1,199
Views
8
CrossRef citations to date
0
Altmetric
Theory and Methods

A Common Atoms Model for the Bayesian Nonparametric Analysis of Nested Data

ORCID Icon, ORCID Icon, ORCID Icon & ORCID Icon
Pages 405-416 | Received 13 Aug 2020, Accepted 19 May 2021, Published online: 14 Jul 2021

References

  • Bandyopadhyay, D., and Canale, A. (2016), “Non-Parametric Spatial Models for Clustered Ordered Periodontal Data,” Journal of the Royal Statistical Society, Series C, 65, 619–640. DOI: 10.1111/rssc.12150.
  • Banerjee, A., Murray, J., and Dunson, D. B. (2013), “Bayesian Learning of Joint Distributions of Objects,” Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, 1–9.
  • Barrientos, A. F., Jara, A., and Quintana, F. A. (2012), “On the Support of MacEachern’s Dependent Dirichlet Processes and Extensions,” Bayesian Analysis, 7, 277–310. DOI: 10.1214/12-BA709.
  • Beraha, M., Guglielmi, A., and Quintana, F. A. (2020), “The Semi-Hierarchical Dirichlet Process and Its Application to Clustering Homogeneous Distributions,” arXiv no. arXiv:2005.10287.
  • Camerlenghi, F., Dunson, D. B., Lijoi, A., Prünster, I., and Rodríguez, A. (2019a), “Latent Nested Nonparametric Priors” (with discussion), Bayesian Analysis, 14, 1303–1356. DOI: 10.1214/19-BA1169.
  • Camerlenghi, F., Lijoi, A., Orbanz, P., and Prünster, I. (2019b), “Distribution Theory for Hierarchical Processes,” The Annals of Statistics, 47, 67–92. DOI: 10.1214/17-AOS1678.
  • Canale, A., and Dunson, D. B. (2011), “Bayesian Kernel Mixtures for Counts,” Journal of the American Statistical Association, 106, 1529–1539. DOI: 10.1198/jasa.2011.tm10552.
  • Canale, A., and Prünster, I. (2017), “Robustifying Bayesian Nonparametric Mixtures for Count Data,” Biometrics, 73, 174–184. DOI: 10.1111/biom.12538.
  • Escobar, M. D., and West, M. (1995), “Bayesian Density Estimation and Inference Using Mixtures,” Journal of the American Statistical Association, 90, 577–588. DOI: 10.1080/01621459.1995.10476550.
  • Ewens, W. J. (1972), “The Sampling Theory of Selectively Neutral Alleles,” Theoretical Population Biology, 3, 87–112. DOI: 10.1016/0040-5809(72)90035-4.
  • Ferguson, T. S. (1983), “Bayesian Density Estimation by Mixtures of Normal Distributions,” Recent Advances in Statistics, 24, 287–303.
  • Graf, D., Di Cagno, R., Fåk, F., Flint, H. J., Nyman, M., Saarela, M., and Watzl, B. (2015), “Contribution of Diet to the Composition of the Human Gut Microbiota,” Microbial Ecology in Health & Disease, 26, 26164.
  • Graziani, R., Guindani, M., and Thall, P. F. (2015), “Bayesian Nonparametric Estimation of Targeted Agent Effects on Biomarker Change to Predict Clinical Outcome,” Biometrics, 71, 188–197. DOI: 10.1111/biom.12250.
  • Hatjispyros, S. J., Nicoleris, T., and Walker, S. G. (2016), “Random Density Functions With Common Atoms and Pairwise Dependence,” Computational Statistics and Data Analysis, 101, 236–249. DOI: 10.1016/j.csda.2016.03.008.
  • Horn, R. A., Johnson, C. R., Horn, R. A., and Johnson, C. R. (2013), “Norms for Vectors and Matrices,” in Matrix Analysis, 313–386.
  • Hubert, L., and Arabie, P. (1985), “Comparing Partitions,” Journal of Classification, 2, 193–218. DOI: 10.1007/BF01908075.
  • Ishwaran, H., and James, L. F. (2001), “Gibbs Sampling Methods for Stick-Breaking Priors,” Journal of the American Statistical Association, 96, 161–173. DOI: 10.1198/016214501750332758.
  • Jovel, J., Patterson, J., Wang, W., Hotte, N., O’Keefe, S., Mitchel, T., Perry, T., Kao, D., Mason, A. L., Madsen, K. L., and Wong, G. K.-S. (2016), “Characterization of the Gut Microbiome Using 16S or Shotgun Metagenomics,” Frontiers in Microbiology, 7, 459. DOI: 10.3389/fmicb.2016.00459.
  • Kalli, M., Griffin, J. E., and Walker, S. G. (2011), “Slice Sampling Mixture Models,” Statistics and Computing, 21, 93–105. DOI: 10.1007/s11222-009-9150-y.
  • Kaul, A., Mandal, S., Davidov, O., and Peddada, S. D. (2017), “Analysis of Microbiome Data in the Presence of Excess Zeros,” Frontiers in Microbiology, 8. DOI: 10.3389/fmicb.2017.02114.
