Homepage of Philip A. Ernst

Philip A. Ernst, Ph.D.


Chair in Statistics and
Royal Society Wolfson Fellow
Department of Mathematics
Imperial College London
p.ernst at imperial.ac.uk



I am currently Chair (and Full Professor) in Statistics and Royal Society Wolfson Fellow at Imperial College London's Department of Mathematics. I was previously an Assistant Professor (2014-2018), Associate Professor (2019-2022), and Full Professor (2022-2023), all at Rice University's Department of Statistics .

My research interests include:

Theory and Methodology: Applied probability, exact distribution theory, mathematical finance, mathematical statistics, operations research, optimal stopping, queueing systems, statistical inference for stochastic processes, stochastic control, and time series analysis.

To get a taste of some of my research interests, see the following videos:

1) Yule's "nonsense correlation solved: Part II (2023)
2) Yule's "nonsense correlation" solved! (2019)
3) The value of foresight (2018)

Applications: Actuarial science, agricultural economics, climate science, quantitative economics, and portfolio management. The first four applications are strongly related to my present work in the Lake Chad Basin. See this Abstract and Summary of Research Proposal describing my current efforts.

I am also deeply invested in teaching and mentoring. See:

a) George R. Brown Teaching Address at Rice University (2023)
b) An article about some of my efforts (2022)

I currently serve as an Associate Editor for the following five journals: Journal of the American Statistical Association (Theory & Methods), Journal of Stochastic Analysis, Mathematics of Operations Research, Statistics & Probability Letters, and Stochastics. I was previously Guest Editor-in-Chief for "In Memoriam: Larry Shepp," a special issue of Stochastic Processes and their Applications, which appeared in August 2022.

I gratefully acknowledge current research funding from a British Academy/Wolfson Fellowship (2023-2026), a Royal Society Wolfson Fellowship (2022-2027), and the U.S. Office of Naval Research Mathematical Data Science Program (2021-2024).

Employment at Imperial College London, Department of Mathematics

(2022-present): Chair in Statistics and Royal Society Wolfson Fellow

Employment at Rice University, Department of Statistics

(2022-2023): Full Professor of Statistics (with tenure)
(2019-2022): Associate Professor of Statistics (with tenure)
(2018-2018): Assistant Professor of Statistics and Dobelman Family Junior Chair of Statistics
(2014-2018): Assistant Professor of Statistics

Education

Ph.D. in Statistics, The Wharton School of the University of Pennsylvania (2014)
M.A. in Statistics, The Wharton School of the University of Pennsylvania (2010)
B.A. cum laude in Statistics, Harvard University (2007)

Research In The News

A 90 Year Old Problem Solved

News


National and International Research Honors

University Research Honors

  • 2022: Appointed Chair in Statistics at Imperial College London
  • 2022: Awarded Noah G. Harding Professorship in Statistics at Rice University (declined)
  • 2022: Awarded promotion to Full Professor at Rice University Press Release
  • 2019: Awarded early tenure at Rice University (Two Years Early) Press Release
  • 2019 Rice University School of Engineering Teaching and Research Excellence Award Press Release
  • (July 2018-Dec 2018) Rice University Dobelman Family Junior Chair of Statistics Press Release

University Teaching Honors

  • 2023 Rice University George R. Brown Award for Superior Teaching Press Release Rice News
  • 2022 Rice University George R. Brown Award for Excellence in Teaching (Rice University's most prestigious teaching award) Rice University Anouncement
  • 2021 Rice University George R. Brown Award for Superior Teaching Press Release Rice News
  • 2017 Rice University Nicolas Salgo Outstanding Teaching Award Press Release Rice News
  • 2016 Rice University Sophia Meyer Farb Prize for Teaching (Phi Beta Kappa Teaching Award) Press Release
  • 2015 Rice University Graduate Student Association Faculty Teaching and Mentoring Award Link
  • 2014 University of Pennsylvania Department of Statistics Donald S. Murray Prize for Excellence in Teaching
  • 2009 University of Pennsylvania Prize for Excellence in Teaching by Graduate Students Link

Research Funding (UK) as PI

Research Funding (USA) as PI

Federal Conference Funding for A symposium on optimal stopping as PI

Local and Private Conference Funding for A symposium on optimal stopping as PI

Representative Publications

  • Ernst, P.A., Shepp, L.A., and Wyner, A.J. (2017) Yule's "nonsense correlation" solved! The Annals of Statistics 45(4): 1789-1809. PDF Link to Journal Video Talk
  • Ernst, P.A., Rogers, L.C.G., and Zhou, Q. (2020) When is it best to follow the leader? Stochastic Processes and their Applications, 130(6): 3394-3407. PDF Link to Journal
  • Ernst, P.A. and Franceschi, S. (2021) Asymptotic behavior of the occupancy density for obliquely reflected Brownian motion in a half-plane and Martin boundary. The Annals of Applied Probability, 31(6): 2991-3016. PDF Link to Journal
  • Ernst, P.A. and Peskir, G. (2022) Quickest real-time detection of a Brownian coordinate drift. The Annals of Applied Probability, 32(4): 2652-2670. PDF Link to Journal

Papers Under Review or Invited Revision

Legend: (*) denotes a postdoctoral fellow co-author. (**) denotes a Ph.D. student co-author.
(***) denotes a co-author who is a Nobel Prize winner.

