Main research interests:
All aspects of random combinatorial objects and combinatorial stochastic processes and their applications in network science, population genetics, physics, and machine learning.
Five specific research lines are:
1. Foundations of statistical and inductive inference
2. Exchangeability and probabilistic invariance principles
3. Foundations of statistical network modeling
4. Combinatorial Markov processes
5. Inference for large combinatorial structures
Selected publications: (Complete publication list with links to pdf files)
Graph- and partition-valued processes and exchangeability theory
H. Crane. (2016). The ubiquitous Ewens sampling formula (with discussion and a rejoinder by the author). Statistical Science, 31(1):1-39.
H. Crane. (2017). Exchangeable graph-valued Feller processes. Probability Theory and Related Fields, in press.
H. Crane. (2016). Dynamic random networks and their graph limits. Annals of Applied Probability, 26(2):691-721.
H. Crane. (2014). The cut-and-paste process. Annals of Probability, 42(5):1952-1979.
H. Crane. (2015). Time-varying network models.
H. Crane and W. Dempsey. (2016). Edge exchangeable models for network data.
H. Crane and W. Dempsey. (2016). A framework for statistical network modeling.
H. Crane. (2015). Clustering from categorical data sequences.
Journal of the American Statistical Association 110(510):810-823. data sets
H. Crane. (2015). Generalized Ewens-Pitman model for Bayesian clustering. Biometrika, 102(1), 231-238.
H. Crane. (2016). A hidden Markov model for latent temporal clustering.
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