2013/12/02 by Dirk Tasche, Tasche, Dirk
Decision Sciences · Mathematics · #60A05 #62H30 #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Probability (math.PR) #Statistics Education and Methodologies #math.PR #msc:60A05 #msc:62H30 #stat.AP #stat.ML
paper · pdf · doi:10.48550/arxiv.1312.0365
12 pages, 1 figure, new references
openalex publication_date 2013/12/02 · arxiv created 2014/02/14 · arxiv updated 2014/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The law of total probability may be deployed in binary classification exercises to estimate the unconditional class probabilities if the class proportions in the training set are not representative of the population class proportions. We argue that this is not a conceptually sound approach and suggest an alternative based on the new law of total odds. We quantify the bias of the total probability estimator of the unconditional class probabilities and show that the total odds estimator is unbiased. The sample version of the total odds estimator is shown to coincide with a maximum-likelihood estimator known from the literature. The law of total odds can also be used for transforming the conditional class probabilities if independent estimates of the unconditional class probabilities of the population are available. Keywords: Total probability, likelihood ratio, Bayes' formula, binary classification, relative odds, unbiased estimator, supervised learning, dataset shift.