Two genotypes: haploid and diploid.

Over a series of 9 days, root lengths on various plants are measured. The goal is, for a new sample, determine whether the sample comes from a haploid or a diploid based on its root length.


Use Bayes Rule. Let H be haploid and L>k be the event the root length is greater than a cutoff of k. Bayes Rule says

P(H L>k) =    
P(L>k H)P(H)/(P(L>k H)P(H) + P(L>k D)P(D)) =
1/[P(L>k D)/P(L>k H) x P(D)/P(H)]  


  • P(H) is the prevalence of haploids, P(D) = 1-P(H)
  • P(L>k H), [P(L>k D)] is the probability a haploid [diploid] has root length greater than k

The prevalence needs to be determined from external data, but the probability the root length is greater than k can be determined from the data at hand. Uncertainty could be incorporated in these probabilities by assuming a prior.

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29 November 2017