Application of Statistical Methods in Quantitative Microscopy*

The purpose of the paper is twofold: first, to describe the aspects of quantitative microscopy where statistical ideas are being applied today; and second, to describe some ways in which more complete use of statistics could improve quantitative microscopy. The typical estimation problem in quantitative microscopy is described with emphasis on the modelling of variability in estimation. A Poisson field model for imbedded particulates is used to illustrate the value of theoretical treatments of variability. Sampling, estimation and multivariate analysis are cited as areas of statistics presently used by quantitative microscopists. The potential role of statistics in quantitative microscopy is discussed. Examples from particle sizing and characterization of alveolar lung structure illustrate the value of statistical ideas. Automatic image analysers, while making the collection of large amounts of data feasible, have complicated statistical estimation. An investigation of the size distribution of random chord lengths through alveolar chambers illustrates how statistical methodology must be modified for valid inference.