Preprints
78. Daly, F., Gaunt, R. E. and Sutcliffe, H. L. Stein's method for asymmetric Laplace approximation. arXiv:2508.07245, 2025.
77. Gaunt, R. E. Inequalities for an integral involving the modified Bessel function of the first kind. arXiv:2501.12197, 2025.
76. Gaunt, R. E. and Sutcliffe, H. L. Bounds for distributional approximation in the multivariate delta method by Stein's method. arXiv2305.06234, 2023.
75. Azmoodeh, E., Gasbarra, D. and Gaunt, R. E. Polynomial Stein operators: a noncommutative algebra perspective. arXiv:2212.07321, 2022.
74. Fischer, A., Gaunt, R. E., Reinert, G. and Swan, Y. Normal approximation for the posterior in exponential families. arXiv:2209.08806, 2022.
Publications
73. Fischer, A., Gaunt, R. E. and Swan, Y. Stein's method of moments on the sphere. To appear in Bernoulli arXiv:2407.02299, 2025+.
72. Gaunt, R. E. On the product of correlated normal random variables and the noncentral chi-square difference distribution. Statistics and Probability Letters 227 Article 110554 (2026), pp. 8.
71. Gaunt, R. E., Nadarajah, S. and Pogany, T. K. Infinite divisibility of the product of two correlated normal random variables and exact distribution of the sample mean. Journal of Mathematical Analysis and Applications 552 Article 129800 (2025), pp. 15.
70. Ebner, B., Fischer, A., Gaunt, R. E., Picker, B. and Swan, Y. Stein's method of moments. Scandinavian Journal of Statistics 52 (2025), pp. 1594-1624.
69. Gaunt, R. E., Li, S. and Sutcliffe, H. L. The Variance-Gamma Product Distribution. Results in Mathematics 80:208 (2025), pp. 23.
68. Gaunt, R. E. and Ye, Z. Asymptotic Expansions Relating to the Distribution of the Product of Correlated Normal Random Variables. Studies in Applied Mathematics 154 (2025), Article e70070, pp. 17.
67. Fischer, A., Gaunt, R. E. and Sarantsev, A. Modified Method of Moments for Generalized Laplace Distributions. Communications in Statistics - Simulation and Computation 54 (2025), pp. 2047-2064. (arXiv)
66. Fischer, A., Gaunt, R. E. and Sarantsev, A. The Variance-Gamma Distribution: A Review. Statistical Science 40 (2025), pp. 235-258.
65. Gaunt, R. E. A probabilistic proof of some integral formulas involving incomplete gamma functions. Communications in Statistics - Theory and Methods 54 (2025), pp. 2246-2250.
64. Fischer, A., Gaunt, R. E. and Swan, Y. Stein's method of moments for truncated multivariate distributions. Electronic Journal of Statistics 19 (2025), pp. 1784-1808 .
63. Gaunt, R. E. On Stein factors in Stein's method for normal approximation. Statistics and Probability Letters 219 Article 110339 (2025), pp. 3.
62. Gaunt, R. E. and Ye, Z. Asymptotic approximations for the distribution of the product of correlated normal random variables. Journal of Mathematical Analysis and Applications 543 Article 128987 (2025), pp. 19.
61. Gaunt, R. E. Absolute moments of the variance-gamma distribution. Journal of Mathematical Analysis and Applications 543 Article 128861 (2025), pp. 11.
60. Gaunt, R. E., Li, S. and Sutcliffe, H. L. A Stein characterisation of the product of correlated normal random variables. Statistics and Probability Letters 216 Article 110269 (2025), pp. 10.
59. Gaunt, R. E. and Li, S. The distribution of the product of independent variance-gamma random variables. Journal of Mathematical Analysis and Applications 539 Article 128530 (2024), pp. 24.
58. Gaunt, R. E. On the cumulative distribution function of the variance-gamma distribution. Bulletin of the Australian Mathematical Society 110 (2024), pp. 389-397.
