Bayesian Inference under Ambiguity: Conditional Prior Belief Functions

Giulianella Coletti, Davide Petturiti, Barbara Vantaggi
Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 62:73-84, 2017.

Abstract

Bayesian inference under imprecise prior information is studied: the starting point is a precise strategy $σ$ and a full B-conditional prior belief function $Bel_B$, conveying ambiguity in probabilistic prior information. In finite spaces, we give a closed form expression for the lower envelope $\underline{P}$ of the class of full conditional probabilities dominating $(Bel_B,σ)$ and, in particular, for the related “posterior probabilities”. The assessment $(Bel_B,σ)$ is a coherent lower conditional probability in the sense of Williams and the characterized lower envelope $\underline{P}$ coincides with its natural extension.

Cite this Paper

BibTeX
@InProceedings{pmlr-v62-coletti17a, title = {{B}ayesian Inference under Ambiguity: Conditional Prior Belief Functions}, author = {Coletti, Giulianella and Petturiti, Davide and Vantaggi, Barbara}, booktitle = {Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {73--84}, year = {2017}, editor = {Antonucci, Alessandro and Corani, Giorgio and Couso, Inés and Destercke, Sébastien}, volume = {62}, series = {Proceedings of Machine Learning Research}, month = {10--14 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v62/coletti17a/coletti17a.pdf}, url = {https://proceedings.mlr.press/v62/coletti17a.html}, abstract = {Bayesian inference under imprecise prior information is studied: the starting point is a precise strategy $σ$ and a full B-conditional prior belief function $Bel_B$, conveying ambiguity in probabilistic prior information. In finite spaces, we give a closed form expression for the lower envelope $\underline{P}$ of the class of full conditional probabilities dominating $(Bel_B,σ)$ and, in particular, for the related “posterior probabilities”. The assessment $(Bel_B,σ)$ is a coherent lower conditional probability in the sense of Williams and the characterized lower envelope $\underline{P}$ coincides with its natural extension.} }
Endnote
%0 Conference Paper %T Bayesian Inference under Ambiguity: Conditional Prior Belief Functions %A Giulianella Coletti %A Davide Petturiti %A Barbara Vantaggi %B Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2017 %E Alessandro Antonucci %E Giorgio Corani %E Inés Couso %E Sébastien Destercke %F pmlr-v62-coletti17a %I PMLR %P 73--84 %U https://proceedings.mlr.press/v62/coletti17a.html %V 62 %X Bayesian inference under imprecise prior information is studied: the starting point is a precise strategy $σ$ and a full B-conditional prior belief function $Bel_B$, conveying ambiguity in probabilistic prior information. In finite spaces, we give a closed form expression for the lower envelope $\underline{P}$ of the class of full conditional probabilities dominating $(Bel_B,σ)$ and, in particular, for the related “posterior probabilities”. The assessment $(Bel_B,σ)$ is a coherent lower conditional probability in the sense of Williams and the characterized lower envelope $\underline{P}$ coincides with its natural extension.
APA
Coletti, G., Petturiti, D. & Vantaggi, B.. (2017). Bayesian Inference under Ambiguity: Conditional Prior Belief Functions. Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 62:73-84 Available from https://proceedings.mlr.press/v62/coletti17a.html.

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