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Topic: Bayes factor

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	BioMed Central \| Full text \| A new mixture model approach to analyzing allelic-loss data using Bayes factors
		For example, factors such as cell viability, fragility of the chromosome arm, and the length of telomeres are believed to influence background loss rates [6].
		Thus, as Bayes factors are proportional to the posterior odds of one model to another, they are desirable measures to use for model selection.
		The averaged Bayes factor would then be a ratio of the posterior probability of a two-component model to the posterior probability of a one-component model.
	www.biomedcentral.com /1471-2105/5/182 (6832 words)

	Stats: Bayesian resources
		The minimum Bayes factor is objective and can be used in lieu of the P value as a measure of the evidential strength.
		Bayes factors show that P values greatly overstate the evidence against the null hypothesis.
		Most important, Bayes factors require the addition of background knowledge to be transformed into inferences--probabilities that a given conclusion is right or wrong.
	www.childrens-mercy.org /stats/library/bayesian.asp (951 words)

	Research Details
		The BIC measure is an approximation to the Bayes Factor.
		It is possible to develop other approximations to the Bayes Factor that make use of fewer approximations than the BIC and thus, hold the potential to be more accurate.
		Our position is that the Bayes Factor could be a useful addition to the SEM literature, yet we need to evaluate the quality of measures that approximate it.
	math.bu.edu /people/sray/research (1994 words)

	BAYESIAN MINITAB MACROS
		The output is the Bayes factor and the posterior probability that the proportion is equal to the specific value.
		The output is the Bayes factor and the posterior probability of equality.
		The output is the Bayes factor and the posterior probability of the hypothesis for each value of the prior standard deviation.
	www-math.bgsu.edu /~albert/mini_bayes/bprog.html (2538 words)

	Plan of the Seminar
		Bayes Factors / Bayes Weights /Likelihood Ratio / Evidence/Logical Sufficiency The Bayes factor (or likelihood ratio) is used to determine weights corresponding to how well a probability distribution fits the observed data; that is, the better the fit, the higher the weighting.
		The Bayes Factor is not a probability but a ratio of probabilities, and it can vary from 0 to infinity.
		This factor is the posterior odds of the null hypothesis when the prior probability on the null is one-half.
	cogweb.iig.uni-freiburg.de /P/plan_of_the_seminar.html (6995 words)

	Implement Bayesian inference using PHP, Part 1 (Site not responding. Last check: 2007-09-17)
		I might arrive at the conclusion that the appearence of these words in the title strongly and specifically co-varies with the message being spam (after all, 18/18 = 100 percent) and this rule might be used to automatically filter such messages.
		In Bayes spam filtering, you need to initially train the software in which e-mails are spam and which are not.
		Bayes theorem is another method you can use to compute a conditional probability.
	www-128.ibm.com /developerworks/web/library/wa-bayes1 (5287 words)

	Bayes factor - Wikipedia, the free encyclopedia
		In statistics, the use of Bayes factors is a Bayesian alternative to classical hypothesis testing
		Bayesian procedures, including Bayes factors, are coherent, so there is no need to draw such a distinction.
		The ability of Bayes factors to take this into account is a reason why Bayesian inference has been put forward as a theoretical justification for and generalisation of Occam's razor, reducing Type I errors.
	en.wikipedia.org /wiki/Bayes_factor (695 words)

	Model comparison taking into account the a priori possible values of the model parameters
		2 the Bayes factors of the models of Fig.
		All other Bayes factors can be calculated as ratio of these.
		Bayes factors, for the four models of Fig.
	www.roma1.infn.it /~dagos/gwdaw2002/node11.html (1235 words)

	factor.bayes: Bayesian Factor Analysis (Site not responding. Last check: 2007-09-17)
		Given some unobserved explanatory variables and observed dependent variables, the Normal theory factor analysis model estimates the latent factors.
		The model is implemented using a Markov Chain Monte Carlo algorithm (Gibbs sampling with data augmentation).
		For factor analysis with ordinal dependent variables, see ordered factor analysis (Section
	gking.harvard.edu /zelig/docs/_TT_factor_bayes_TT__B.html (64 words)

	Bayes' Theorem (Stanford Encyclopedia of Philosophy)
		The odds of a hypothesis conditional on a body of data is equal to the unconditional odds of the hypothesis multiplied by the degree to which it surpasses its negation as a predictor of the data.
		In short, a rational believer who learns for certain that E is true should factor this information into her doxastic system by conditioning on it.
		Bayes, T. "An Essay Toward Solving a Problem in the Doctrine of Chances", Philosophical Transactions of the Royal Society of London 53, 370-418.
	plato.stanford.edu /entries/bayes-theorem (7479 words)

	Bayes factor analysis for the genetic background of physiological and vitality variables of F2 Iberian x Meishan ...
		Bayes factor analysis for the genetic background of physiological and vitality variables of F2 Iberian x Meishan newborn piglets -- Varona et al.
		Bayes factor analysis for the genetic background of physiological and vitality variables of F
		Bayes factors for detection of quantitative trait loci.
	www.animal-science.org /cgi/content/full/83/2/334 (2684 words)

