Regression analysis using the imprecise Bayesian normal model

International Journal of Data Analysis Techniques and Strategies

Volumn 2, Issue 4, 2010, Pages 356-372

  Utkin, Lev V ^a  

^a SAINT PETERSBURG STATE FOREST TECHNICAL UNIVERSITY   (Russian Federation)

Author keywords

Bayesian inference; imprecise probabilities; learning problem; lower and upper probability distributions; regression; risk

Indexed keywords

EID: 84859416856     PISSN: 17558050     EISSN: 17558069     Source Type: Journal    
DOI: 10.1504/IJDATS.2010.037477     Document Type: Article

References (16)

1. Bernardo, J. and Smith, A. (1994) Bayesian Theory, Wiley, Chichester.
2. Chakravorty, S., Hales, D., and Herbert, J. (2008) ‘How problem-solving really works’, Int. J. Data Analysis Techniques and Strategies, Vol. 1, No. 1, pp.44-59.
3. Hastie, T., Tibshirani, R. and Friedman, J. (2001) The Elements of Statistical Learning: Data Mining, Inference and Prediction, Springer, New York.
4. Huhn, J. and Hullermeier, E. (2008) ‘Is an ordinal class structure useful in classifier learning?’, Int. J. Data Mining, Modelling and Management, Vol. 1, No. 1, pp.45-67.
5. Luo, R. and Wang, H. (2008) ‘A composite logistic regression approach for ordinal panel data regression’, Int. J. Data Analysis Techniques and Strategies, Vol. 1, No. 1, pp.29-43.
6. Quaeghebeur, E. and de Cooman, G. (2005) ‘Imprecise probability models for inference in exponential families’, in J-M. Bernard, T. Seidenfeld and M. Zaffalon (Eds.): Proc. of the 4rd Int. Symposium on Imprecise Probabilities and Their Applications, ISIPTA’05, pp.287-296, Carnegie Mellon University, Pittsburgh, Pennsylvania.
7. Robert, C. (1994) The Bayesian Choice, Springer, New York.
8. Syversveen, A. (1998) Noninformative Bayesian Priors. Interpretation and Problems with Construction and Applications, Preprint Statistics 3, Department of Mathematical Sciences, NTNU, Trondheim.
9. Utkin, L. (2007) ‘Risk analysis under partial prior information and non-monotone utility functions’, International Journal of Information Technology and Decision Making, Vol. 6, No. 4, pp.625-647.
10. Utkin, L. and Destercke, S. (2007) ‘Computing expectations with p-boxes: two views of the same problem’, in G. de Cooman, J. Vejnarova, M.Z. (Eds.): Proc. of the 5th Int. Symposium on Imprecise Probabilities and their Applications, ISIPTA’07, pp.435-444, SIPTA, Prague, Czech Republic.
11. Utkin, L. and Destercke, S. (2009) ‘Computing expectations with continuous p-boxes: univariate case’, International Journal of Approximate Reasoning, Vol. 50, No. 5, pp.778-798.
12. Utkin, L., Zatenko, S. and Coolen, F. (2009) ‘Combining imprecise Bayesian and maximum likelihood estimation for reliability growth models’, in T. Augustin, F. Coolen, S. Moral and M. Troffaes (Eds.): Proc. of the Sixth Int. Symposium on Imprecise Probabilities: Theories and Applications, ISIPTA’09, pp.421-430, Durham University, SIPTA, Durham, UK.
13. Vapnik, V. (1995) The Nature of Statistical Learning Theory, Springer, New York.
14. Vapnik, V. (1998) Statistical Learning Theory, Wiley, New York.
15. Walley, P. (1991) Statistical Reasoning with Imprecise Probabilities, Chapman and Hall, London.
16. Walley, P. (1996) ‘Inferences from multinomial data: learning about a bag of marbles’, Journal of the Royal Statistical Society, Series B, Vol. 58, pp.3-57, with discussion.