Generalized data thinning using sufficient statistics

Area of Science:

• Statistics
• Probability Theory
• Statistical Inference

Background:

• Traditional methods for decomposing random variables can fail in certain inference tasks.
• Prior work demonstrated data thinning for specific natural exponential families, requiring a summation constraint.

Purpose of the Study:

• To develop a general strategy for decomposing a random variable into independent random variables.
• To relax the summation requirement of previous thinning methods.
• To unify data thinning and sample splitting under the principle of sufficiency.

Main Methods:

• Generalizing the procedure of thinning random variables.
• Relaxing the summation constraint to a functional reconstruction.
• Applying generalized thinning to diverse statistical families.

Main Results:

• Expanded the range of distributions amenable to thinning.
• Demonstrated that data thinning and sample splitting are unified applications of sufficiency.
• Developed a general strategy applicable to a wider array of statistical families.

Conclusions:

• The generalized thinning procedure offers a more flexible approach to random variable decomposition.
• Sufficiency is identified as the unifying principle behind data thinning and sample splitting.
• The method enhances capabilities for model validation and inference.