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Personal profile

Research interests

My research is in applied probability.  In many real-life situations probability distributions of interest are tricky to handle, but can be well approximated by distributions which are much easier to work with (such as a Gaussian or Poisson distribution).  Much of my work has been in the theory and application of Stein's method, which allows the quality of such probability approximations to be explicitly evaluated in a wide variety of settings without relying on assumptions of independence.  Stein's method also has several links with information theory which have provided a fruitful area of research.

Biography

I completed a PhD in Mathematics at the University of Nottingham in 2008.  I then spent around 18 months at the University of Zurich and three years at the University of Bristol.  I took up a lectureship at Heriot-Watt in August 2013.

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Compound Poisson Approximation Mathematics
Stein's Method Mathematics
Poisson Approximation Mathematics
Random variable Mathematics
Poisson distribution Mathematics
Approximation Mathematics
Negative Dependence Mathematics
Negative Association Mathematics

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Research Output 2008 2019

Bounds on the Poincaré constant under negative dependence

Daly, F. & Johnson, O., Feb 2013, In : Statistics and Probability Letters. 83, 2, p. 511-518 8 p.

Research output: Contribution to journalArticle

Stein's method and stochastic orderings

Daly, F. A., Lefèvre, C. & Utev, S., Jun 2012, In : Advances in Applied Probability. 44, 2, p. 343-372 30 p.

Research output: Contribution to journalArticle

Stein's method for compound geometric approximation

Daly, F., Mar 2010, In : Journal of Applied Probability. 47, 1, p. 146-156 11 p.

Research output: Contribution to journalArticle

Upper bounds for Stein-type operators

Daly, F. A., 12 Apr 2008, In : Electronic Journal of Probability. 13, p. 566-587 22 p., 20.

Research output: Contribution to journalArticle

Hitting Time
Markov chain
Explicit Bounds
Stationarity
Approximation