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.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.ArchivesWriting: The act or practice of literary composition, the occupation of writer, or producing or engaging in literary work as a profession.Sequence Analysis, DNA: A multistage process that includes cloning, physical mapping, subcloning, determination of the DNA SEQUENCE, and information analysis.Libraries: Collections of systematically acquired and organized information resources, and usually providing assistance to users. (ERIC Thesaurus, http://www.eric.ed.gov/ accessed 2/1/2008)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, LaboratoryJuvenile 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.NebraskaBasal 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.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.Eye Hemorrhage: Intraocular hemorrhage from the vessels of various tissues of the eye.Epidemiology: Field of medicine concerned with the determination of causes, incidence, and characteristic behavior of disease outbreaks affecting human populations. It includes the interrelationships of host, agent, and environment as related to the distribution and control of disease.Decision Making: The process of making a selective intellectual judgment when presented with several complex alternatives consisting of several variables, and usually defining a course of action or an idea.Coronary Artery Disease: Pathological processes of CORONARY ARTERIES that may derive from a congenital abnormality, atherosclerotic, or non-atherosclerotic cause.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)Cemeteries: Areas set apart as burial grounds.LondonGraves 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.

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)

  • Theorem and demonstrates its unexpected applications and points to possible future applications, such as, solving the Bayesian Missing Data Problem (MDP) when the joint support of parameter and missing data is not one piece, and de-conditioning in the distribution theory that also serves as a tool to detect incompatible conditional specifications. (qbd.com.au)
  • They guide the viewer through Bayes' thought process coming up with the theory, explain its workings, but also acknowledge some of the issues when applying Bayesian statistics in society. (paulvanderlaken.com)
  • The name "Bayesian" comes from the frequent use of Bayes' theorem in the inference process. (academic.ru)
  • Under Bayesian inference, Bayes' theorem therefore measures how much new evidence should alter a belief in a hypothesis. (academic.ru)
  • The Naive Bayes Classifier technique is based on the so-called Bayesian theorem and is particularly suited when the dimensionality of the inputs is high. (knoldus.com)
  • Building on prior research of using Bayes' theorem to handle uncertainty in input, this paper formalized Bayes' theorem as a generic guiding principle for deciding targets in command input (referred to as "BayesianCommand"), developed three models for estimating prior and likelihood probabilities, and carried out experiments to demonstrate the effectiveness of this formalization. (research.google)
  • We then use Bayes Theorem to compute posterior probabilities for several non-nested models of industry equilibrium. (repec.org)
  • 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)
  • In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule ) describes the probability of an event, based on prior knowledge of conditions that might be related to the event. (knoldus.com)
  • O fewn damcaniaeth tebygolrwydd ac o fewn ystadegau , mae theorem Bayes (a elwir hefyd yn gyfraith Bayes ) yn disgrifio tebygolrwydd rhyw ddigwyddiad, yn seiliedig ar wybodaeth flaenorol o amodau a allai fod yn gysylltiedig â'r digwyddiad. (wikipedia.org)
  • 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)
  • In technical terms, in Bayes' theorem the impact of new data on the merit of competing scientific hypotheses is compared by computing for each hypothesis the product of the antecedent plausibility and the likelihood of the current data given that particular hypothesis and rescaling them so that their total is unity. (medical-library.net)
  • The equations for multiple parameter estimation are found by applyhg the method of maximum Ilkellhood to Bayes' theorem probability dlstrlbution for data obtained In the shot noise limit. (usu.edu)
  • Ei gyfaill, y Cymro a'r dyngarwr byd enwog Richard Price o Langeinwyr a sylwodd ar y wybodaeth newydd hon, wrth iddo fynd drwy bapurau Bayes, wedi'i angladd. (wikipedia.org)
  • Bayes' theorem is employed in clinical epidemiology to determine the probability of a particular disease in a group of people with a specific characteristic on the basis of the overall rate of that disease and of the likelihood of that specific characteristic in healthy and diseased individuals, respectively. (medical-library.net)
  • A really good understanding of Bayes' Theorem implies that experimentation is essential: if you've been doing the same thing for a long time and getting the same result - that you're not necessarily happy with - maybe it's time to change. (paulvanderlaken.com)
  • Naive Bayes implies that classes of the training dataset are known and should be provided hence the supervised aspect of the technique. (xlstat.com)