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Abstract
This short paper presents a new idea leading to a very sharp upper bound on the variance of intervalvalued data. The computation of this sharp bound can be carried out in polynomial time in the worst case. For a whole class of interval data this bound is exact as it can be shown that it coincides with the maximum. The algorithm derives from posing the optimisation problem in probabilistic terms, i.e. thinking beyond the deterministic interpretation of an interval. Intervalvalued variance can be seen from an imprecise probability’s perspective. There are two alternative and noncompeting connotations of an interval: a set of real values, and a credal set of all possible probability measures in the given interval. These two connotations do not precipitate any quantitative discrepancies for interval arithmetic. In fact, interval arithmetic provides a means to compute with these imprecise probabilistic objects. This work demonstrates the computational advantage that originates from looking at intervals from an imprecise probabilistic angle, and it may serve as a testimony towards filling the computational void that has for too long discouraged practitioners from computing with interval statistics.
Original language  English 

Title of host publication  Combining, Modelling and Analyzing Imprecision, Randomness and Dependence 
Editors  Jonathan Ansari, Sebastian Fuchs, Wolfgang Trutschnig, María Asunción Lubiano, María Ángeles Gil, Przemyslaw Grzegorzewski, Olgierd Hryniewicz 
Place of Publication  Cham 
Publisher  Springer 
Pages  7684 
Number of pages  9 
ISBN (Electronic)  9783031659935 
ISBN (Print)  9783031659928 
DOIs  
Publication status  Published  10 Aug 2024 
Event  Soft Methods in Probability and Statistics  Salzburg, Austria Duration: 3 Sept 2024 → 6 Sept 2024 http://www.smps2024.com 
Publication series
Name  Advances in Intelligent Systems and Computing 

Volume  1458 
ISSN (Print)  21945357 
ISSN (Electronic)  21945365 
Conference
Conference  Soft Methods in Probability and Statistics 

Country/Territory  Austria 
City  Salzburg 
Period  3/09/24 → 6/09/24 
Internet address 
Keywords
 imprecise statistics
 interval computation
 interval variance
 polynomialtime algorithm
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Dive into the research topics of 'Sharp polynomial upper bound on the variance'. Together they form a unique fingerprint.Activities
 1 Participation in conference

11. International Conference on Soft Methods in Probability and Statistics
Marco De Angelis (Participant)
3 Sept 2024Activity: Participating in or organising an event types › Participation in conference