Abstract
This paper presents a refinement of the Bayesian Information Criterion (BIC). 7 While the original BIC selects models on the basis of complexity and fit, the 8 so-called prior-adapted BIC allows us to choose among statistical models that 9 differ on three scores: fit, complexity, and model size. The prior-adapted BIC 10 can therefore accommodate comparisons among statistical models that differ only 11 in the admissible parameter space, e.g., for choosing among models with different 12 constraints on the parameters. The paper ends with an application of this idea to a 13 well-known puzzle from the psychology of reasoning, the conjunction fallacy.
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References
Akaike, H. (1973). Information Theory and an Extension of the MaximumLikelihood Principle. In 2nd International Symposium on Information Theory, B. N. Petrov and F. Csaki (Eds.), Akademiai Kiado, Budapest, pp. 267–281.
Anraku, K. (1999). An Information Criterion for Parameters under a Simple Order Restriction. Journal of the Royal Statistical Society B, 86, pp. 141–152.
Balasubramanian, V. (2005).MDL, Bayesian inference, and the geometry of the space of probability distributions. In Advances in Minimum Description Length: Theory and Applications, P. J. Grunwald et al. (Eds.), pp. 81–99. MIT Press, Boston.
Crupi, V., Fitelson, B. and Tentori, K. (2008). Probability, confirmation and the conjunction fallacy. Thinking and Reasoning 14, pp. 182–199.
Gelfand, A. E., Smith, A. F. M., and Lee, T. (1992). Bayesian analysis of constrained parameter and truncated data problems using Gibbs sampling. Journal of the American Statistical Association, 87, pp. 523–532.
Grunwald, P. (2007). The Minimum Description Length Principle. MIT press, Cambridge (MA).
Henderson, L., Goodman, N. D., Tenenbaum, J. B. and Woodward, J. F. (2010). The structure and dynamics of scientific theories: a hierarchical Bayesian perspective. Philosophy of Science 77(2), pp. 172–200.
Hoijtink, H., Klugkist, I., and Boelen, P. A. (2008). Bayesian Evaluation of Informative Hypotheses, Springer, New York.
Jeffreys, H. (1961). Theory of Probability. Oxford University Press, Oxford.
Kahneman, D., Slovic, P. and Tversky, A. (Eds.) (1982). Judgment under Uncertainty: Heuristics and Biases. Cambridge University Press, New York.
Kass, R. E. and Raftery A. E. (1995). Bayes Factors. Journal of the American Statistical Association, 90, pp. 773–795.
Kass, R. E., and Wasserman, L. (1992). A Reference Bayesian Test for Nested Hypotheses with Large Samples. Technical Report No. 567, Department of Statistics, Carnegie Mellon University.
Klugkist, I., Laudy, O. and Hoijtink, H. (2005). Inequality Constrained Analysis of Variance: A Bayesian Approach. PsychologicalMethods 10(4), pp. 477–493.
Lipton, P. (2004). Inference to the Best Explanation. Routledge, London.
Myung, J. et al. (2000). Counting probability distributions: Differential geometry and model selection. Proceedings of the National Academy of Sciences 97(21), pp. 11170–11175.
Raftery, A. E. (1995). Bayesian model selection in social research. Sociological Methodology, 25, pp. 111–163.
Rissanen, J. (1996). IEEE Transactions of Information Theory, 42, pp. 40–47.
Romeijn, J. W. and van de Schoot, R. (2008). A Philosophical Analysis of Bayesian model selection. In Hoijtink, H., Klugkist, I., and Boelen, P. A. (2008). Bayesian Evaluation of Informative Hypotheses, Springer, New York.
Schoot, R. van de, Hoijtink, H., Mulder, J., van Aken, M. A. G. Orobio de Castro, B., Meeus,W. and Romeijn, J.W. (2010a). Evaluating Expectations about Negative Emotional States of Aggressive Boys using Bayesian Model Selection. Developmental Psychology, in press.
Schoot, R. van de, Hoijtink, H., Brugman, D. and Romeijn, J. W. (2010b). A Prior Predictive Loss Function for the Evaluation of Inequality Constrained Hypotheses, manuscript under review.
Schwarz, G. (1978). Estimating the Dimension of a Model. Annals of Statistics, 6, pp. 461–464.
Silvapulle,M. J. and Sen, P. K. (2005). Constrained Statistical Inference: Inequality, Order, and Shape Restrictions, JohnWiley, Hoboken (NJ).
Sober, E. and Hitchcock, C. (2004). Prediction Versus Accommodation and the Risk of Overfitting. British Journal for the Philosophy of Science 55, pp. 1–34.
Spiegelhalter, D. J., Best, N. G. Carlin, B. P. and van der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of Royal Statistical Society B, 64, pp. 583–639.
Stone, M. (1977). An Asymptotic Equivalence of Choice of Model by Cross- Validation and Akaike’s Criterion. Journal of the Royal Statistical Society B, 39(1), pp. 44–47.
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Romeijn, JW., van de Schoot, R., Hoijtink, H. (2012). One Size Does Not Fit All: Proposal for a Prior-adapted BIC . In: Dieks, D., Gonzalez, W., Hartmann, S., Stöltzner, M., Weber, M. (eds) Probabilities, Laws, and Structures. The Philosophy of Science in a European Perspective, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-3030-4_7
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