	Sensitivity measures of the fractional Bayes factor - Conigliani, O'Hagan (ResearchIndex) (Site not responding. Last check: 2007-09-17)
		Calculation of a suitable Bayes factor is required for Bayesian model comparison.
		In recent years, several alternative Bayes factors have been introduced to address the problem of sensitivity of the usual Bayes factor when prior information is weak.
		Sensitivity of the fractional Bayes factor with respect to prior distributions is easy to assess when...
	citeseer.ist.psu.edu /45063.html (513 words)

	Derivation of a Bayes Factor to Distinguish Between Linked or Pleiotropic Quantitative Trait Loci -- Varona et al. 166 ...
		The Bayes factor is the ratio between the marginal probabilities
		The Bayes factor (BF) is defined as the ratio of marginal probabilities
		Bayes factors between the linkage and the pleiotropic model (top diagonal) with the posterior probability of the linkage model (in parentheses), and significance of the KH method for the detection of linkage under the null pleiotropy model (bottom diagonal)
	www.genetics.org /cgi/content/full/166/2/1025 (4277 words)

	[No title] (Site not responding. Last check: 2007-09-17)
		Generate random values of p from H1, and for each p generate a random value of r and compute the Bayes factor p(rH1)/p(rH0).
		Do that enough times so that a histogram of the Bayes factors is fairly stable.
		In Bayesian analysis, sample size is determined in various ways, but one approach is to determine the minimal N that yields a desired probability of the Bayes factor being greater than, say, 20.0.
	www.indiana.edu /~jkkteach/P747_2005/P747_Bayes_HW11.html (584 words)

	Using Data: The Bayes Factor (Site not responding. Last check: 2007-09-17)
		Bayes factor measures relative support data give to models
		Computation of Bayes factor often involves difficult integrals
		Bayes factor is sensitive to choice of prior distribution for qi
	ite.gmu.edu /~klaskey/modelco/tsld016.htm (47 words)

	Amazon.com: Bayes and Empirical Bayes Methods for Data Analysis: Books: Bradley P. Carlin,Thomas A. Louis (Site not responding. Last check: 2007-09-17)
		Bayes and Empirical Bayes Methods for Data Analysis answers the need for a ready reference that can be read and appreciated by practicing statisticians as well as graduate students.
		It introduces Bayes and EB methods, demonstrates their usefulness in challenging applied settings, and shows how they can be implemented using modern Markov chain Monte Carlo (MCMC) computational methods.
		Introduces Bayes and Empirical Bayes methods and demonstrates their usefulness in challenging applied settings and shows how they can be implemented using modern Markov chain Monte Carlo computational methods.
	www.amazon.com /Bayes-Empirical-Methods-Data-Analysis/dp/0412056119 (1330 words)

	The Intrinsic Bayes Factor for Model Comparison E. Moreno, F. Bertolino and W. Ragcuno University of Valencia, Spain (Site not responding. Last check: 2007-09-17)
		Thus the use of some kind of noninformative or default priors in constructing the Bayes Factor for models selection has recently received much attention.
		This fact makes these priors unsuitable to be used in constructing the associated Bayes Factor as long as it is also defined up to multiplicative constants.
		The most important theoretical justification of the IBF is that it is asymptotically equivalent to an actual Bayes Factor associated with the so-called Intrinsic Prior Distributions.
	web.uct.ac.za /depts/maths/isba96/abstracts/node32.html (325 words)

	Bayesian Phylogenetic Model Selection Using Reversible Jump Markov Chain Monte Carlo -- Huelsenbeck et al. 21 (6): 1123 ...
		Bayes factor the ratio of the average likelihoods is used instead.
		Bayes factor, or giving less prior weight to a good model.
		Bayes factors: what they are and what they are not.
	mbe.oxfordjournals.org /cgi/content/full/21/6/1123 (5399 words)

	R: Empirical Bayes thresholding on a sequence
		Given the mixing weight, and possibly a scale factor in the symmetric distribution, are estimated by marginal maximum likelihood.
		If hard or soft thresholding is chosen, then there is the additional choice of using the Bayes factor threshold, which is the value such that the posterior probability of zero is exactly half if the data value is equal to the threshold.
		Johnstone, I. and Silverman, B. Needles and straw in haystacks: Empirical Bayes estimates of possibly sparse sequences.
	www.stats.ox.ac.uk /~silverma/ebayesthresh/ebayethresh.html (439 words)

	No Title (Site not responding. Last check: 2007-09-17)
		The evolution equations characterizing likelihoods, posteriors, and Bayes factor are derived.
		Recursive algorithms are constructed via the Markov chain approximation method to compute likelihoods, posteriors, and Bayes factor.
		Simulation results show that the Bayes estimates for time-invariant parameters are consistent, the Bayes estimates for stochastic volatility capture the movement of volatility, and the Bayes factor can effectively select the right model.
	www.uwm.edu /~gb/COLLOQUIA/03-10-24/03-10-24.html (191 words)

