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Abstract Phylodynamics is an area of population genetics that uses genetic sequence data to estimate past population dynamics. Modern state‐of‐the‐art Bayesian nonparametric methods for recovering population size trajectories of unknown form use either change‐point models or Gaussian process priors. Change‐point models suffer from computational issues when the number of change‐points is unknown and needs to be estimated. Gaussian process‐based methods lack local adaptivity and cannot accurately recover trajectories that exhibit features such as abrupt changes in trend or varying levels of smoothness. We propose a novel, locally adaptive approach to Bayesian nonparametric phylodynamic inference that has the flexibility to accommodate a large class of functional behaviors. Local adaptivity results from modeling the log‐transformed effective population size a priori as a horseshoe Markov random field, a recently proposed statistical model that blends together the best properties of the change‐point and Gaussian process modeling paradigms. We use simulated data to assess model performance, and find that our proposed method results in reduced bias and increased precision when compared to contemporary methods. We also use our models to reconstruct past changes in genetic diversity of human hepatitis C virus in Egypt and to estimate population size changes of ancient and modern steppe bison. These analyses show that our new method captures features of the population size trajectories that were missed by the state‐of‐the‐art methods.
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On Functional Processes with Multiple Discontinuities
Abstract We consider the problem of estimating multiple change points for a functional data process. There are numerous examples in science and finance in which the process of interest may be subject to some sudden changes in the mean. The process data that are not in a close vicinity of any change point can be analysed by the usual nonparametric smoothing methods. However, the data close to change points and contain the most pertinent information of structural breaks need to be handled with special care. This paper considers a half-kernel approach that addresses the inference of the total number, locations and jump sizes of the changes. Convergence rates and asymptotic distributional results for the proposed procedures are thoroughly investigated. Simulations are conducted to examine the performance of the approach, and a number of real data sets are analysed to provide an illustration.
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- Award ID(s):
- 1916226
- PAR ID:
- 10398620
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Volume:
- 84
- Issue:
- 3
- ISSN:
- 1369-7412
- Format(s):
- Medium: X Size: p. 933-972
- Size(s):
- p. 933-972
- Sponsoring Org:
- National Science Foundation
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