
	Where results make sense

Topic: Posterior distribution

Related Topics

Likelihood

Bayesian inference

	Posterior distribution Encyclopedia (Site not responding. Last check: 2007-08-19)
		The specification of mixture posterior distributions means that the presence...
		Asymptotic normality of semiparametric and nonparametric posterior distributions.
		of the marginal posterior distribution of [THETA] in a...
	www.hallencyclopedia.com /topic/Posterior_distribution.html (116 words)

	Posterior probability - Wikipedia, the free encyclopedia
		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:
		is the posterior density of X given the data Y = y.
	en.wikipedia.org /wiki/Posterior_probability (214 words)

	NationMaster - Encyclopedia: Posterior distribution
		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.
		Since the distribution of posterior model parameters is identical to the prior distribution on those parameters, it follows that the posterior predictive distribution for the observations X' (marginalised over observations and model parameters) is the same as the distribution of observations implied by the model (marginalised over model parameters).
	www.nationmaster.com /encyclopedia/Posterior-distribution (366 words)

	Maximum a posteriori - Wikipedia, the free encyclopedia
		Analytically, when the mode(s) of the posterior distribution can be given in closed form.
		Bayesian methods tend to report the posterior mean or median together with posterior intervals, rather than the posterior mode.
		This is especially so when the posterior distribution does not have a simple analytic form: in this case, the posterior distribution can be simulated using Markov chain Monte Carlo techniques, while optimization to find its mode(s) may be difficult or impossible.
	en.wikipedia.org /wiki/Maximum_a_posteriori (440 words)

	Procedures - Posterior Distributions - Details
		The calculations of the moments of a multivariate posterior distribution most tractable when analytic results are available, as is the case for the normal distribution, and the prior distribution is multivariate normal.
		Our estimate of the standard error of the posterior mean begins as though the posterior distributions were approximated as normal, although in the case of subscales, they need not be.
		Readers should note that the posterior distributions for individual subscales are calculated on a finite set of points and may take on any shape.
	am.air.org /help/NAEPTextbook/htm/dPosteriorDistribution.htm (727 words)

	The Posterior Probability Distribution of Alignments
		P(H) is the prior probability of the hypothesis H. P(HD) is the posterior probability of H. The message length (ML) of an event E is the minimal length, in bits, of a message to transmit E using an optimal code.
		It is sufficient to hold many of those degrees of freedom fixed while sampling the remainder from the conditional posterior distribution so that is what is done: Given a multiple alignment, the tree is "broken" on a random edge which partitions the strings into two disjoint sets, as in section 4.
		A random realignment is sampled from the posterior distribution of alignments (of the subalignments) as described for just two strings in section 3 and using the costs for K-tuples as described in section 4.
	www.csse.monash.edu.au /~lloyd/tildeStrings/Multiple/94.JME (7572 words)

	Posterior Predictive p-values
		From this and the observed data you derive a posterior distribution for the model parameters by applying Bayes' Theorem.
		Note that we have equality iff the variance of P(xt), according to our prior distribution on t, is zero, which is to say that the probability of x given t is constant almost everywhere the prior distribution on t is positive.
		This implies that, in the long run, the distribution of S(X) is the same as the distribution of S(X') assuming that the model and its prior distribution are correct.
	www.mcdowella.demon.co.uk /PosteriorPredictive.html (1870 words)

	Approximations of posterior pdf
		As we have shown earlier, the posterior distribution is a synonym for our available knowledge of a system after we have made a set of observations.
		This is because the MAP estimate does not guarantee a high probability mass in the peak of the posterior distribution and so the posterior distribution may be sharp around the MAP estimate.
		The posterior distribution could contain many peaks, but when there is lots of data, most of the probability mass is typically contained in a few peaks of the posterior distribution.
	www.cis.hut.fi /~harri/ch6/node3.html (454 words)

	Bayesian inference - Wikipedia, the free encyclopedia
		In the United Kingdom, Bayes' theorem was explained to the jury in the odds form by a statistician expert witness in the rape case of Regina versus Denis John Adams.
		He argues that if the posterior probability of guilt is to be computed by Bayes' theorem, the prior probability of guilt must be known.
		A conjugate prior is a prior distribution, such as the beta distribution in the above example, which has the property that the posterior is the same type of distribution.
	en.wikipedia.org /wiki/Bayesian_inference (3588 words)

	Appendix B: Brief Intro. to Bayesian Inference
		Of course, many other distributional shapes share these two numerical properties, but we choose a member of the beta family because it makes the mathematics easier and because we have no reason to believe its shape is inappropriate here.
		According to this posterior distribution, P(0.570 < P < 0.618) = 0.95, so that a 95% posterior probability interval for the percent in favor is (57.0%, 61.8%).
		After he sees the results of the poll with 621 out of 1000 in favor, his posterior beta distribution has parameters 677 and 425, so that his 95% posterior interval estimate is (59.5%, 65.2%).
	www.sci.csuhayward.edu /statistics/Gibbs/GibbsAppendixB.htm (994 words)