	Consider a proof consisting of n steps
		A low Bayesian trick is to eliminate the prior probability by considering the so-called Bayes factor, defined as the ratio of the prior to posterior odds in favor of C, which in this case reduces to
		In this case, to achieve a Bayes factor of 0.05, you only have to check that around 15 randomly chosen steps are correct.
		Result: It is harder to check a correct theorem of a good mathematician than of an error-prone mathematician.
	www1.cs.columbia.edu /~traub/sloan/bayes.htm (329 words)

	Table 3 (Site not responding. Last check: 2007-09-17)
		Change in prior probabilities of cafestol not affecting serum cholesterol to posterior probabilities using data of the present study and Bayesian analysis
		A priori probabilities were converted to a priori odds and multiplied by the minimum Bayes factor*.
		Bayes factor* = e to the power -Z
	www.nutritionj.com /content/3/1/7/table/T3 (90 words)

	[No title]
		CN ------------------------------------------------------------ BAYES RULE: ------------------------------------------------------------ bayes_se (sets up models, priors, and likelihoods) bayes (sequentially implements bayes rule for independent sequence of observations) ------------------------------------------------------------ BINOMIAL P - DISCRETE MODELS: ------------------------------------------------------------ Learning about a proportion: p_disc C1 C2 K1 K2; store C3; plot.
		subcommand: a simulation sample size of K2 is taken scale factor for the Metropolis algorithm is K3 gibbs K1 K2 C1 C2; iter K3; scale K4 K5.
		subcommand: iterates Gibbs sampler for K3 cycles scale factors for the Metropolis algorithm are K4 and K5
	www-math.bgsu.edu /~albert/mini_bayes/local_macros/List_of_programs.txt (857 words)

	Default Bayes Factors for Non-Nested Hypothesis Testing - Berger, Mortera (ResearchIndex) (Site not responding. Last check: 2007-09-17)
		Abstract: Bayesian hypothesis testing for non-nested hypotheses is studied, using various "default" Bayes factors, such as the fractional Bayes factor, the median intrinsic Bayes factor and the encompassing and expected intrinsic Bayes factors.
		14 Approximate Bayes Factors and Orthogonal Parameters, with Ap..
		3 Bayes Factors for Intrinsic and Fractional Priors in Nested..
	citeseer.ist.psu.edu /401264.html (553 words)

	Bayesian inference
		where Prob(Null) is the prior probability for the null hypothesis that there is no real difference in the toxin level in the children, and BF is the so-called Bayes Factor, which measures how much we should alter our prior belief about the null hypothesis in the light of the new data, as captured by z.
		This highlights another factor in the continuing failure of Bayesian methods to supplant frequentist methods: the existence of many other apparently plausible explanations capable of masking the failings of frequentist methods.
		That, in any case, the effect of the choice of prior becomes increasingly irrelevant as data accumulates, with the only persistent effect of priors being the entirely natural one that sceptics of a specific claim require stronger evidence to reach the same level of belief than its advocates.
	ourworld.compuserve.com /homepages/rajm/twooesef.htm (7413 words)

	Testing for Cointegration Rank Using Bayes Factors
		Since using conjugate priors requires that we assign the prior parameters of which we often do not have prior information, and testing by Bayes factor is very sensitive to the parameters, we propose in this paper using the maximum likelihood estimators for the prior parameters.
		Since normal Bayes factor cannot be computed with non-informative priors, we apply the intrinsic Bayes factor (IBF) proposed by Berger and Pericchi (1996).
		Monte Carlo simulations show that using Bayes factor with conjugate priors and the IBF with non-informative priors produce fairly good results.
	ideas.repec.org /p/ecj/ac2002/171.html (293 words)

	CiteULike: Toward evidence-based medical statistics. 2: The Bayes factor. (Site not responding. Last check: 2007-09-17)
		Unlike P values, Bayes factors have a sound theoretical foundation and an interpretation that allows their use in both inference and decision making.
		They make the distinction clear between experimental evidence and inferential conclusions while providing a framework in which to combine prior with current evidence.
		They make the distinction clear between experimental evidence and inferential conclusions while providing a framework in which to combine prior with current evidence.}, address = {Johns Hopkins University School of Medicine, Baltimore, Maryland, USA.
	www.citeulike.org /user/garyfeng/article/496972 (508 words)

	Zool 575 - lab 23 - Model Selection
		The 'total' harmonic mean of the marginal likelihood is what you'll use to calculate the Bayes Factor.
		Also NOTE: If these models are very similar (Bayes Factor 3 or less) you can double-check the value of Gamma by looking in the sump output for the Mkv+G run and looking at the value of the parameter 'alpha'.
		So if the Bayes Factor is small then the alpha should be large.
	www.ucalgary.ca /~dsikes/zool575/z575_lab23a.htm (1757 words)

	Bayes Factor of Model Selection Validates FLMP (ResearchIndex) (Site not responding. Last check: 2007-09-17)
		Bayes Factor of Model Selection Validates FLMP (ResearchIndex)
		Bayes Factor of Model Selection Validates FLMP (2001)
		78.2%: Bayes Factor of Model Selection Validates FLMP - Massaro, Cohen, Campbell..
	citeseer.ist.psu.edu /644569.html (235 words)

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