An increasingly common activity in the field of High Energy Physics is the setting of limits on unobserved phenomena. Examples include searches for the Higgs, B_s mixing, Physics beyond the Standard Model, dark matter, etc., as well as measurements of the mass of the electron-neutrino and accelerator experiments on neutrino oscillations.

Workshops were recently held at CERN and FNAL, devoted to setting confidence limits in difficult cases. Several different approaches (Bayesian; Feldman-Cousins and modifications thereof; CL_s method for Higgs searches) were discussed. There were also talks on specific analyses, as well as a concluding Panel discussion.

This seminar will review these Workshops. Topics will include:

• What is the problem?
• Frequentist and Bayesian approaches
• Application to simple problems
• More realsitic examples
• Where does this leave us?