Using Bayesian phylogeographic analysis, evolutionary biologists have proposed that the Indo-European language expansion coincided with the migration of Anatolian farmers occurring about 9000 years ago.

A full Bayesian analysis of the WMAP power spectrum demonstrates that the quadrupole prediction of Lambda-CDM cosmology is consistent with the data at the 10 % level and that the observed octupole is not remarkable.

In a clinical trial it is strictly not valid to conduct an unplanned interim analysis of the data by frequentist methods, whereas this is permissible by Bayesian methods.

Furthermore, as mentioned above, frequentist analysis is open to unscrupulous manipulation if the experimenter is allowed to choose the stopping point, whereas Bayesian methods are immune to such manipulation.

Genetic ancestry of 105 captive tigers from 14 countries and regions was assessed by using Bayesian analysis and diagnostic genetic markers defined by a prior analysis of 134 voucher tigers of significant genetic distinctiveness.

Thus my analysis suggests that this response to the paradox the Standard Bayesian one cannot be correct.

Bayesian updating is especially important in the dynamic analysis of a sequence of data.

There is also an ever growing connection between Bayesian methods and simulation-based Monte Carlo techniques since complex models cannot be processed in closed form by a Bayesian analysis, while a graphical model structure may allow for efficient simulation algorithms like the Gibbs sampling and other Metropolis – Hastings algorithm schemes.

* Bayesian tool for methylation analysis

Bayesian inference can be applied in the analysis of chronological information, including radiocarbon-derived dates.

In 2004, analysis of the Bayesian classification problem has shown that there are some theoretical reasons for the apparently unreasonable efficacy of naive Bayes classifiers.

The Student ’ s t-distribution also arises in the Bayesian analysis of data from a normal family.

* Bayesian analysis of UK place-names

Several methods of computational statistics have close connections with Bayesian analysis:

The Bayesian approach also fails to provide an answer that can be expressed as straightforward simple formulae, but modern computational methods of Bayesian analysis do allow essentially exact solutions to be found.

MixSIR is a free graphical user interface ( GUI ) program built on the MATLAB platform that carries out Bayesian analysis of stable isotope mixing models using sampling-importance-resampling ( SIR ).

* SIAR-Stable isotope analysis in R .. Bayesian mixing model package for the R environment.

For example, the beta distribution can be used in Bayesian analysis to describe initial knowledge concerning probability of success such as the probability that a space vehicle will successfully complete a specified mission.

In Bayesian statistics, hypothesis testing of the type used in classical power analysis is not done.

With newer hierarchical Bayesian analysis techniques, individual level utilities can be imputed back to provide individual level data.

Analysis is traditionally carried out with some form of multiple regression, but more recently the use of hierarchical Bayesian analysis has become widespread, enabling fairly robust statistical models of individual respondent decision behaviour to be developed.

Using this phylogenetic framework, we inferred the genus ' historical biogeography by using weighted ancestral-area analysis and dispersal-vicariance analysis in combination with a Bayesian relaxed molecular-clock approach and paleogeographical data.

Similarly, Jeffrey D. Scargle believes unless both Bayesian and classical p-value analysis agree and both show the same anomalous effects, the kind of result GCP proposes will not be generally accepted.

Bayesian spam filtering is a very powerful technique for dealing with spam, that can tailor itself to the email needs of individual users, and gives low false positive spam detection rates that are generally acceptable to users.

For example, model calibration can be also used to refer to Bayesian inference about the value of a model's parameters, given some data set, or more generally to any type of fitting of a statistical model.

When point estimates need to be derived, generally the mean is used rather than the mode, as is normal in Bayesian inference.

Since computer power has advanced rapidly and punched cards are no longer used, more sophisticated methods of imputation have generally superseded the original random and sorted hot deck imputation techniques, such as the nearest neighbour hot deck imputation and the approximate Bayesian bootstrap.

For Bayesian model, the prior and likelihood generally represent the statistics of the environment and the sensory representations.

As the laws of probability derived by Cox's theorem are applicable to any proposition, logical probability is a type of Bayesian probability.

Some of the advantages of Bayesian Network include the knowledge and conclusions of experts in the form of probabilities, assistance in decision making as new information is available and are based on unbiased probabilities that are applicable to many models.

Those who promote Bayesian inference view " frequentist statistics " as an approach to statistical inference that recognises only physical probabilities.

The Bayesian approach to hypothesis testing is to base rejection of the hypothesis on the posterior probability.

" Noteworthy approaches using Bayesian techniques include Earman, Eells, Gibson, Hosaisson-Lindenbaum, Howson and Urbach, Mackie, and Hintikka, who claims that his approach is " more Bayesian than the so-called ' Bayesian solution ' of the same paradox.

Much of the discussion of the paradox in general and the Bayesian approach

The reason is that the background knowledge which Good and others use can not be expressed in the form of a sample proposition-in particular, variants of the standard Bayesian approach often suppose ( as Good did in the argument quoted above ) that the total numbers of ravens, non-black objects and / or the total number of objects, are known quantities.

Hintikka was motivated to find a Bayesian approach to the paradox which did not make use of knowledge about the relative frequencies of ravens and black things.

This contrasts with the Bayesian approach, which requires that the hypothesis be assigned a prior probability, which is revised in the light of the observed data to obtain the final probability of the hypothesis.

The Bayesian approach provides a predictive distribution which takes into account the uncertainty of the estimated parameter, although this may depend crucially on the choice of prior.

A predictive distribution free of the issues of choosing priors that arise under the subjective Bayesian approach is

The benefit of a Bayesian approach is that it gives the juror an unbiased, rational mechanism for combining evidence.

Eric R. Bittner's group at the University of Houston has advanced a statistical variant of this approach that uses Bayesian sampling technique to sample the quantum density and compute the quantum potential on a structureless mesh of points.

In the Bayesian approach to this problem, instead of choosing a single parameter vector, the probability of a given label for a new instance is computed by integrating over all possible values of, weighted according to the posterior probability:

* MML is a fully subjective Bayesian approach: it starts from the idea that one represents one's beliefs about the data generating process in the form of a prior distribution.

* On-line book: Information Theory, Inference, and Learning Algorithms, by David MacKay, gives a detailed account of the Bayesian approach to machine learning.

Bayesian inference is an approach to statistical inference, that is distinct from the more traditional frequentist inference.

Another approach to supporting trade study information is to use the Bayesian Team Support ( BTS ) methods.

In a Bayesian approach, the expectation is calculated using the posterior distribution π < sup >*</ sup > of the parameter θ:

Although this will result in choosing the same action as would be chosen using the Bayes risk, the emphasis of the Bayesian approach is that one is only interested in choosing the optimal action under the actual observed data, whereas choosing the actual Bayes optimal decision rule, which is a function of all possible observations, is a much more difficult problem.

One approach, suggested by writers such as Stephen D. Unwin, is to treat ( particular versions of ) theism and naturalism as though they were two hypotheses in the Bayesian sense, to list certain data ( or alleged data ), about the world, and to suggest that the likelihoods of these data are significantly higher under one hypothesis than the other.

Judea Pearl ( born 1936 ) is an Israeli American computer scientist and philosopher, best known for championing the probabilistic approach to artificial intelligence and the development of Bayesian networks ( see the article on belief propagation ).