57. Gaunt, R. E., Nadarajah, S. and Pogany, T. K. On Polya's random walk constants. Proceedings of the American Mathematical Society 152 (2024), pp. 3593-3597. (arXiv)
56. Gaunt, R. E. and Sutcliffe, H. L. Improved bounds in Stein's method for functions of multivariate normal random vectors. Journal of Theoretical Probability 37 (2024), pp. 642-670.
55. Gaunt, R. E. and Li, S. The variance-gamma ratio distribution. Comptes Rendus Mathematique 361 (2023), pp. 1151-1161.
54. Gaunt, R. E. On the moments of the variance-gamma distribution. Statistics and Probability Letters 201 Article 109884 (2023), pp. 4.
53. Gaunt, R. E. and Reinert, G. Bounds for the chi-square approximation of Friedman's statistic by Stein's method. Bernoulli 29 (2023), pp. 2008-2034. (arXiv)
52. Gaunt, R. E. and Li, S. Bounding Kolmogorov distances through Wasserstein and related integral probability metrics. Journal of Mathematical Analysis and Applications 522 Article 126985 (2023), pp. 24.
51. Silva, M. E. P., Gaunt, R. E., Ospina-Forero, L., Jay, C. and House, T. Comparing directed networks via denoising graphlet distributions. Journal of Complex Networks 11 (2023), cnad006, pp. 36. (arXiv)
50. Azmoodeh, E., Gasbarra, D. and Gaunt, R. E. An asymptotic approach to proving sufficiency of Stein characterisations. ALEA: Latin American Journal of Probability and Mathematical Statistics 20 (2023), pp. 127-152.
49. Anastasiou, A., Barp, A., Briol, F.-X., Ebner, B., Gaunt, R. E., Ghaderinezhad, F., Gorham, J., Gretton, A., Ley, C., Liu, Q., Mackey, L., Oates, C. J., Reinert, G. and Swan, Y. Stein's Method Meets Computational Statistics: A Review of Some Recent Developments. Statistical Science 38 (2023), pp. 120-139.
48. Azmoodeh, E., Gasbarra, D. and Gaunt, R. E. On algebraic Stein operators for Gaussian polynomials. Bernoulli 29 (2023), pp. 350-376. (arXiv) (code)
47. Gaunt, R. E. Bounds for the chi-square approximation of the power divergence family of statistics. Journal of Applied Probability 59 (2022), pp. 1059-1080. (arXiv)
46. Gaunt, R. E. The basic distributional theory for the product of zero mean correlated normal random variables. Statistica Neerlandica 76 (2022), pp. 450-470.
45. Gaunt, R. E. Stein factors for variance-gamma approximation in the Wasserstein and Kolmogorov distances. Journal of Mathematical Analysis and Applications 514 Article 126274 (2022), pp. 1-32. (arXiv)
44. Gaunt, R. E. Bounds for an integral involving the modified Lommel function of the first kind. Results in Mathematics 77:159 (2022), pp. 1-19.
43. Gaunt, R. E. Functional inequalities and monotonicity results for modified Lommel functions of the first kind. Results in Mathematics 77:1 (2022), pp. 1-16.
42. Anastasiou, A. and Gaunt R. E. Wasserstein distance error bounds for the multivariate normal approximation of the maximum likelihood estimator. Electonic Journal of Statistics 15 (2021), pp. 5758-5810.
41. Gaunt, R. E. Bounds for an integral of the modified Bessel function of the first kind and expressions involving it. Journal of Mathematical Analysis and Applications 502 Article 125216 (2021), pp. 1-16. (arXiv)
40. Gaunt, R. E. Bounds for an integral involving the modified Struve function of the first kind. Proceedings of the American Mathematical Society 149 (2021), pp. 3889-3904. (arXiv)
39. Gaunt, R. E. New error bounds for Laplace approximation via Stein's method. ESAIM: Probability and Statistics 25 (2021), pp. 325-345.
