Particle count estimation in dilution series experiments

Yajie Duan, Chun Pang Lin, Davit Sargsyan, Javier Cabrera, Christine Livingston, Robert Vogel, Jocelyn Sendecki, Willem Talloen, Helena Geys, Surya Mohanty

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Estimation of microorganism concentration in samples (bacterial cells or viral particles) has been a focal point in biomedical experiments for more than a century. Serial dilution of the samples is often used to estimate the target concentrations in immunology, virology, and pharmaceutical industry. A new methodology, called joint likelihood estimation (JLE), is proposed to estimate particles such as the number of microorganisms in a sample from counts obtained by serially diluting the sample. It models count data from the entire single dilution series rather than using only specific dilutions. The theoretical framework is based on the binomial and the Poisson distributions and is consistent with the actual experimental process. The estimator of the target concentration is obtained by MLE with derived joint likelihood functions of the observed counts including right-censored values. Simulations demonstrated that the new JLE method significantly increases precision and accuracy of the estimate compared to the existing methods. It can be applied to a variety of studies with similar experimental designs, especially when the number of particles in the neat sample is very large.

Original languageEnglish (US)
Pages (from-to)472-479
Number of pages8
JournalNaval Research Logistics
Issue number5
StatePublished - Aug 2023

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Ocean Engineering
  • Management Science and Operations Research


  • Poisson approximation
  • binomial distribution
  • joint likelihood estimation
  • maximum likelihood estimation
  • neat sample concentration
  • serial dilutions


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