Is there a difference between Bayesian and Classical sufficiency?

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The title pretty much says it all. I wonder whether there is any difference in the way Bayesians understand sufficiency vs. the way orthodox statistics understands sufficiency, or are they equivalent? If there is a difference, what is it?






bayesian definition frequentist sufficient-statistics







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    The title pretty much says it all. I wonder whether there is any difference in the way Bayesians understand sufficiency vs. the way orthodox statistics understands sufficiency, or are they equivalent? If there is a difference, what is it?






    bayesian definition frequentist sufficient-statistics







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      The title pretty much says it all. I wonder whether there is any difference in the way Bayesians understand sufficiency vs. the way orthodox statistics understands sufficiency, or are they equivalent? If there is a difference, what is it?






      bayesian definition frequentist sufficient-statistics







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      The title pretty much says it all. I wonder whether there is any difference in the way Bayesians understand sufficiency vs. the way orthodox statistics understands sufficiency, or are they equivalent? If there is a difference, what is it?






      bayesian definition frequentist sufficient-statistics




      bayesian definition frequentist sufficient-statistics






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      Sebastian

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          Here is one example of differentiation between classical and Bayesian statistics: when comparing two models $mathcalM_1$ and $mathcalM_2$, a statistic $S(cdot)$ may be sufficient for both models, hence sufficient in a classical sense, but insufficient for model comparison as e.g. in Bayes factors, when the conditional distribution of the data given $S$ varies between models. The difference is due to the fact that the model index is a parameter from a Bayesian perspective but not a parameter from a classical one. (This is discussed further in our ABC model choice papers.)






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            Here is one example of differentiation between classical and Bayesian statistics: when comparing two models $mathcalM_1$ and $mathcalM_2$, a statistic $S(cdot)$ may be sufficient for both models, hence sufficient in a classical sense, but insufficient for model comparison as e.g. in Bayes factors, when the conditional distribution of the data given $S$ varies between models. The difference is due to the fact that the model index is a parameter from a Bayesian perspective but not a parameter from a classical one. (This is discussed further in our ABC model choice papers.)






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              Here is one example of differentiation between classical and Bayesian statistics: when comparing two models $mathcalM_1$ and $mathcalM_2$, a statistic $S(cdot)$ may be sufficient for both models, hence sufficient in a classical sense, but insufficient for model comparison as e.g. in Bayes factors, when the conditional distribution of the data given $S$ varies between models. The difference is due to the fact that the model index is a parameter from a Bayesian perspective but not a parameter from a classical one. (This is discussed further in our ABC model choice papers.)






              share|cite|improve this answer






















                up vote
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                down vote










                up vote
                3
                down vote









                Here is one example of differentiation between classical and Bayesian statistics: when comparing two models $mathcalM_1$ and $mathcalM_2$, a statistic $S(cdot)$ may be sufficient for both models, hence sufficient in a classical sense, but insufficient for model comparison as e.g. in Bayes factors, when the conditional distribution of the data given $S$ varies between models. The difference is due to the fact that the model index is a parameter from a Bayesian perspective but not a parameter from a classical one. (This is discussed further in our ABC model choice papers.)






                share|cite|improve this answer












                Here is one example of differentiation between classical and Bayesian statistics: when comparing two models $mathcalM_1$ and $mathcalM_2$, a statistic $S(cdot)$ may be sufficient for both models, hence sufficient in a classical sense, but insufficient for model comparison as e.g. in Bayes factors, when the conditional distribution of the data given $S$ varies between models. The difference is due to the fact that the model index is a parameter from a Bayesian perspective but not a parameter from a classical one. (This is discussed further in our ABC model choice papers.)







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                answered 1 hour ago









                Xi'an

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