Note: Four other preprints are currently not available on arXiv but are available upon request.

  1. Ernst, P.A. and Peskir, G. (2024) The Gapeev-Shiryaev Conjecture. PDF
  2. Ernst, P.A. and Mei, H*. (2023) The minimax Wiener sequential testing problem. PDF
  3. Ernst, P.A. and Huang, D.** (2023) Exact and asymptotic distribution theory for the empirical correlation of two AR(1) processes. PDF

Published Papers and Papers in Press

  1. Ernst, P.A., Mei, H*, and Peskir, G. (2024+) Quickest real-time detection of multiple Brownian drifts. SIAM Journal on Control and Optimization, to appear. PDF
  2. Ernst, P.A., Rogers, L.C.G., and Zhou, Q.* (2024+) Yule's "nonsense correlation": moments and density. Bernoulli, to appear. PDF Video Talk
  3. Bednarz, E., Ernst, P.A., and Osekowski, A. (2024) On the diameter of the stopped spider process. Mathematics of Operations Research, 49(1): 346–365. PDF Link to Journal
  4. Ernst, P.A. and Mei, H.* (2023) Exact optimal stopping for multidimensional linear switching diffusions. Mathematics of Operations Research, 48(3): 1589-1606. PDF Link to Journal
  5. Ernst, P.A., Huang, D.** and Viens, F.G. (2023) Yule’s “nonsense correlation” for Gaussian random walks. Stochastic Processes and their Applications, 162: 423-455. PDF Link to Journal
  6. Ernst, P.A. and Peskir, G. (2022) Quickest real-time detection of a Brownian coordinate drift. The Annals of Applied Probability, 32(4): 2652-2670. PDF Link to Journal
  7. Ernst, P.A., Imerman, M.B., Shepp, L.A., and Zhou, Q.* (2022). Fiscal stimulus as an optimal control problem. Stochastic Processes and their Applications, 150: 1091-1108. PDF Link to Journal
  8. Bruss, F.T., Ernst, P.A., and Huang, D.** (2022) The rencontre problem. Stochastic Processes and their Applications, 150: 938-971. PDF Link to Journal
  9. Ernst, P.A., Kagan, A.M., and Rogers, L.C.G. (2022) The least favorable noise. Electronic Communications in Probability, 27: 1-11. Link to Journal (with PDF)
  10. Gerber, S., Markowitz, H.M.***, Ernst, P.A., Miao, Y.**, Javid, B., and Sargen, P. (2022) The Gerber statistic: a robust co-movement measure for portfolio optimization. The Journal of Portfolio Management, 48(3): 87-102. PDF Link to Journal
  11. Ernst, P.A. and Franceschi, S. (2021) Asymptotic behavior of the occupancy density for obliquely reflected Brownian motion in a half-plane and Martin boundary. The Annals of Applied Probability, 31(6): 2991-3016. PDF Link to Journal
  12. Ernst, P.A., Franceschi, S., and Huang, D.** (2021) Escape and absorption probabilities for obliquely reflected Brownian motion in a quadrant. Stochastic Processes and their Applications, 142: 634-670. Link to Journal (with PDF)
  13. Ernst, P.A. and Rogers, L.C.G. (2020) The value of insight. Mathematics of Operations Research, 45(4): 1193-1209. PDF Link to Journal
  14. Ernst, P.A., Peskir, G., and Zhou, Q.* (2020) Optimal real-time detection of a drifting Brownian coordinate. The Annals of Applied Probability 30(3): 1032-1065. PDF Link to Journal
  15. Ernst, P.A., Rogers, L.C.G., and Zhou, Q.* (2020) When is it best to follow the leader? Stochastic Processes and their Applications, 130(6): 3394-3407. PDF Link to Journal
  16. Ernst, P.A. and Shaman, P. (2019) The bias mapping of the Yule-Walker estimator is a contraction. Statistica Sinica, 29(4):1831-1849. Link to Journal
  17. Ernst, P.A. and Viens, F.G. (2019) In memory of Larry Shepp: An editorial. High Frequency, 2(2): 74-75. Link to Journal
  18. Ernst, P.A., Kendall, W.S., Roberts, G.O, and Rosenthal, J.S. (2019) MEXIT: Maximal un-coupling times for stochastic processes. Stochastic Processes and their Applications, 129(2): 355-380. PDF Link to Journal
  19. Ernst, P.A. and Soleymani, F. (2019) A Legendre-based computational method for solving a class of Ito stochastic delay differential equations. Numerical Algorithms, 80(4): 1267-1282. PDF Link to Journal
