×

zbMATH — the first resource for mathematics

A hierarchical dependent Dirichlet process prior for modelling bird migration patterns in the UK. (English) Zbl 1439.62218
Summary: Environmental changes in recent years have been linked to phenological shifts which in turn are linked to the survival of species. The work in this paper is motivated by capture-recapture data on blackcaps collected by the British Trust for Ornithology as part of the Constant Effort Sites monitoring scheme. Blackcaps overwinter abroad and migrate to the UK annually for breeding purposes. We propose a novel Bayesian nonparametric approach for expressing the bivariate density of individual arrival and departure times at different sites across a number of years as a mixture model. The new model combines the ideas of the hierarchical and the dependent Dirichlet process, allowing the estimation of site-specific weights and year-specific mixture locations, which are modelled as functions of environmental covariates using a multivariate extension of the Gaussian process. The proposed modelling framework is extremely general and can be used in any context where multivariate density estimation is performed jointly across different groups and in the presence of a continuous covariate.
MSC:
62P10 Applications of statistics to biology and medical sciences; meta analysis
62P12 Applications of statistics to environmental and related topics
62N05 Reliability and life testing
62H11 Directional data; spatial statistics
60G15 Gaussian processes
92B25 Biological rhythms and synchronization
Software:
Rcpp; R
PDF BibTeX XML Cite
Full Text: DOI Euclid
References:
[1] Álvarez, M. A. and Lawrence, N. D. (2011). Computationally efficient convolved multiple output Gaussian processes. J. Mach. Learn. Res. 12 1459-1500. · Zbl 1280.68153
[2] Both, C., Bouwhuis, S., Lessells, C. and Visser, M. E. (2006). Climate change and population declines in a long-distance migratory bird. Nature 441 81.
[3] Camerlenghi, F., Lijoi, A., Orbanz, P. and Prünster, I. (2019). Distribution theory for hierarchical processes. Ann. Statist. 47 67-92. · Zbl 07036195
[4] Chen, Z., Wang, B. and Gorban, A. N. (2017). Multivariate Gaussian and Student-t process regression for multi-output prediction. ArXiv preprint. Available at arXiv:1703.04455.
[5] De Iorio, M., Müller, P., Rosner, G. L. and MacEachern, S. N. (2004). An ANOVA model for dependent random measures. J. Amer. Statist. Assoc. 99 205-215. · Zbl 1089.62513
[6] Diana, A., Matechou, E., Griffin, J. and Johnston, A. (2020). Supplement to “A hierarchical dependent Dirichlet process prior for modelling bird migration patterns in the UK.” https://doi.org/10.1214/19-AOAS1315SUPP.
[7] Dorazio, R. M., Mukherjee, B., Zhang, L., Ghosh, M., Jelks, H. L. and Jordan, F. (2008). Modeling unobserved sources of heterogeneity in animal abundance using a Dirichlet process prior. Biometrics 64 635-644. · Zbl 1137.62084
[8] Eddelbuettel, D., François, R., Allaire, J., Ushey, K., Kou, Q., Russel, N., Chambers, J. and Bates, D. (2011). Rcpp: Seamless R and \(C++\) integration. J. Stat. Softw. 40 1-18.
[9] Eglington, S. M., Julliard, R., Gargallo, G., van der Jeugd, H. P., Pearce-Higgins, J. W., Baillie, S. R. and Robinson, R. A. (2015). Latitudinal gradients in the productivity of e uropean migrant warblers have not shifted northwards during a period of climate change. Glob. Ecol. Biogeogr. 24 427-436.
[10] Escobar, M. D. and West, M. (1995). Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. 90 577-588. · Zbl 0826.62021
[11] Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1 209-230. · Zbl 0255.62037
[12] Ford, J. H., Patterson, T. A. and Bravington, M. V. (2015). Modelling latent individual heterogeneity in mark-recapture data with Dirichlet process priors. ArXiv preprint. Available at arXiv:1511.07103.
