Bayesian inference from count data using discrete uniform priors.

Area of Science:

• Statistical inference
• Population dynamics
• Quantitative biology

Background:

• Accurate population size estimation is crucial in many scientific disciplines.
• Traditional methods can be limited by sampling fractions and count data characteristics.
• Bayesian approaches offer a robust framework for handling uncertainty in count data.

Purpose of the Study:

• To derive a Bayesian method for inferring population size from sample counts.
• To develop a computationally feasible formula for absolute quantification under uncertainty.
• To provide a versatile algorithm applicable to diverse biological and physical problems.

Main Methods:

• Bayesian derivation of posterior probability distribution for population size.
• Utilized binomial likelihood with non-conjugate, discrete uniform priors.
• Implemented algorithm in the R package dupiR for practical application.

Main Results:

• Developed a computationally feasible formula for population size inference.
• Demonstrated applicability in estimating bacterial survival curves with low/zero counts.
• Compared favorably with existing Bayesian methods using Gamma priors.

Conclusions:

• The derived algorithm offers a versatile, general-purpose solution for inferring population sizes from count data.
• The method is particularly useful for scenarios with high sampling fractions and limited or zero counts.
• This framework enhances absolute quantification under uncertainty across various scientific domains.