Adaptive Bayesian Nonparametric Regression via Stationary Smoothness Priors
A procedure for Bayesian nonparametric regression is described that automatically adjusts the degree of smoothing as the curvature of the underlying function changes. Relative to previous work adopting a similar approach that either employs a single global smoothing parameter or assumes that the smo...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-03-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/7/1162 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850184546497069056 |
|---|---|
| author | Justin L. Tobias |
| author_facet | Justin L. Tobias |
| author_sort | Justin L. Tobias |
| collection | DOAJ |
| description | A procedure for Bayesian nonparametric regression is described that automatically adjusts the degree of smoothing as the curvature of the underlying function changes. Relative to previous work adopting a similar approach that either employs a single global smoothing parameter or assumes that the smoothing process follows a random walk, the model considered here permits adaptive smoothing and imposes stationarity in the autoregressive smoothing process. An efficient Markov Chain Monte Carlo (MCMC) scheme for model estimation is fully described for this stationary case, and the performance of the method is illustrated in several generated data experiments. An application is also provided, analyzing the relationship between behavioral problems in students and academic achievement. Point estimates from the nonparametric methods suggest (a) expected achievement declines monotonically with a behavioral problems index (BPI) score and (b) the rate of decline is relatively flat at the left tail of the BPI distribution and then becomes sharply more negative. |
| format | Article |
| id | doaj-art-694127f29b3f4237a82a345159f0d2bb |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-694127f29b3f4237a82a345159f0d2bb2025-08-20T02:17:00ZengMDPI AGMathematics2227-73902025-03-01137116210.3390/math13071162Adaptive Bayesian Nonparametric Regression via Stationary Smoothness PriorsJustin L. Tobias0Economics Department, Purdue University, West Lafayette, IN 47907, USAA procedure for Bayesian nonparametric regression is described that automatically adjusts the degree of smoothing as the curvature of the underlying function changes. Relative to previous work adopting a similar approach that either employs a single global smoothing parameter or assumes that the smoothing process follows a random walk, the model considered here permits adaptive smoothing and imposes stationarity in the autoregressive smoothing process. An efficient Markov Chain Monte Carlo (MCMC) scheme for model estimation is fully described for this stationary case, and the performance of the method is illustrated in several generated data experiments. An application is also provided, analyzing the relationship between behavioral problems in students and academic achievement. Point estimates from the nonparametric methods suggest (a) expected achievement declines monotonically with a behavioral problems index (BPI) score and (b) the rate of decline is relatively flat at the left tail of the BPI distribution and then becomes sharply more negative.https://www.mdpi.com/2227-7390/13/7/1162BayesianMCMCnonparametric regression |
| spellingShingle | Justin L. Tobias Adaptive Bayesian Nonparametric Regression via Stationary Smoothness Priors Mathematics Bayesian MCMC nonparametric regression |
| title | Adaptive Bayesian Nonparametric Regression via Stationary Smoothness Priors |
| title_full | Adaptive Bayesian Nonparametric Regression via Stationary Smoothness Priors |
| title_fullStr | Adaptive Bayesian Nonparametric Regression via Stationary Smoothness Priors |
| title_full_unstemmed | Adaptive Bayesian Nonparametric Regression via Stationary Smoothness Priors |
| title_short | Adaptive Bayesian Nonparametric Regression via Stationary Smoothness Priors |
| title_sort | adaptive bayesian nonparametric regression via stationary smoothness priors |
| topic | Bayesian MCMC nonparametric regression |
| url | https://www.mdpi.com/2227-7390/13/7/1162 |
| work_keys_str_mv | AT justinltobias adaptivebayesiannonparametricregressionviastationarysmoothnesspriors |