[13] Ge, H., Chen, Y., Wan, M. and Ghahramani, Z. (2015). Distributed inference for Dirichlet process mixture models. In International Conference on Machine Learning 2276-2284.
[14] Gienapp, P., Leimu, R. and Merilä, J. (2007). Responses to climate change in avian migration time—microevolution versus phenotypic plasticity. Clim. Res. 35 25-35.
[15] Griffin, J. E. and Leisen, F. (2017). Compound random measures and their use in Bayesian non-parametrics. J. R. Stat. Soc. Ser. B. Stat. Methodol. 79 525-545. · Zbl 1412.60071
[16] Hjort, N. L., Holmes, C., Müller, P. and Walker, S. G. (2010). Bayesian Nonparametrics 28. Cambridge Univ. Press, Cambridge.
[17] Jain, S. and Neal, R. M. (2004). A split-merge Markov chain Monte Carlo procedure for the Dirichlet process mixture model. J. Comput. Graph. Statist. 13 158-182.
[18] Johnston, A., Robinson, R. A., Gargallo, G., Julliard, R., Jeugd, H. and Baillie, S. R. (2016). Survival of Afro-palaearctic passerine migrants in western Europe and the impacts of seasonal weather variables. Ibis 158 465-480.
[19] Kingman, J. F. C. (1967). Completely random measures. Pacific J. Math. 21 59-78. · Zbl 0155.23503
[20] Kingman, J. F. C. (1993). Poisson Processes. Oxford Studies in Probability 3. The Clarendon Press, Oxford University Press, New York.
[21] MacEachern, S. N. (1999). Dependent nonparametric processes. In ASA Proceedings of the Section on Bayesian Statistical Science 50-5. Amer. Statist. Assoc., Alexandria, Va.
[22] MacKenzie, D. I., Nichols, J. D., Lachman, G. B., Droege, S., Royle, J. A. and Langtimm, C. A. (2002). Estimating site occupancy rates when detection probabilities are less than one. Ecology 83 2248-2255.
[23] Manrique-Vallier, D. (2016). Bayesian population size estimation using Dirichlet process mixtures. Biometrics 72 1246-1254. · Zbl 1390.62046
[24] Matechou, E. and Caron, F. (2017). Modelling individual migration patterns using a Bayesian nonparametric approach for capture-recapture data. Ann. Appl. Stat. 11 21-40. · Zbl 1366.62260
[25] Møller, A. P., Rubolini, D. and Lehikoinen, E. (2008). Populations of migratory bird species that did not show a phenological response to climate change are declining. Proc. Natl. Acad. Sci. USA.
[26] Peach, W., Buckland, S. and Baillie, S. (1996). The use of constant effort mist-netting to measure between-year changes in the abundance and productivity of common passerines. Bird Study 43 142-156.
[27] R Core Team (2014). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
[28] Rasmussen, C. E. (2006). Gaussian Processes in Machine Learning. MIT Press. · Zbl 1177.68165
[29] Robson, D. and Barriocanal, C. (2011). Ecological conditions in wintering and passage areas as determinants of timing of spring migration in trans-saharan migratory birds. J. Anim. Ecol. 80 320-331.
[30] Royle, J. A. (2004a). \(N\)-mixture models for estimating population size from spatially replicated counts. Biometrics 60 108-115. · Zbl 1130.62380
[31] Royle, J. A. (2004b). \(N\)-mixture models for estimating population size from spatially replicated counts. Biometrics 60 108-115. · Zbl 1130.62380
[32] Sethuraman, J. (1994). A constructive definition of Dirichlet priors. Statist. Sinica 4 639-650. · Zbl 0823.62007
[33] Teh, Y. W., Jordan, M. I., Beal, M. J. and Blei, D. M. (2006). Hierarchical Dirichlet processes. J. Amer. Statist. Assoc. 101 1566-1581. · Zbl 1171.62349
[34] Wolpert, R. L. and Ickstadt, K. (1998). Poisson/gamma random field models for spatial statistics. Biometrika 85 251-267. · Zbl 0951.62082
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.