The use of Thompson sampling to increase estimation precision.

Area of Science:

• Statistics
• Experimental Design
• Biostatistics

Background:

• Estimating differences between two independent treatment means is crucial in comparative studies.
• Unequal population variances across groups pose challenges for traditional estimation methods.
• Sequential sampling offers adaptive approaches to data collection.

Purpose of the Study:

• To propose a novel sequential sampling scheme for efficient estimation of the difference between two independent treatment means.
• To adapt Thompson sampling, typically used for maximizing cumulative payoff, for enhancing estimation precision.
• To address scenarios with unequal population variances between groups.

Main Methods:

• The study employs Thompson sampling, a method originating from bandit problems, as the core of the sequential sampling scheme.
• The proposed method is designed to balance the exploration of treatment effects with the exploitation of existing information.
• Effectiveness is evaluated through simulation studies.

Main Results:

• The simulations demonstrate the effectiveness of the proposed Thompson sampling-based sequential design.
• The method successfully balances exploration and exploitation to improve estimation precision.
• The sequential sampling scheme is efficient even when population variances are unequal.

Conclusions:

• Thompson sampling provides a powerful and flexible framework for sequential experimental design.
• This novel approach enhances the efficiency of estimating treatment mean differences, particularly under unequal variances.
• The method offers a valuable tool for experimenters aiming to optimize precision in comparative studies.