38. Gaunt, R. E. A simple proof of the characteristic function of Student's t-distribution. Communications in Statistics - Theory and Methods 50 (2021), pp. 3380-3383. (arXiv)
37. Gaunt, R. E. Stein's method and the distribution of the product of zero mean correlated normal random variables. Communications in Statistics - Theory and Methods 50 (2021), pp. 280-285. (arXiv)
36. Gaunt, R. E. and Merkle, M. On bounds for the mode and median of the generalized hyperbolic and related distributions. Journal of Mathematical Analysis and Applications 493 Article 124508 (2021), pp. 1-19. (arXiv)
35. Gaunt, R. E., Mijoule, G. and Swan, Y. Some new Stein operators for product distributions. Brazilian Journal of Probability and Statistics 34 (2020), pp. 795-808. (arXiv)
34. Gaunt, R. E. Bounds for modified Lommel functions of the first kind and their ratios. Journal of Mathematical Analysis and Applications 486 Article 123893 (2020), pp. 1-18. (arXiv)
33. Gaunt, R. E. Stein's method for functions of multivariate normal random variables. Annales de l'Institut Henri Poincare (B) Probabilites et Statistiques 56 (2020), pp. 1484-1513. (arXiv)
32. Gaunt, R. E. Inequalities for some integrals involving modified Lommel functions of the first kind. Results in Mathematics 75:7 (2020), pp. 1-15.
31. Gaunt R. E. Wasserstein and Kolmogorov error bounds for variance-gamma approximation via Stein's method I. Journal of Theoretical Probability 33 (2020), pp. 465-505.
30. Anastasiou, A. and Gaunt R. E. Multivariate normal approximation of the maximum likelihood estimator via the delta method. Brazilian Journal of Probability and Statistics 34 (2020), pp. 136-149. (arXiv)
29. Gaunt, R. E. and Walton, N. Stein's Method for the Single Server Queue in Heavy Traffic. Statistics and Probability Letters 156 Article 108566 (2020), pp. 1-9. (arXiv)
28. Gaunt, R. E. Inequalities for some integrals involving modified Bessel functions. Proceedings of the American Mathematical Society 147 (2019), pp. 2937-2951. (arXiv)
27. Gaunt, R. E. A note on the distribution of the product of zero mean correlated normal random variables. Statistica Neerlandica 73 (2019), pp. 176-179. (arXiv)
26. Gaunt, R. E. Inequalities for integrals of the modified Struve function of the first kind II. Results in Mathematics 74:57 (2019), pp. 1-10.
25. Gaunt, R. E. Stein operators for variables from the third and fourth Wiener chaoses. Statistics and Probability Letters 145 (2019), pp. 118-126. (arXiv)
24. Gaunt, R. E., Iyengar, S., Olde Daalhuis, A. B. and Simsek, B. An asymptotic expansion for the normalizing constant of the Conway-Maxwell-Poisson distribution. Annals of the Institute of Statistical Mathematics 71 (2019), pp. 163-180. (arXiv)
23. Gaunt, R. E., Mijoule, G. and Swan, Y. An algebra of Stein operators. Journal of Mathematical Analysis and Applications 469 (2019), pp. 260-279.
22. Gaunt, R. E. Bounds for modified Struve functions of the first kind and their ratios. Journal of Mathematical Analysis and Applications 468 (2018), pp. 547-566. (arXiv)
21. Wegner, A. E., Ospina-Forero, L., Gaunt, R. E., Deane, C. M. and Reinert, G. Identifying networks with common organizational principles. Journal of Complex Networks 6 (2018), pp. 887-913. (arXiv)
20. Coulson, M., Gaunt, R. E. and Reinert, G. Compound Poisson approximation of subgraph counts in a stochastic block model with multiple edges. Advances in Applied Probability 50 (2018), pp. 759-782. (arXiv)
19. Gaunt, R. E. Inequalities for integrals of the modified Struve function of the first kind. Results in Mathematics 73:65 (2018), pp. 1-10.
