Multivariate density estimation by Bayesian sequential partitioning and its applications
Abstract/Contents
- Abstract
- Consider a class of densities which 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 and data compression methods competitive with or even superior to the state of the art. For the data compression application, we use sequence data of format FASTQ from human chromosome 21 and validate the performance of our method on both lossless and lossy compression.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2013 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Lu, Luo |
|---|---|
| Associated with | Stanford University, Department of Statistics. |
| Primary advisor | Wong, Wing Hung |
| Thesis advisor | Wong, Wing Hung |
| Thesis advisor | Hastie, Trevor |
| Thesis advisor | Walther, Guenther |
| Advisor | Hastie, Trevor |
| Advisor | Walther, Guenther |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Luo Lu. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2013. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2013 by Luo Lu
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