Reporting Bayes factors or probabilities to decision makers of unknown loss functions

ABSTRACT

When competing interests seek to influence a decision maker, a scientist must report a posterior probability or a Bayes factor among those consistent with the evidence. The disinterested scientist seeks to report the value that is least controversial in the sense that it is best protected from being discredited by one of the competing interests. If the loss function of the decision maker is not known but can be assumed to satisfy two invariance conditions, then the least controversial value is a weighted generalized mean of the upper and lower bounds of the interval.

KEYWORDS:

• Benford’s law
• combining distributions
• imprecise probability
• logarithmic opinion pooling
• measure of evidence
• strength of statistical evidence.

Acknowledgments

The careful reading by two referees led to important improvements, especially the addition of Section 5. This research was partially supported by the Natural Sciences and Engineering Research Council of Canada (RGPIN/356018-2009) and by the Faculty of Medicine of the University of Ottawa.

Additional information

Funding

Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada [RGPIN/356018-2009]; University of Ottawa.