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Multivariate Density Estimation by Bayesian Sequential Partitioning

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  • Luo Lu
  • Hui Jiang
  • Wing H. Wong

Abstract

Consider a class of densities that are piecewise constant functions over partitions of the sample space defined by sequential coordinate partitioning. We introduce a prior distribution for a density in this function class and derive in closed form the marginal posterior distribution of the corresponding partition. A computationally efficient method, based on sequential importance sampling, is presented for the inference of the partition from this posterior distribution. Compared to traditional approaches such as the kernel method or the histogram, the Bayesian sequential partitioning (BSP) method proposed here is capable of providing much more accurate estimates when the sample space is of moderate to high dimension. We illustrate this by simulated as well as real data examples. The examples also demonstrate how BSP can be used to design new classification methods competitive with the state of the art.

Suggested Citation

  • Luo Lu & Hui Jiang & Wing H. Wong, 2013. "Multivariate Density Estimation by Bayesian Sequential Partitioning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1402-1410, December.
  • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:504:p:1402-1410
    DOI: 10.1080/01621459.2013.813389
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    Cited by:

    1. Kirschenmann, T.H. & Damien, P. & Walker, S.G., 2015. "A note on the e–a histogram," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 105-109.
    2. Mammen, Enno & Martínez Miranda, María Dolores & Nielsen, Jens Perch, 2015. "In-sample forecasting applied to reserving and mesothelioma mortality," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 76-86.
    3. Ye Henry Li & Dangna Li & Nikolay Samusik & Xiaowei Wang & Leying Guan & Garry P Nolan & Wing Hung Wong, 2017. "Scalable multi-sample single-cell data analysis by Partition-Assisted Clustering and Multiple Alignments of Networks," PLOS Computational Biology, Public Library of Science, vol. 13(12), pages 1-37, December.

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