Bayes factor

Kass, R. E. and Raftery, A. (1995). Bayes factors. Journal of the American Statistical... 

Berger, J. O. and Pericchi, L. R. (1996). The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association, 91, 109-122. 

The Petri-Net based visualization depicts a sequential, flat view of the trace chunks consisting of the addressed situations and the contexts executed at each situation. The displayed trace chunks are sorted according to their Bayes factor calculated at the final step of the FIST algorithm, and annotated with values of their timestamp, similarity, frequency and Bayes factor. Moreover, the displayed situations that are similar to the current one are highlighted, and their exact similarity to the current situation can be shown by clicking on them. 

Currently, research is still going on with respect to the best visual representation of the reference situations and the counter-measures. Additionally, aspects such as the Bayes factor (see FIST algorithm in Subsect. 3.1.5 and [80]) are to be integrated, to improve the recommendation quality based on the operators previous decisions. 

Kass, R. Raftery, A. 1995. Bayes factors. X Amer. Stat. Assoc., 90 773-795. 

A final mention of data on real systems is worth, although this paper is not concerned with comparisons with experimental data. It is however interesting to mention that by comparing the experimental data on S.Cerevisiae with the theoretical distribution of Eq. 1, using the jackknife method [16,17], it is possible to loeate the k parameter in the 95 % confidence interval [0.84, 0.93]. Moreover, an analysis of the same data using Bayes factors [18,19], leads to reject the hypothesis that the network is precisely critical, since the probability that X = 1 given the data is smaller than 10 under a broad range of prior distributions. The interested reader is referred to [15] for further details. 

Jiang and Mahadevan (Jiang and Mahadevan 2008) derived the expression for the natural logarithm of the Bayes factor, as ... 

Damage detection can be achieved through the use of Bayes factor (B) which is defined as the... 

To remove the dependence on the priors PCMo, ), we compare models a and by computing the Bayes factor... 

Here we provide an approximation of the Bayes factor for single-response data that does not require MCMC simulation. Let the sum of squared errors for a model be... 

This approximate result tells us that we should choose the model with the largest value of BIC. The second term in the square brackets in (8.236) adds to the weighted sum of squared errors an additional penalty per parameter, encouraging the use of models with smaller numbers of adjustable parameters. Clearly, tiiis is only an approximation of the Bayes factor, and should be applied only when N is large. For more exact analysis, the Bayes factor should be computed by MCMC evaluation of the integrals (8.219). 

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