Checking for model failure and for prior-data conflict with the constrained multinomial model.

Area of Science:

• Statistics
• Computational Statistics

Background:

• Multinomial models are widely used but challenging with probability constraints.
• Existing methods for constrained multinomial models lack exact procedures.

Purpose of the Study:

• To develop an exact model checking procedure for constrained multinomial models.
• To introduce a new methodology for eliciting ordered probabilities in these models.

Main Methods:

• Developed an exact model checking procedure using a uniform prior on the full multinomial model.
• Proved a consistency theorem for checking prior-data conflict with nonuniform priors.
• Introduced a novel elicitation methodology for ordered probabilities.

Main Results:

• An exact procedure for model checking constrained multinomial models is established.
• A method for assessing prior-data conflict in multinomial models is provided.
• A new, practical elicitation methodology for ordered probabilities is presented.

Conclusions:

• The developed methods enhance the usability and reliability of constrained multinomial models.
• The findings offer practical solutions for statistical inference and probability elicitation.