  • Lo, A. Y. (1984), “On a Class of Bayesian Nonparametric Estimates: I. Density Estimates,” The Annals of Statistics, 12, 351–357. DOI: 10.1214/aos/1176346412.
  • MacEachern, S. N. (2000), “Dependent Dirichlet Processes,” Technical Report, Department of Statistics, The Ohio State University.
  • Mao, J., Chen, Y., and Ma, L. (2020). Bayesian Graphical Compositional Regression for Microbiome Data,” Journal of the American Statistical Association, 115, 610–624. DOI: 10.1080/01621459.2019.1647212.
  • McMurdie, P. J., and Holmes, S. (2014), “Waste Not, Want Not: Why Rarefying Microbiome Data Is Inadmissible,” PLoS Computational Biology, 10, e1003531. DOI: 10.1371/journal.pcbi.1003531.
  • Meilúa, M. (2007), “Comparing Clusterings — An Information Based Distance,” Journal of Multivariate Analysis, 98, 873–895.
  • O’Keefe, S. J., Li, J. V., Lahti, L., Ou, J., Carbonero, F., Mohammed, K., Posma, J. M., Kinross, J., Wahl, E., Ruder, E., Vipperla, K., Naidoo, V., Mtshali, L., Tims, S., Puylaert, P. G., Delany, J., Krasinskas, A., Benefiel, A. C., Kaseb, H. O., Newton, K., Nicholson, J. K., De Vos, W. M., Gaskins, H. R., and Zoetendal, E. G. (2015), “Fat, Fibre and Cancer Risk in African Americans and Rural Africans,” Nature Communications, 6. DOI: 10.1038/ncomms7342.
  • Paisley, J., Wang, C., Blei, D. M., and Jordan, M. I. (2015), “Nested Hierarchical Dirichlet Processes,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 37, 256–270. DOI: 10.1109/TPAMI.2014.2318728.
  • Pitman, J. (1995), “Exchangeable and Partially Exchangeable Random Partitions,” Probability Theory and Related Fields, 102, 145–158. DOI: 10.1007/BF01213386.
  • Porteous, I., Ihler, A., Smyth, P., and Welling, M. (2006), “Gibbs Sampling for (Coupled) Infinite Mixture Models in the Stick-Breaking Representation,” Proceedings of UAI, 22, 385–392.
  • Preda, M., Popa, M. I., Mihai, M. M., Oţelea, T. C., and Holban, A. M. (2019), “Effects of Coffee on Intestinal Microbiota, Immunity, and Disease,” in Caffeinated and Cocoa Based Beverages, eds. Alexandru Mihai Grumezescu and Alina Maria Holban, Woodhead Publishing, pp. 391–421. DOI: 10.1016/B978-0-12-815864-7.00012-X.
  • Rodriguez, A., and Dunson, D. B. (2014), “Functional Clustering in Nested Designs: Modeling Variability in Reproductive Epidemiology Studies,” Annals of Applied Statistics, 8, 1416–1442.
  • Rodríguez, A., Dunson, D. B., and Gelfand, A. E. (2008), “The Nested Dirichlet Process,” Journal of the American Statistical Association, 103, 1131–1144. DOI: 10.1198/016214508000000553.
  • Sethuraman, A. J. (1994), “A Constructive Definition of Dirichlet Priors,” Statistica Sinica, 4, 639–650.
  • Shannon, C. E. (1948), “A Mathematical Theory of Communication,” The Bell System Technical Journal, 27, 379–423. DOI: 10.1002/j.1538-7305.1948.tb01338.x.
  • Teh, Y. W., Jordan, M. I., Beal, M. J., and Blei, D. M. (2006), “Hierarchical Dirichlet Processes,” Journal of the American Statistical Association, 101, 1566–1581. DOI: 10.1198/016214506000000302.
  • Tekumalla, L. S., Agrawal, P., and Bhattacharya, I. (2015), “Nested Hierarchical Dirichlet Processes for Multi-Level Non-Parametric Admixture Modeling. Arxiv no. arXiv no. 1508.06446.
  • Wade, S., and Ghahramani, Z. (2018), “Bayesian Cluster Analysis: Point Estimation and Credible Balls” (with discussion), Bayesian Analysis, 13, 559–626. DOI: 10.1214/17-BA1073.
  • Walker, S. G. (2007), “Sampling the Dirichlet Mixture Model With Slices. Communications in Statistics: Simulation and Computation, 36, 45–54. DOI: 10.1080/03610910601096262.
  • Whittaker, R. H. (2006). Vegetation of the Siskiyou Mountains, Oregon and California. Ecological Monographs, 30, 279–338. DOI: 10.2307/1943563.
  • Zuanetti, D. A., Müller, P., Zhu, Y., Yang, S., and Ji, Y. (2018), “Clustering Distributions with the Marginalized Nested Dirichlet Process,” Biometrics, 74, 584–594. DOI: 10.1111/biom.12778.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.