	Laboratoire Génome et Populations
		Another useful summary is the posterior distribution of the number of source populations represented in the sample.
		The output from the exact linkage algorithm is a tree of all the individuals in the sample, where the height of each node is equal to the posterior probability that all the individuals in the se defined by that node belong to the same source population (this is the posterior co-assignment probability of the set).
		The posterior distribution of the number of source populations, k, is plotted as a histogram.
	www.univ-montp2.fr /%7Egenetix/partition/partition.htm (4461 words)

	Plausible Values
		Plausible values represent random draws from an empirically derived distribution of proficiency values that are conditional on the observed values of the assessment items and the background variables.
		As plausible values are random draws from a student's posterior distribution, plausible values are not appropriate to be used as individual student scores for reporting back to the students.
		In contrast, if we look at the area of the curves of the posterior distributions that is below -1.0, we see that this is a continuous function, and that this area contains contributions from all posterior distributions (corresponding to all scores).
	www.rasch.org /rmt/rmt182c.htm (1567 words)

	BAYESIAN MINITAB MACROS
		The output is an estimate at the posterior mode and standard deviation and an estimate at the logarithm of the normalizing constant.
		The output is an estimate at the mode and posterior standard deviations and covariance and an estimate at the logarithm of the normalizing constant.
		The output is estimates at the posterior moments and an estimate at the logarithm of the normalizing constant.
	www-math.bgsu.edu /~albert/mini_bayes/bprog.html (2538 words)

	Stat Jargon (Site not responding. Last check: 2007-08-19)
		The posterior distribution represents the updated knowledge regarding the unknown model parameters after observing the data and other information pertaining to the unknown parameters.
		Thus, the posterior distribution combines the information in the prior distribution and the likelihood (via Bayes theorem) and is a complete summary of the knowledge regarding the unknown model parameters.
		The prior distribution is a probability distribution that quantifies knowledge regarding unknown quantities (e.g., model parameters) prior to observing the data or other information pertaining to the the unknown quantities.
	hea-www.harvard.edu /AstroStat/statjargon.html (627 words)

	Stat 8701 (Geyer, Spring 2003) Homework 3
		That is, the posterior density is the likelihood renormalized to be a probability density.
		(θ)] of the log unnormalized posterior is negative everywhere, hence this function is strictly concave, hence the posterior is unimodal.
		You will find that the posterior conditional distribution of μ given λ is normal (with some parameters that depend on λ that you have to figure out) and the posterior conditional distribution of λ given μ is gamma (with some parameters that depend on μ that you have to figure out).
	www.stat.umn.edu /geyer/8701/hw3 (942 words)

	Definition of Exponential family
		It is the cumulant-generating function of the probability distribution of the sufficient statistic T(X) when the distribution of X is that whose density function is h.
		In Bayesian statistics a prior distribution is multiplied by a likelihood function and then normalised to produce a posterior distribution.
		A conjugate prior is one which, when combined with the likelihood and normalised, produces a posterior distribution which is of the same type as the prior.
	www.wordiq.com /definition/Exponential_family (577 words)

	Posterior of the number of components in a finite mixture (Site not responding. Last check: 2007-08-19)
		The posterior distribution of the number of components k in a finite mixture satisfies a set of inequality constraints.
		Bounds on the posterior probability of k components are derived using the constraints.
		Implications on prior distribution specification and on the adequacy of the posterior distribution of k as a tool for selecting an adequate number of components in the mixture are also explored.
	www.stats.gla.ac.uk /~agostino/mixpostk.html (193 words)

	2. METHODS FOR COMPUTING POSTERIOR DISTRIBUTIONS
		The objective of the assessment is to determine posterior distributions for the parameters of the model.
		It is often necessary to compare the prior distribution for a quantity of interest, such as the current biomass, with a numerical representation of its marginal posterior distribution to gauge the information content of the data.
		The marginal prior and posterior distributions for the current depletion are shown in the sheet "Summary".
	www.fao.org /DOCREP/005/Y1958E/y1958e04.htm (4396 words)

	Bayesian Statistics
		By incorporating prior information about the parameter(s), a posterior distribution for the parameter(s) can be obtained and inferences on the model parameters and their functions can be made.
		This posterior distribution of the parameter may or may not resemble in form the assumed prior distribution.
		The influence of the prior distribution on the posterior is related to the sample size of the data and the form of the prior.
	www.weibull.com /LifeDataWeb/bayesian_statistics.htm (1050 words)

