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Topic: Posterior probability

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	POSTERIOR PROBABILITY DECODING, CONFIDENCE ESTIMATION AND SYSTEM COMBINATION
		The posterior probability estimates were used as the basis for the estimation of word-level confidence scores.
		The estimation of word-level posterior probabilities is based on the word lattices generated by a conventional Viterbi decoder.
		The word posterior probabilities that result from the confusion network clustering procedure can be used directly as confidence scores but they tend to overestimate the probabilities of correct recognition.
	www.nist.gov /speech/publications/tw00/html/cp230/cp230.htm (3138 words)

	NationMaster - Encyclopedia: Posterior probability distribution (Site not responding. Last check: )
		Compare with prior probability, which may be assessed in the absence of empirical data, or which may incorporate pre-existing data and information.
		The posterior probability can be calculated by Bayes' theorem from the prior probability and the likelihood.
		Similarly a posterior probability distribution is the conditional probability distribution of the uncertain quantity given the data.
	www.nationmaster.com /encyclopedia/Posterior-probability-distribution (264 words)

	Argument from Probability - SkepticWiki (Site not responding. Last check: )
		This fallacy is often combined with mis-estimations of the probabilities involved or a confusion between prior and posterior probabilities, resulting in mathematically incorrect calculations.
		To misinterpret a statement of probability in such a fashion is to commit the fallacy of equivocation.
		The prior probability is the probability of an event occurring without taking evidence into account, while the posterior probability is the probability calculated when subsequent evidence is observed and analyzed.
	www.skepticwiki.org /wiki/index.php/Argument_from_Probability (662 words)

	Highbeam Encyclopedia - Search Results for posterior
		In Bayesian inference, the probability assigned to an event, in accordance with Bayes' theorem, in the light of empirical evidence as to its observed relative frequency.
		A form of statistical reasoning in which prior probabilities (2) are modified in the light of data or empirical evidence in accordance with Bayes' theorem to yield posterior probabilities, which may then be used as prior probabilities for further updating in the light of...
		Transoral resection of spinal cord tumors and posterior cervical spine stabilization.
	www.encyclopedia.com /SearchResults.aspx?Q=posterior (909 words)

	The Expectation of Posterior Beliefs
		This stands to reason, because if our initial 'prior' is in the right direction, our posterior results won't change very much, but if our initial prior is wrong, our sequence of posterior estimates will have to migrate farther and therefore more trials will be needed to gain the same level of confidence.
		Since h(p) and t(p) are inverses of each other, the posterior probability after m heads and n tails (in any order) is the same as after mn heads in a row.
		Notice that if m = n the final posterior probability is simply p, meaning that if we get an equal number of heads and tails we end up with the same "belief" as at the start.
	www.mathpages.com /home/kmath436/kmath436.htm (979 words)

	Curiosity is bliss: Bayesian probability and networks (Site not responding. Last check: )
		In particular, you can assign a probability before even doing the experiment: there is no need to toss a coin a thousand times to determine the probability of heads being the result of the next toss.
		Each node is then described by a probability distribution that is conditioned on the state of the nodes that it depends on.
		A) is the probability of being in B (or actually inside the intersection of A and B) given that you are within A. Posted by Julien.
	blog.monstuff.com /archives/000108.html (1661 words)

	Posterior probability - Encyclopedia, History, Geography and Biography
		The posterior probability of a random event or an uncertain proposition is the conditional probability it is assigned when the relevant evidence is taken into account.
		The posterior probability distribution of one random variable given the value of another can be calculated by Bayes' theorem by multiplying the prior probability distribution by the likelihood function, and then dividing by the normalizing constant, as follows:
		$f_{X\mid Y=y}(x)$ is the posterior density of X given the data Y = y.
	www.arikah.com /encyclopedia/Posterior_distribution (253 words)

	BioMed Central \| Full text \| Bayesian meta-analysis models for microarray data: a comparative study
		The gene-specific posterior probability of differential expression is again produced; however, this probability is based upon the separate mean levels of each study rather than an overall mean level, as in Model (1).
		This is due to keeping the study means separate in the PI model, and thus genes with high probability of differential expression in one study are not overly offset by genes with lower probability of differential expression in the second study.
		By calculating the probability of differential expression based on the separate study means in the PI model, genes with high probability of differential expression in at least one study produce a higher overall probability of differential expression in the PI meta-analysis.
	www.biomedcentral.com /1471-2105/8/80 (8538 words)

	Presentation: Additional Practical and Computational Issues - Potential Information Requested by FDA
		Posterior predictive distribution is the distribution of a new, hypothetical observation from the trial, under the assumptions of the current model
		Posterior odds refer to the ratio of the posterior probability of the model to its complement.
		Prior predictive probability should be reasonably lower than the posterior probability needed to meet the study claim.
	www.fda.gov /cdrh/meetings/072706-bayesian/presentation5.html (796 words)

	BAYESACT Call
		is the prior probability of contamination for the ith observation.
		Based on the prior probability of contamination for each observation, the call gives the posterior probability of contamination for each observation and the posterior probability that the entire sample is uncontaminated.
		To adequately explore posterior probabilities, examine them over a range of values for prior probabilities and a range of contamination coefficients.
	www.colostate.edu /Services/ACNS/swmanuals/sasdoc/sashtml/qc/chapc/sect6.htm (572 words)

