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Definition of transformed canonical uninformative parameters and observations.pdf (1.74 MB)

Frequentist MCMC

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posted on 2013-10-05, 11:27 authored by Christian BartelsChristian Bartels

Some definitions are introduced and exemplified that may help to relate Bayesian statistics to frequentist statistics. The idea is interesting. More work is required.

 

Practical implications would be:

- Opens up the possibility to use MCMC algorithms sampling parameters given data, e.g., Stan or WinBUGS, for frequentist hypothesis testing.

 

Conceptual implications would be:

- Formally relate results from Bayesian statistics to those from frequentist statistics.

- Define approaches and situations, in which frequentist and Bayesian approaches give identical results, or to explain differences obtained with different approaches.

 

References: 

- Kass RE, Wasserman L (1996) The Selection of Prior Distributions by Formal Rules. JASA, 91 (435), 1343-1370

- Berger, James. "The case for objective Bayesian analysis." Bayesian Analysis 1.3 (2006): 385-402.

- Bernardo, José M. "Intrinsic credible regions: An objective Bayesian approach to interval estimation." Test 14.2 (2005): 317-384.

- Efron, Bradley. "A 250-year argument: Belief, behavior, and the bootstrap." Bulletin of the American Mathematical Society 50.1 (2013): 129-146.

- Berger, James O, Brunero Liseo, and Robert L Wolpert. "Integrated likelihood methods for eliminating nuisance parameters." Statistical Science 14.1 (1999): 1-28.

- Severini, Thomas A. "Integrated likelihood functions for non-Bayesian inference." Biometrika 94.3 (2007): 529-542.

- Berger, James O, José M Bernardo, and Dongchu Sun. "The formal definition of reference priors." The Annals of Statistics (2009): 905-938.

- Bjørnstad, Jan F. "On the generalization of the likelihood function and the likelihood principle." Journal of the American Statistical Association 91.434 (1996): 791-806.

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