	Statistical Inference
		For example, N(mu,sigma^2) represents the family of normal distributions where mu corresponds to the mean of a normal distribution and ranges over the real numbers (R) and sigma^2 corresponds to the variance of a normal distribution and ranges over the positive real numbers (R^+).
		In many practical cases, we are forced to choose a family of distributions not knowing whether or not the distribution generating the observed samples is in this particular family.
		For example, if the generating distribution is a zero-mean normal distribution, then the sample variance is a sufficient statistic for estimating sigma^2.
	www.cs.brown.edu /research/ai/dynamics/tutorial/Documents/StatisticalInference.html (792 words)

	Journal of Vision - Bayesian inference for psychometric functions, by Kuss, Jäkel, & Wichmann (Site not responding. Last check: 2007-08-19)
		The estimated posterior distributions for the lapse parameter (a), the threshold (b), and the width (c) of the psychometric function.
		When comparing priors and posteriors, we observe that the priors for the threshold and the width parameter were flat relative to the posterior distributions.
		Figure 10 compares the posteriors of both conditions, confirming that the approximated posterior distributions over the parameters are highly overlapping.
	journalofvision.org /5/5/8/article.aspx (8723 words)

	HUT / LCE Models and Methods: Sequential Monte Carlo Methods in Multiple Target Tracking
		The particles in the figures are used for visualizing the distribution, such that the particles are a random sample drawn from the posterior distribution estimate.
		The actual posterior distribution estimate is a mixture of Gaussians, which is hard to visualize directly.
		The prior distribution is on purpose selected such that all the four crossings of measurements from the two sensors contain some probability mass, and the distributions of targets are two-modal as can be seen in Figure 1.
	www.lce.hut.fi /research/compinf/mttracking (472 words)

	Posterior Distribution of a Parameter
		Below is a graph from Example 32 of the User's Guide.
		It shows the posterior distribution of the regression weight for using age to predict timesqr.
		The graph shows everything that is known about the value of the regression weight.
	www.amosdevelopment.com /ss_posterior.htm (75 words)

	BIO 580
		In this exercise, we fitted two growth models to sea otter counts along the coast of California between 1938 and 1999. Distributions of parameter values were calculated by using a Bayesian inference approach. We avoided the algebraic calculation of the joint distribution of parameters and used numerical approaches to simulate the joint distribution.
		The posterior distribution of the joint distribution of the growth rate (α) and the carrying capacity (K) indicated a narrow peak at α = 0.09 and K = 1,723 (Fig.
		Predicted and actual counts of southern sea otters along the coast of California between 1992 and 1999. The exponential model (equation 1.1) and the mean of posterior distribution of the growth rate were used to calculate the predicted counts.
	www.esg.montana.edu /eguchi/bayes/final_project.htm (607 words)

	Free Form Q
		Instead of assuming the form for the approximate posterior distribution we could instead derive the optimal separable distribution (the functions that minimise the cost function subject to the constraint that they be normalised).
		Figure 4 shows a comparison of the true posterior distribution and the approximate posterior.
		The contours for the two distributions are qualitatively similar, the approximate distribution also shows the assymmetric density.
	www.cis.hut.fi /~harri/ch6/node12.html (390 words)

	Methods of Estimation
		Usually the posterior distribution will have some common distributional form (such as Gamma, Normal, Beta, etc.) and you can compute the mean from the parameters using the cover of the book.
		Therefore, the parameters of the posterior distribution, and hence the posterior mean, are functions of the sufficient statistics.
		The posterior mean is consistent, asymptotically unbiased (meaning the bias tends to 0 as the sample size increases), and the asymptotic efficiency of the MLE compared to the posterior mean is 1.
	www.ms.uky.edu /~viele/sta321s98/estimation/estimation.html (1649 words)

	Bayesian Parameter Estimation
		The Beta distribution is conjugate to the binomial distribution which gives the likelihood of iid Bernoulli trials.
		More importantly, conjugacy allows for efficient sequential updating of the posterior distribution, where the posterior at one stage is used as prior for the next.
		We would choose the mean of the posterior distribution, because we know conditional mean minimizes mean square error.
	www-ccrma.stanford.edu /%7Ejos/bayes/Bayesian_Parameter_Estimation.html (413 words)

	Citations: Improving Markov chain Monte Carlo model search for data mining - Giudici, Castelo (ResearchIndex) (Site not responding. Last check: 2007-08-19)
		....GB N The proposal distribution we use is to sample uniformly from the neighborhood of G, de ned to be the set of all DAGs that di er from G by a single edge addition, deletion or reversal.
		The motivation behind this approach is to obtain samples from a (posterior) distribution of probabilistic network structures (the models M) given the (discrete) data D, rather than learning a particular probabilistic network structure that maximizes a certain criterion such as the maximum....
		The motivation behind this approach is to obtain samples from a (posterior) distribution of probabilistic network structures (the models #) given the (discrete) data #, rather than learning a particular probabilistic network structure that maximizes a certain criterion such as the maximum....
	citeseer.ist.psu.edu /context/1753871/0 (592 words)

Try your search on: Qwika (all wikis)