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In this essay, I argue about the relevance and the ultimate unity of the Bayesian approach in a neutral and agnostic manner. My main theme is that Bayesian data analysis is an effective tool for handling complex models, as proven by the increasing proportion of Bayesian studies in the applied...
Persistent link: https://www.econbiz.de/10008683492
the thorough coverage of testing problems and the construction of both estimation and testing noninformative priors based …
Persistent link: https://www.econbiz.de/10010706449
The choice of the summary statistics in Bayesian inference and in particular in ABC algorithms is paramount to produce a valid outcome. We derive necessary and sufficient conditions on those statistics for the corresponding Bayes factor to be convergent, namely to asymptotically select the true...
Persistent link: https://www.econbiz.de/10011166507
Persistent link: https://www.econbiz.de/10010861573
When testing a null hypothesis H0: θ=θ0 in a Bayesian framework, the Savage–Dickey ratio (Dickey, 1971) is known as a … constraints on the prior distributions. We completely clarify the measure-theoretic foundations of the Savage …
Persistent link: https://www.econbiz.de/10011073847
Approximate Bayesian computation (ABC) have become a essential tool for the analysis of complex stochastic models. Earlier, Grelaud et al. (2009) advocated the use of ABC for Bayesian model choice in the specific case of Gibbs random fields, relying on a inter-model sufficiency property to show...
Persistent link: https://www.econbiz.de/10010706662
In Chib (1995), a method for approximating marginal densities in a Bayesian setting is proposed, with one proeminent application being the estimation of the number of components in a normal mixture. As pointed out in Neal (1999) and Fruhwirth-Schnatter (2004), the approximation often fails short...
Persistent link: https://www.econbiz.de/10010706383
hypothesis testing based on comparisons of posterior distributions of likelihoods under competing models. Aitkin develops and …
Persistent link: https://www.econbiz.de/10014622233
We extend the asymmetric, stochastic, volatility model by modeling the return-volatility distribution nonparametrically. The novelty is modeling this distribution with an infinite mixture of Normals, where the mixture unknowns have a Dirichlet process prior. Cumulative Bayes factors show our...
Persistent link: https://www.econbiz.de/10010730133
We present a dependent Bayesian nonparametric model for the proba- bilistic modelling of species-by-site data, i.e. population data where observations at different sites are classified into distinct species. We use a dependent version of the Griffiths-Engen-McCloskey distribution, the...
Persistent link: https://www.econbiz.de/10010781520