Fabio Cozman's Errata (as of June 2008)

Across the years I have noticed some errors in papers I have published (well, there are remaining typos here and there, but unfortunately here I refer to real mistakes).

Here is a list:

1) There is an incorrect result on divergence of posterior distributions that appears in several papers. Actually, divergence of posteriors does not occur under the conditions proved there. But note that divergence of posteriors can occur, and the best study of the phenomenon I know is given in: Timothy Herron; Teddy Seidenfeld; Larry Wasserman, The Extent of Dilation of Sets of Probabilities and the Asymptotics of Robust Bayesian Inference, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Volume One: Contributed Papers. (1994), pp. 250-259.

The papers with incorrect statements are: F. G. Cozman, Computing posterior upper expectations, International Journal of Approximate Reasoning, Vol. 24, pp. 191-205, 2000; F. G. Cozman, Calculation of Posterior Bounds Given Convex Sets of Prior Probability Measures and Likelihood Functions, Journal of Computational and Graphical Statistics, Vol. 8(4), pp. 824-838, 1999; F. G. Cozman, Computing Posterior Upper Expectations, First International Symposium on Imprecise Probabilities and Their Applications (ISIPTA), pp. 131-140, Ghent, Belgium, June/July, 1999.

2) Theorem 3 in the paper:

F. G. Cozman, Computing lower expectations with Kuznetsov's independence condition, Third International Symposium on Imprecise Probabilities and Their Applications, pp. 177-187, Carleton Scientific, 2003.

gives a number of constraints that must be satisfied by a Kuznetsov extension; the theorem claims that the list is exhaustive, but the proof does not actually prove this. I do not know of any counterexample (that is, a Kuznetsov extension that requires more constraints), but the theorem only gives necessary conditions, not sufficient ones. I conjecture that more constraints may be necessary, but constructing an example seems quite hard. Besides, the proof of the theorem is used to prove weak union of Kuznetsov independence, which may lead to problems there too. I conjecture that weak union holds, but have had no time to get back to this problem.

3) The paper:

J. C. F. da Rocha, F. G. Cozman, Inference with separately specified sets of probabilities in credal networks, XVIII Conference on Uncertainty in Artificial Intelligence, editors, pp. 430-437, Morgan Kaufmann, San Francisco, California, 2002.

has several problems. First, the result on complexity of inferences for credal networks is correct, but its proof is not (the result was latter proved correctly by Cassio Polpo de Campos and appeared in IJCAI 2005). Second, the inference algorithm is presented so tersely that several key steps are not given, and these steps are actually the ones that have the most complexity. Third, the theorem on why separately specified sets decompose the inference is incomplete; the decomposition happens as stated but not in all cases. And finally, the connection with the 2U algorithm is correct, but it is so complicated to write that you should use the 2U algorithm, not the variable elimination version sketched in this paper. Well, I hope I never write anything else with so many mistakes. In any case, everything in this paper has been superseded by papers at UAI2003, UAI2004 and IJCAI2005.

4) The paper:

D. Kikuti, F. G. Cozman, C. P. de Campos. Partially ordered preferences in decision trees: computing strategies with imprecision in probabilities, IJCAI Workshop on Advances in Preference Handling, Edinburgh, United Kingdom, 2005.

contains a few problems with examples and calculations; an errata has been produced with corrected versions.

Finally, some of the algorithms for credal networks in my PhD thesis were not written with all necessary steps, and a couple of lemmas were correct but had problems in their proofs; these problems were corrected in a subsequent journal paper (F. G. Cozman, Credal networks, Artificial Intelligence Journal, vol. 120, pp. 199-233, 2000). Actually, I don't see any reason for you to read my PhD thesis, as the relevant results appeared in papers published in 2000.
Fabio Cozman, 2008/06/24.