NPIstats: NPIstats: Nonparametric Predictive Inference

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An implementation of the Nonparametric Predictive Inference approach in R. It provides tools for quantifying uncertainty via lower and upper probabilities. It includes useful functions for pairwise and multiple comparisons: comparing two groups with and without terminated tails, selecting the best group, selecting the subset of best groups, selecting the subset including the best group.


Nonparametric Predictive Inference (NPI) is a statistical method which uses few modelling assumptions, enabled by the use of lower and upper probabilities to quantify uncertainty. NPI has been presented for many problems in Statistics, Risk and Reliability and Operations Research. NPI approach is based on Hill’s assumption A(n), which gives a direct conditional probability for a future observable random quantity, conditional on observed values of related random quantities. Inferences based on A(n) are predictive and nonparametric, and can be considered suitable if there is hardly any knowledge about the random quantity of interest, other than the n observations, or if one does not want to use such information, e.g. to study effects of additional assumptions underlying other statistical methods. A(n) is not sufficient to derive precise probabilities for many events of interest, but it provides optimal bounds for probabilities for all events of interest involving the next future observation. These bounds are lower and upper probabilities in the theories of imprecise probability and interval probability, and as such they have strong consistency properties. NPI is a framework of statistical theory and methods that use these A(n)-based lower and upper probabilities, and also considers several variations of A(n) which are suitable for different inferences. For more info, visit NPI webpage.


Augustin, T. and Coolen, F.P.A. (2004). Nonparametric predictive inference and interval probability. Journal of Statistical Planning and Inference 124, 251-272.

Coolen, F.P.A. (1998). Low structure imprecise predictive inference for Bayes’ problem. Statistics & Probability Letters 36, 349-357.

Coolen, F.P.A. and van der Laan, P. (2001). Imprecise predictive selection based on low structure assumptions. Journal of Statistical Planning and Inference 98, 259-277.

Coolen, F.P.A. (1996). Comparing two populations based on low stochastic structure assumptions. Statistics & Probability Letters 29, 297-305.

Hill, B.M. (1968). Posterior distribution of percentiles: Bayes’ theorem for sampling from a population. Journal of the American Statistical Association 63, 677-691.

Weichselberger K. (2000). The theory of interval-probability as a unifying concept for uncertainty. International Journal of Approximate Reasoning, 24(2-3), 149–170.

NPIstats documentation built on Feb. 16, 2021, 5:07 p.m.