preprint · arXiv (Cornell University) · 2023

Bayesian Boundary Trend Filtering

Takahiro Onizuka, Fumiya Iwashige, Shintaro Hashimoto

Cited by 0Open access

Abstract

Estimating boundary curves has many applications such as economics, climate science, and medicine. Bayesian trend filtering has been developed as one of locally adaptive smoothing methods to estimate the non-stationary trend of data. This paper develops a Bayesian trend filtering for estimating the boundary trend. To this end, the truncated multivariate normal working likelihood and global-local shrinkage priors based on the scale mixtures of normal distribution are introduced. In particular, well-known horseshoe prior for difference leads to locally adaptive shrinkage estimation for boundary trend. However, the full conditional distributions of the Gibbs sampler involve high-dimensional truncated multivariate normal distribution. To overcome the difficulty of sampling, an approximation of truncated multivariate normal distribution is employed. Using the approximation, the proposed models lead to an efficient Gibbs sampling algorithm via the Pólya-Gamma data augmentation. The proposed method is also extended by considering a nearly isotonic constraint. The performance of the proposed method is illustrated through some numerical experiments and real data examples.

Cite this paper

APA 7

Onizuka, T., Iwashige, F., & Hashimoto, S. (2023). Bayesian Boundary Trend Filtering. arXiv (Cornell University). https://doi.org/10.48550/arxiv.2304.11491

MLA 9

Onizuka, Takahiro, et al. “Bayesian Boundary Trend Filtering.” arXiv (Cornell University), 2023, https://doi.org/10.48550/arxiv.2304.11491.

Chicago

Onizuka, Takahiro, Fumiya Iwashige, and Shintaro Hashimoto. 2023. “Bayesian Boundary Trend Filtering.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.2304.11491.

Harvard

Onizuka, T., Iwashige, F. and Hashimoto, S. (2023) ‘Bayesian Boundary Trend Filtering’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.2304.11491.

BibTeX

@misc{onizuka2023bayesian,
  title = {{Bayesian Boundary Trend Filtering}},
  author = {Onizuka, Takahiro and Iwashige, Fumiya and Hashimoto, Shintaro},
  journal = {arXiv (Cornell University)},
  year = {2023},
  doi = {10.48550/arxiv.2304.11491}
}

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