) = 1024 - B(n)\). A box is picked at random, and a ball is chosen randomly from that box. If the ball is blue, and the probability that the \(10^\text{th}\) box was picked can be expressed as \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\). ...

Hyperparameter: In Bayesian statistics, a hyperparameter is a parameter of a prior distribution; the term is used to distinguish them from parameters of the model for the underlying system under analysis.P-adic Hodge theory: In mathematics, p-adic Hodge theory is a theory that provides a way to classify and study p-adic Galois representations of characteristic 0 local fieldsIn this article, a local field is complete discrete valuation field whose residue field is perfect. with residual characteristic p (such as Qp).Clonal Selection Algorithm: In artificial immune systems, Clonal selection algorithms are a class of algorithms inspired by the clonal selection theory of acquired immunity that explains how B and T lymphocytes improve their response to antigens over time called affinity maturation. These algorithms focus on the Darwinian attributes of the theory where selection is inspired by the affinity of antigen-antibody interactions, reproduction is inspired by cell division, and variation is inspired by somatic hypermutation.Bill Parry (mathematician)Inverse probability weighting: Inverse probability weighting is a statistical technique for calculating statistics standardized to a population different from that in which the data was collected. Study designs with a disparate sampling population and population of target inference (target population) are common in application.Index of information theory articles: This is a list of information theory topics, by Wikipedia page.Von Neumann regular ring: In mathematics, a von Neumann regular ring is a ring R such that for every a in R there exists an x in R such that . To avoid the possible confusion with the regular rings and regular local rings of commutative algebra (which are unrelated notions), von Neumann regular rings are also called absolutely flat rings, because these rings are characterized by the fact that every left module is flat.Interval boundary element method: Interval boundary element method is classical boundary element method with the interval parameters.
Negative probability: The probability of the outcome of an experiment is never negative, but quasiprobability distributions can be defined that allow a negative probability for some events. These distributions may apply to unobservable events or conditional probabilities.Enzyme Commission number: The Enzyme Commission number (EC number) is a numerical classification scheme for enzymes, based on the chemical reactions they catalyze.Yarrow oilMatrix model: == Mathematics and physics ==Decoding methods: In coding theory, decoding is the process of translating received messages into codewords of a given code. There have been many common methods of mapping messages to codewords.

(1/6254) Bayesian inference on biopolymer models.

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  (+info)

(2/6254) Genetic determination of individual birth weight and its association with sow productivity traits using Bayesian analyses.

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)

(3/6254) Bayesian mapping of multiple quantitative trait loci from incomplete outbred offspring data.

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  (+info)

(4/6254) The validation of interviews for estimating morbidity.

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)

(5/6254) Bayesian analysis of birth weight and litter size in Baluchi sheep using Gibbs sampling.

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)

(6/6254) Thermodynamics and kinetics of a folded-folded' transition at valine-9 of a GCN4-like leucine zipper.

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)

(7/6254) Iterative reconstruction based on median root prior in quantification of myocardial blood flow and oxygen metabolism.

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)

(8/6254) Taking account of between-patient variability when modeling decline in Alzheimer's disease.

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)

  • Pythagorean
  • Examples include Hubble's law which was derived by Georges Lemaître two years before Edwin Hubble, the Pythagorean theorem although it was known to Babylonian mathematicians before Pythagoras, and Halley's comet which was observed by astronomers since at least 240 BC. (
  • statistics
  • According to one historian of statistics, he may have been the earliest discoverer of Bayes theorem. (
  • It was Pierre-Simon Laplace (1749-1827) who introduced a general version of the theorem and used it to approach problems in celestial mechanics, medical statistics, reliability, and jurisprudence. (
  • Science
  • The use of the Bayes theorem has been extended in science and in other fields. (
  • Eponym List of examples of Stigler's law List of misnamed theorems List of persons considered father or mother of a scientific field Matthew effect Matilda effect Obliteration by incorporation Scientific priority Standing on the shoulders of giants Theories and sociology of the history of science Gieryn, T. F., ed. (1980). (
  • allows
  • The incredible thing about Bayes' theorem is that it allows us to account for the two different starting points in probabilistic terms and it has the facility for us to engage in an analysis that can resolve the issue. (
  • Logic
  • According to the objectivist view, probability is a reasonable expectation that represents the state of knowledge, can be interpreted as an extension of logic, and its rules can be justified by Cox's theorem. (
  • case
  • c. 1701 - 7 April 1761) was an English statistician, philosopher and Presbyterian minister who is known for having formulated a specific case of the theorem that bears his name: Bayes' theorem. (
  • example
  • For example, if cancer is related to age, then, using Bayes' theorem, a person's age can be used to more accurately assess the probability that they have cancer, compared to the assessment of the probability of cancer made without knowledge of the person's age. (