Creating discrete joint densities from continuous ones: the moment matching-maximum entropy approach

Area of Science:

• Computational statistics
• Pharmacometrics

Background:

• Individualized drug therapies require discrete probability distributions for modeling.
• Existing methods for converting continuous to discrete distributions may lack flexibility or introduce bias.

Purpose of the Study:

• To develop a principled method for converting continuous probability densities into discrete ones.
• To ensure the generated discrete distributions are least-informative and satisfy moment constraints.

Main Methods:

• Developed a maximum entropy algorithm to find a discrete distribution.
• Incorporated moment constraints (e.g., mean, variance) from the continuous distribution.
• Ensured discrete support points are pre-assigned.

Main Results:

• Successfully converted continuous densities to discrete distributions.
• The method preserves key statistical moments (e.g., mean, variance).
• The generated discrete distributions are maximally non-informative given the constraints.

Conclusions:

• The developed method provides a robust way to generate discrete distributions for computational modeling.
• This approach is particularly suitable for applications in individualized drug therapies using multiple model control.
• Facilitates the creation of model sets essential for personalized medicine.