	TheFetus.net - How to use Bayes theorem to estimate sequential conditional risks-DJR Hutchon and A Khattab
		Bayes theorem does refer to probabilities, which is equivalent to the word "risk".
		(Prior probability) If we are told that all the small balls are white (the equivalent of a likelihood ratio), then knowing the size will allow us to determine whether or not we have picked a white or red (posterior probability).
		The probability of Down syndrome in the new population is (P+Q)/(P+Q+R+S).
	www.thefetus.net /page.php?id=1115 (1149 words)

	Methods for approximating the posterior probability
		The methods are complementary because the accuracy of the approximation depends on the complexity of the posterior probability which can be affected by the design of the model.
		If it is known in advance which prediction or decision is going to be made based on the posterior probability, the approximation can and should take this into account.
		In many cases this information is not available, however, and then the best thing to do is to try to approximate those parts of the posterior probability which have the highest probability mass because those are the ones which have the strongest impact on the predictions and decisions.
	www.cis.hut.fi /harri/thesis/valpola_thesis/node21.html (227 words)

	Background
		The posterior probability estimates for each group are based on the posterior probabilities of the observations classified into that same group.
		The posterior probability estimates provide good estimates of the error rate when the posterior probabilities are accurate.
		They conclude that the cross validation posterior probability estimator has a lower mean squared error in their simulations.
	www.okstate.edu /sas/v7/sashtml/books/stat/chap23/sect17.htm (2338 words)

	Simulations for Pro-Busqueda
		Assuming that both the biological and the adoptive families know those three data, then perhaps that typically reduces the possible (original) identities for a particular adoptee down to 10 choices (factors of 1/2, 1/5, 1/5).
		The average posterior probability seems like a sensible summary statistic.
		And that is the way the average posterior probability works – it is mostly a measure of the less successful simulations.
	dna-view.com /ProBusqueda.htm (752 words)

	Implement Bayesian inference using PHP, Part 1
		In other words, the probability of a customer buying product A given that they have purchased product B can be estimated at 83 percent by using a method that involves enumerating relative frequencies of A and B events from the data gathered to date.
		The exact nature of the full posterior probability computation is made clearer by seeing that the posterior and likelihood terms appear in a PHP implementation as two-dimensional arrays (the closest you can currently get to a matrix datatype in PHP).
		The probability appearing in the denominator * serves a normalizing role in the computation - it ensures that * posterior probabilities sum to 1.
	www-128.ibm.com /developerworks/web/library/wa-bayes1 (5297 words)

	Posterior Probability
		The posterior probability of an event is the probability of the event computed following the collection of new data.
		One begins with a prior probability of an event and revises it in the light of new data.
		For example, if 0.01 of a population has schizophrenia then the probability that a person drawn at random would have schizophrenia is 0.01.
	davidmlane.com /online_stat/glossary/posterior_probability.html (83 words)

	Proc. SPIE (1991) - Abstract (Site not responding. Last check: )
		This approximation to the likelihood function was used because a full characterization of the posterior probability function had not yet been performed.
		In this case the reconstruction is chosen to maximize the posterior probability and task performance involves using the posterior probability of the various alternatives as the decision variable.
		This full Bayesian approach should lead to optimal results because the posterior probability incorporates the full dependence on the measurements and constraints, yet is based on the relatively simple likelihood and prior probability distributions.
	public.lanl.gov /kmh/publications/medim91m.abs.html (264 words)

	A Model-Based Method for Identifying Species Hybrids Using Multilocus Genetic Data -- Anderson and Thompson 160 (3): ...
		(b) Posterior probabilities of genotype frequency class for fish 19, 48, 16, and 72—the four plotted as triangles in a.
		The solid symbols are for alleles in the steelhead population, and the open symbols denote the cutthroat allele frequencies.
		(c) Posterior probability of either Pure Cutt or Pure St for 45 simulated hybrid trout of genotype frequency classes denoted by the different symbols as given in the inset.
	www.genetics.org /cgi/content/full/160/3/1217 (7601 words)

	Bayes' Theorem: Clinical Decision Making: Merck Manual Professional
		To illustrate how this table can be used to revise probabilities, consider a 2nd woman with dysuria and frequency, but no vaginal discharge or irritation, who has had frequent UTIs in the past; assume that her prior probability of UTI is high, say 77%.
		The process of using the pre-test probability of disease and the test characteristics to calculate the post-test probability is called Bayes' theorem or bayesian revision.
		The conditional probability used for interpreting subsequent test results must be based on the gold standard for diagnosis and on the observed results of the preceding test.
	www.merck.com /mmpe/print/sec22/ch328/ch328e.html (1961 words)

