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  • 8 - Quantitative Analysis of Programs with Probabilities and Concentration of Measure Inequalities

  • Edited by Gilles Barthe, Joost-Pieter Katoen, RWTH Aachen University, Germany, Alexandra Silva, University College London
  • Book:
    Foundations of Probabilistic Programming
    Published online:
    18 November 2020
    Print publication:
    03 December 2020, pp 259-294
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  • Summary

    The quantitative analysis of probabilistic programs answers queries involving the expected values of program variables and expressions involving them, as well as bounds on the probabilities of assertions. In this chapter, we will present the use of concentration of measure inequalities to reason about such bounds. First, we will briefly present and motivate standard concentration of measure inequalities. Next, we survey approaches to reason about quantitative properties using concentration of measure inequalities, illustrating these on numerous motivating examples. Finally, we discuss currently open challenges in this area for future work.