  20. Ernst, P.A., Kimmel, M., Kurpas, M., and Zhou, Q.* (2018) Heavy-tailed distributions in branching process models of secondary cancerous tumors. Advances in Applied Probability, 50(A): 99-114. PDF Link to Journal
  21. Ernst, P.A., Asmussen, S., and Hasenbein, J.J. (2018) Stability and busy periods in a multiclass queue with state-dependent arrival rates. Queueing Systems, 90: 207-224. PDF Link to Journal
  22. Zhou, Q.*, Ernst, P.A., Morgan, K.L, Rubin, D.B., and Zhang, A. (2018) Sequential rerandomization. Biometrika, 105(3): 745-752. PDF Link to Journal
  23. Ernst, P.A., Rogers, L.C.G, and Zhou, Q.* (2017) The value of foresight. Stochastic Processes and their Applications, 127(12): 3913-3927. PDF Link to Journal
  24. Ernst, P.A., Shepp, L.A., and Wyner, A.J. (2017) Yule's "nonsense correlation" solved! The Annals of Statistics 45(4): 1789-1809. PDF Link to Journal Video Talk
  25. Ernst, P.A. (2017) Minimizing Fisher information with absolute moment constraints. Statistics and Probability Letters 129: 167-170. Link to Journal
  26. Ernst, P.A. and Grigorescu, I. (2017) Asymptotics for the time of ruin in the war of attrition. Advances in Applied Probability 49(2): 388-410. PDF Link to Journal
  27. Ernst, P.A., Thompson, J.R., and Miao, Y.** (2017). Portfolio selection: the power of equal weight. In Models and Reality: A Festschrift for James R. Thompson , pp. 225-236. PDF
  28. Ernst, P.A., Thompson, J.R., and Miao, Y.** (2017) Tukey's transformational ladder for portfolio management. Financial Markets and Portfolio Management 31(3): 317-355. PDF Link to Journal
  29. Ernst, P.A. and Shepp, L.A. (2017) On occupation times of the first and third quadrants for planar Brownian motion. Journal of Applied Probability 54(1): 337-342. PDF Link to Journal
  30. Ernst, P.A., Brown, L.D., Shepp, L.A., and Wolpert, R.L. (2017) Stationary Gaussian Markov processes as limits of stationary autoregressive time series. Journal of Multivariate Analysis 155: 180-186. Link to Journal
  31. Ernst, P.A. (2017) On the arbitrage price of European call options. Stochastic Models 33(1): 48-58. Link to Journal
  32. Ernst, P.A. and Shepp, L.A. (2016) Eliminating a loophole in the national flood insurance program. Law, Probability and Risk 15(4): 251-258. Link to Journal
  33. Ernst, P.A., Pemantle, R., Satopaa, V., and Ungar, L. (2016) Bayesian aggregation of two forecasts in the partial information framework. Statistics and Probability Letters 119: 170-180.
  34. Ernst, P.A. (2016) Exercising control when confronted by the (Brownian) spider. Operations Research Letters 44: 487-490. PDF Link to Journal
  35. Ernst, P.A. and Shepp, L.A. (2016) On the time for Brownian motion to visit every point on a circle. Journal of Statistical Planning and Inference 171: 130-134. PDF Link to Journal
  36. Ernst, P.A. and Shepp, L.A. (2015) Revisiting a theorem of L.A. Shepp on optimal stopping. Communications on Stochastic Analysis 9(3): 419-423. PDF Link to Journal
  37. Ernst, P.A., Foster, D.P., and Shepp, L.A. (2014). On optimal retirement. Journal of Applied Probability 51(2): 333-345. Link to Journal


Current Ph.D. students (sole advisor)

Former Ph.D. Students (sole advisor)

Former Postdoctoral Fellows (sole advisor)

  • Hongwei Mei, Ph.D. (May 2020-August 2022)
    First Job: Assistant Professor of Mathematics and Statistics (tenure-track), Texas Tech University.
  • Richard Chen, Ph.D. (September 2020-August 2021)
    First Job: Research scientist, Amazon.
  • Quan Zhou, Ph.D. (April 2017-August 2019)
    First Job: Assistant Professor of Statistics (tenure-track), Texas A&M University

Public Outreach

Course Reviews

At Rice University, I taught STAT 310 (undergraduate probability and statistics), STAT 581 (A Ph.D. course in measure-theoretic probability), and STAT 650 (A Ph.D. course in stochastic differential equations). Course reviews may be found below.

As a Ph.D. candidate at Wharton Statistics, I taught STAT 101 (undergraduate business statistics). The course review is below.

STAT 101 Instructor Review