	Joint Program in Nuclear Medicine
		In this case, nuclear medicine physicians have a natural understanding of the probability of pulmonary embolism before and after the lung scan.
		Bayes' Theorem relates prior probability of disease, the test result which can be given as a likelihood ratio, and the posterior probability of disease (see for example: Parker JA: Java Calculators for Radiology Applications: Absorbed Dose and Bayes' Theorem.
		Since she denied a family history of clotting problems at the time of evaluation, this piece of information cannot be used in assessment of prior probability.
	www.med.harvard.edu /JPNM/InterestingImages/Case17ii/Dx17.html (626 words)

	Bayesian Phylogenetic Analysis
		These are clade-credibility values, and are in fact the posterior probability that the clade is real (based on the present data set).
		Secondly, the posterior probability distribution of each parameter is summarized by giving the mean, variance, median, and 95% credible interval.
		If the prior probability distribution is flat (i.e., if all possible parameter values have the same prior probability) then the posterior distribution is simply proportional to the likelihood distribution, and the parameter value with the maximum likelihood then also has the maximum posterior probability.
	www.cbs.dtu.dk /courses/PR/bayes.php (3911 words)

	[No title]
		The posterior mean of p1 is 1/42 = 0.024, the posterior variance is 0.0235.
		In example 4, we get the posterior distribution of p1 and p2 as the product of beta(1, 35) and beta(18.2, 0.13) In cases when the p1 and p2 are not apriori independent we apply Bayes Rule to the joint distributions.
		The 95% posterior probability interval for the difference is: -1.2 ± 1.96 (5.152).
	www.itl.nist.gov /div898/education/bayes/bayesclassday2.doc (2459 words)

	Bayesian Analysis and Risk Assessment in Genetic Counseling and Testing -- Ogino and Wilson 6 (1): 1 -- Journal of ...
		the prior probabilities are the probability that she is a carrier
		represents the prior probability that the consultand is a non-carrier
		probability that the consultand is a carrier (1/2), and that
	jmd.amjpathol.org /cgi/content/full/6/1/1 (5088 words)

	Posterior probability Details, Meaning Posterior probability Article and Explanation Guide
		Compare with prior probability, which may be assessed in the absence of empirical data, or which may incorporate pre-existing data and information.
		The posterior probability can be calculated by Bayes' theorem from the prior probability and the likelihood.
		Similarly a posterior probability distribution is the conditional probability distribution of the uncertain quantity given the data.
	www.e-paranoids.com /p/po/posterior_probability.html (161 words)

	Posterior Probability Error-Rate Estimates
		The posterior probability error-rate estimates (Fukunaga and Kessell 1973; Glick 1978; Hora and Wilcox 1982) for each group are based on the posterior probabilities of the observations classified into that same group.
		When the prior probabilities of the group membership are proportional to the group sizes, the stratified estimate is the same as the unstratified estimator.
		which is one minus the average value of the maximum posterior probabilities for each observation in the sample.
	www.dnr.state.ak.us /ssd/whtest/sashtml/stat/chap25/sect18.htm (415 words)

	Bayes's Theorem and the Likelihood Function
		The likelihood function, by definition, is the probability density of getting the data that we actually observed, as a function of the value of
		Bayes's theorem says that the posterior probability density is the product of the prior probability density and the likelihood function (times a constant):
		The constant of proportionality is chosen to make the posterior probability density integrate to 1.
	www.richmond.edu /~ebunn/bayes/node4.html (597 words)

	Posterior Probability Error-Rate Estimates
		The posterior probability error-rate estimates (Fukunaga and Kessell 1973; Glick 1978; Hora and Wilcox 1982) for each group are based on the posterior probabilities of the observations classified into that same group.
		the set of observations from group u such that the posterior probability belonging to group t is the largest.
		To have a reliable estimate for group-specific error rate estimates, you should use group sizes that are at least approximately proportional to the prior probabilities of group membership.
	www.okstate.edu /sas/v7/sashtml/books/stat/chap23/sect18.htm (415 words)

	Implement Bayesian inference using PHP, Part 1
		In other words, the probability of a customer buying product A given that they have purchased product B can be estimated at 83 percent by using a method that involves enumerating relative frequencies of A and B events from the data gathered to date.
		The exact nature of the full posterior probability computation is made clearer by seeing that the posterior and likelihood terms appear in a PHP implementation as two-dimensional arrays (the closest you can currently get to a matrix datatype in PHP).
		The probability appearing in the denominator * serves a normalizing role in the computation - it ensures that * posterior probabilities sum to 1.
	www.ibm.com /developerworks/web/library/wa-bayes1 (5295 words)

	PROBABILITY THEORY -- THE LOGIC OF SCIENCE
		4-1 Chapter 5 Queer Uses for Probability Theory Chapter 6 Elementary Parameter Estimation Fig.
		Appendix A Other Approaches to Probability Theory Appendix B Formalities and Mathematical Style Appendix C Convolutions and Cumulants Appendix D Dirichlet Integrals and Generating Functions Appendix E The Binomial -- Gaussian Hierarchy of Distributions Appendix F Fourier Analysis Appendix G Infinite Series Appendix H Matrix Analysis and Computation Appendix I Computer Programs
		Probability Theory is Different COMMENTS Gamesmanship What Does `Bayesian' Mean?
	omega.albany.edu:8008 /JaynesBook.html (429 words)

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