Bayesian optimal designs for estimating a set of symmetrical quantiles

Area of Science:

• Statistics
• Biostatistics
• Experimental Design

Background:

• Logit models are widely used in statistical analysis, particularly in biostatistics.
• Optimal experimental design is crucial for efficient data collection and reliable inference.
• Estimating specific percentiles (e.g., quartiles) is a common goal in data analysis.

Purpose of the Study:

• To propose and evaluate multiple-objective Bayesian optimal designs for the logit model.
• To investigate the efficiency of these designs for estimating multiple percentiles with varying interests.
• To compare Bayesian optimal designs with sequential designs and locally optimal designs.

Main Methods:

• Development of multiple-objective Bayesian optimal design criteria for logit models.
• Application to the problem of estimating three quartiles with unequal importance.
• Comparison with sequential designs generated by a generalized Pólya urn model.
• Comparison with locally optimal designs.

Main Results:

• The proposed Bayesian optimal designs are suitable for estimating multiple percentiles in logit models.
• Sequential designs based on the generalized Pólya urn model demonstrated high efficiency.
• Bayesian optimal designs showed advantages over locally optimal designs in certain scenarios.

Conclusions:

• Multiple-objective Bayesian optimal designs offer a flexible framework for logit model applications.
• Generalized Pólya urn sequential designs are efficient alternatives for percentile estimation.
• The choice between Bayesian and locally optimal designs depends on specific study objectives and prior information.