data, is via a formula for the midpoint of an interval estimate, particularly a binomial proportion confidence interval. The best-known is due to Edwin Bidwell Wilson, in : the midpoint of the Wilson score interval corresponding to standard deviations on either side is: Taking standard deviations to approximate a 95% confidence interval () yields pseudocount of 2 for each outcome, so 4 in total, colloquially known as the "plus four rule": This is also the midpoint of the Agresti–Coull interval, . Generalized to the case of known incidence rates Often you are testing the bias of an unknown trial population against a control population with known parameters (incidence rates) . In this case the uniform probability should be replaced by the known incidence rate of the control population to calculate the smoothed estimator : As a consistency check, if the empirical estimator happens to equal the incidence rate, i.e. , the smoothed estimator is independent of and also equals the incidence rate. Applications Classification Additive smoothing is commonly a component of naive Bayes classifiers. Statistical language modelling In a bag of words model of natural language processing and information retrieval, the data consists of the number of occurrences of each word in a document. Additive smoothing allows the assignment of non-zero probabilities to words which do not occur in the sample. Recent studies have proven that additive smoothing is more effective than other probability smoothing methods in several retrieval tasks such as language-model-based pseudo-relevance feedback and recommender systems. See also Bayesian average Prediction by partial matching Categorical distribution References Sources External links SF Chen, J Goodman (1996). "An empirical study of smoothing techniques for language modeling". Proceedings of the 34th annual meeting on Association for Computational Linguistics. Pseudocounts Bayesian interpretation of pseudocount regularizers Statistical natural language processing Categorical data Probability theory