Bayesian Statistics:  A Brief Overview and an Application to Quantifying Uncertainty in Qualitative Botanical Analysis 

Sidney’s Overview:

Qualitative botanical analysis, or identification, is a classification process; botanicals are assigned to some class based on tests made against established criteria. An identification is a classification made based on evidence. Misidentifications that may occur arise from analysis of specific evidence when the material is in a different class (‘false positive’) and lack of evidence for a particular class, in which the material belongs (‘false negative’).  Bayes’ Theorem, which will be described, provides a framework for expressing uncertainty in classification problems. The necessary numerical information or metrics are then obtained, using a statistical model, to be able to calculate and report identification certainty which can accompany a qualitative assessment, to indicate the analyst’s confidence in its veracity. 

  

Bayes Theorem provides the oldest method available for updating probabilities and is a natural candidate for application to qualitative analysis of Botanical Identification, since it both allows the analyst to modify the expectation (of identity) in a cumulative and systematic way and considers the probabilities of both correct and incorrect outcomes.