Reviews

Reviewer 1 – Report on Computing with Confidence: Imprecise Posteriors and Predictive Distributions. By S. Ferson et al., for ICVRAM 2014

Confidence structures (c-boxes) have recently been introduced by one of the authors. They transfer the concept of confidence distributions (introduced by Cox in 1958) to the setting of imprecise probability. Confidence structures are much more flexible than confidence distributions (e.g., one can construct a c-box for the binomial distribution) and can be propagated in computational models. The full paper definitely delivers what the abstract promised. It contains a well-written introduction to the concept and its history, a wealth of connections with competing notions, and a very illuminating selection of examples.

The exposition is concise and clear. In my view, the concept of c-boxes will become an important one both in imprecise probability and in classical probability, extending the range of applicability and promoting the notion of confidence distributions.

I recommend that the paper be accepted for publication at the ICVRAM conference. I have only a few minor remarks:

p. 2, line 18: The word “interval” is missing after “confidence”.

pp. 3-4: A bit more explanations of Table 1 would be welcome. At least, explain what is the meaning of “next.binomialnp”, “cbox.binomialnp.n” etc.

p. 4, line 4 after table: Shouldn’t it be “online”?

p. 6, second paragraph: I was a bit confused at first reading by the interjection about the ratio k/n, followed by the estimate p = 0 and the right graph in Figure 1, before I remembered that the example was about k = 0. May be the sentence about general k/n can be entangled from the example, in which k = 0.

Reviewer 2 – Report on Computing with Confidence: Imprecise Posteriors and Predictive Distributions. By S. Ferson et al., for ICVRAM 2014

By raising again attention to confidence distributions it makes a valuable contribution to the conference. The paper clearly is interesting, and it will initiate interesting discussions about foundations of statistics that are also of great importance for risk modelling.