| Title:
|
Modeling biased information seeking with second order probability distributions (English) |
| Author:
|
Kleiter, Gernot D. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
51 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
469-485 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Updating probabilities by information from only one hypothesis and thereby ignoring alternative hypotheses, is not only biased but leads to progressively imprecise conclusions. In psychology this phenomenon was studied in experiments with the “pseudodiagnosticity task”. In probability logic the phenomenon that additional premises increase the imprecision of a conclusion is known as “degradation”. The present contribution investigates degradation in the context of second order probability distributions. It uses beta distributions as marginals and copulae together with C-vines to represent dependence structures. It demonstrates that in Bayes' theorem the posterior distributions of the lower and upper probabilities approach 0 and 1 as more and more likelihoods belonging to only one hypothesis are included in the analysis. (English) |
| Keyword:
|
probability logic |
| Keyword:
|
Bayes' theorem |
| Keyword:
|
degradation |
| Keyword:
|
pseudodiagnosticity task |
| Keyword:
|
second order probability distributions |
| MSC:
|
03B48 |
| MSC:
|
49N30 |
| MSC:
|
62F15 |
| MSC:
|
62H05 |
| MSC:
|
68T30 |
| MSC:
|
68T35 |
| MSC:
|
91E10 |
| idZBL:
|
Zbl 06487091 |
| idMR:
|
MR3391680 |
| DOI:
|
10.14736/kyb-2015-3-0469 |
| . |
| Date available:
|
2015-09-01T09:15:08Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144381 |
| . |
| Reference:
|
[1] Boole, G.: An Investigation of the Laws of Thought..Macmillan/Dover Publication, New York 1854/1958. Zbl 1205.03003, MR 1802120 |
| Reference:
|
[2] Coletti, G., Petturiti, D., Vantaggi, B.: Bayesian inference: the role of coherence to deal with a prior belief function..Statist. Methods Appl., online, 2014. MR 3278926 |
| Reference:
|
[3] Coletti, G., Scozzafava, R.: Probabilistic Logic in a Coherent Setting..Kluwer, Dordrecht 2002. Zbl 1040.03017, MR 2042026 |
| Reference:
|
[4] Doherty, M. E., Mynatt, C. R., Tweney, R. D., Schiavo, M. D.: Pseudodiagnosticity..Acta Psychologica 43 (1979), 111-121. MR 1872198, 10.1016/0001-6918(79)90017-9 |
| Reference:
|
[5] Gilio, A.: Generalization of inference rules in coherence-based probabilistic default reasoning..Int. J. Approx. Reasoning 53 (2012), 413-434. MR 2902403, 10.1016/j.ijar.2011.08.004 |
| Reference:
|
[6] Hanea, A.: Dependence modeling. Vine copula handbook..In: Dependence Modeling. Vine Copula Handbook (D. Kurowicka and H. Joe, eds.), chapter Non-parametric Bayesian belief nets versus vines, World Scientific, New Jersey 2011, pp. 281-303. MR 2856979, 10.1142/9789814299886_0014 |
| Reference:
|
[7] Joe, H.: Dependence Modeling with Copulas..Chapman and Hall/CRC, Boca Raton 2015. MR 3328438 |
| Reference:
|
[8] Kern, L., Doherty, M. E.: “Pseudodiagnosticity” in an idealized medical problem-solving environment..J. Medical Education 57 (1982), 100-104. |
| Reference:
|
[9] Kleiter, G. D.: Propagating imprecise probabilities in Bayesian networks..Artificial Intelligence 88 (1996), 143-161. Zbl 0906.68114, 10.1016/s0004-3702(96)00021-5 |
| Reference:
|
[10] Kleiter, G. D.: Ockham's razor in probability logic..In: Synergies of Soft Computing and Statistics for Intelligent Data Analysis (R. Kruse, M.xQ,R. Berthold, C. Moewes, M. A. Gil, P. Grzegorzewski, and O. Hryniewicz, eds.), Advances in Intelligent Systems and Computation 190, Springer, Heidelberg 2012. pp. 409-417. 10.1007/978-3-642-33042-1_44 |
| Reference:
|
[11] Kurowicka, D., Cooke, R.: Distribution-free continuous Bayesian belief nets..In: Proc. Fourth International Conference on Mathematical Methods in Reliability Methodology and Practice, Santa Fe 2004. Zbl 1083.62054, MR 2230715 |
| Reference:
|
[12] Kurowicka, D., Cooke, R.: Uncertainty Analysis with High Dimension Dependence Modelling..Wiley, Chichester, 2006. MR 2216540 |
| Reference:
|
[13] Kurowicka, D., Joe, R.: Dependence Modeling: Vine Copula Handbook..World Scientific, Singapure 2011. MR 2849701 |
| Reference:
|
[14] Mai, J.-F., Scherer, M.: Simulating Copulas. Stochastic Models, Sampling Algorithms, and Applications..Imperial College Press, London 2012. Zbl 1301.65001, MR 2906392 |
| Reference:
|
[15] Nelsen, R. B.: An introduction to Copulas..Springer, Berlin 2006. Zbl 1152.62030, MR 2197664 |
| Reference:
|
[16] Team, R Development Core, Vienna, Austria: R: A Language and Environment for Statistical Computing, 2014.. |
| Reference:
|
[17] Schepsmeier, U., Stoeber, J., Brechmann, E. C., Graeler, B.: Statistical inference of vine copulas..Version 1.2 edition, 2013. |
| Reference:
|
[18] Seidenfeld, T., Wasserman, L.: Dilation for sets of probabilities..Ann. Statist. 21 (1993), 1139-1154. Zbl 0796.62005, MR 1241261, 10.1214/aos/1176349254 |
| Reference:
|
[19] Tweney, R. D., Doherty, M. E., Kleiter, G. D.: The pseudodiagnosticity trap. Should subjects consider alternative hypotheses?.Thinking and Reasoning 16 (2010), 332-345. 10.1080/13546783.2010.525860 |
| Reference:
|
[20] Wallmann, C., Kleiter, G. D.: Exchangeability in probability logic..In: Communications in Computer and Information Science (S. Greco, B. Bouchon-Meunier, G. Coletti, M. Fedrizzi, B. Matarazzo, and R. R. Yager, eds.), IPMU (4) 300, Springer, Berlin 2012, pp. 157-167. Zbl 1252.03043, 10.1007/978-3-642-31724-8_17 |
| Reference:
|
[21] Wallmann, C., Kleiter, G. D.: Degradation in probability logic: When more information leads to less precise conclusions..Kybernetika 50 (2014), 268-283. Zbl 1296.03018, MR 3216994, 10.14736/kyb-2014-2-0268 |
| Reference:
|
[22] Wallmann, C., Kleiter, G. D.: Probability propagation in generalized inference forms..Studia Logica 102 (2014), 913-929. MR 3249556, 10.1007/s11225-013-9513-4 |
| Reference:
|
[23] Wasserman, L. A.: Prior envelopes based on belief functions..Annals Statist. 18 (1990), 454-464. Zbl 0711.62001, MR 1041404, 10.1214/aos/1176347511 |
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