18. Gaunt, R. E. Inequalities for integrals of modified Bessel functions and expressions involving them. Journal of Mathematical Analysis and Applications 462 (2018), pp. 172-190.
17. Gaunt, R. E. Products of normal, beta and gamma random variables: Stein operators and distributional theory. Brazilian Journal of Probability and Statistics 32 (2018), pp. 437-466. (arXiv)
16. Gaunt, R. E. A probabilistic proof of some integral formulas involving the Meijer G-function. The Ramanujan Journal 45 (2018), pp. 253-264. (arXiv)
15. Gaunt, R. E. A Stein characterisation of the generalized hyperbolic distribution. ESAIM: Probability and Statistics 21 (2017), pp. 303-316. (arXiv)
14. Dobler, C., Gaunt, R. E. and Vollmer, S. J. An iterative technique for bounding derivatives of solutions of Stein equations. Electronic Journal of Probability 22 No. 96 (2017), pp. 1-39.
13. Gaunt, R. E. Inequalities for the modified Bessel function of the second kind and the kernel of the Kratzel integral transformation. Mathematical Inequalities and Applications 20 (2017), pp. 987-990. (arXiv)
12. Gaunt, R. E. Derivative formulas for Bessel, Struve and Anger-Weber functions. Journal of Classical Analysis 11 (2017), pp. 69-78.
11. Gaunt, R. E., Pickett, A. M. and Reinert, G. Chi-square approximation by Stein's method with application to Pearson's statistic. Annals of Applied Probability 27 (2017), pp. 720-756. (arXiv)
10. Gaunt, R. E. On Stein's method for products of normal random variables and zero bias couplings. Bernoulli 23 (2017), pp. 3311-3345. (arXiv)
9. Gaunt, R. E. Uniform bounds for expressions involving modified Bessel functions. Mathematical Inequalities and Applications 19 (2016), pp. 1003-1012. (arXiv)
8. Coulson, M., Gaunt, R. E. and Reinert, G. Poisson approximation of subgraph counts in stochastic block models and a graphon model. ESAIM: Probability and Statistics 20 (2016), pp. 131-142. (arXiv)
7. Daly, F. and Gaunt, R. E. The Conway-Maxwell-Poisson distribution: distributional theory and approximation. ALEA: Latin American Journal of Probability and Mathematical Statistics 13 (2016), pp. 635-658.
6. Ali, W., Wegner, A. E., Gaunt, R. E., Deane, C. M. and Reinert, G. Comparison of large networks with sub-sampling strategies. Scientific Reports 6 No. 28955 (2016).
5. Gaunt, R. E. Rates of Convergence in Normal Approximation Under Moment Conditions Via New Bounds on Solutions of the Stein Equation. Journal of Theoretical Probability 29 (2016), pp. 231-247. (arXiv)
4. Gaunt, R. E. Inequalities for modified Bessel functions and their integrals. Journal of Mathematical Analysis and Applications 420 (2014), pp. 373-386.
3. Pavlides, M., Cleland, J., Rahman, M., Christian, A., Doyle, J., Gaunt, R. E., Travis, S., Mortensen, N. and Chapman, R. Outcomes after ileal pouch anal anastomosis in patients with primary sclerosing cholangitis. Journal of Crohn's and Colitis 8 (2014), pp. 662-670.
2. Gaunt, R. E. Variance-gamma approximation via Stein's method. Electronic Journal of Probability 19 No. 38 (2014), pp. 1-33.
1. Gill, D., Gaunt R. E. and Hamdulay, S. No substitute for experience: do consultants that have been practising for longer lead faster post-take medical ward rounds? Acute Medicine 12 (2013), pp. 141-145.
DPhil thesis
Rates of Convergence of Variance-Gamma Approximations via Stein's Method. DPhil thesis, University of Oxford, 2013.