Convergence of Limiting Cases of Continuous-Time, Discrete-Space Jump Processes to Diffusion Processes for Bayesian Inference
Jump-diffusion algorithms are applied to sampling from Bayesian posterior distributions. We consider a class of random sampling algorithms based on continuous-time jump processes. The semigroup theory of random processes lets us show that limiting cases of certain jump processes acting on discretize...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-03-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/7/1084 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849739049841983488 |
|---|---|
| author | Aaron Lanterman |
| author_facet | Aaron Lanterman |
| author_sort | Aaron Lanterman |
| collection | DOAJ |
| description | Jump-diffusion algorithms are applied to sampling from Bayesian posterior distributions. We consider a class of random sampling algorithms based on continuous-time jump processes. The semigroup theory of random processes lets us show that limiting cases of certain jump processes acting on discretized spaces converge to diffusion processes as the discretization is refined. One of these processes leads to the familiar Langevin diffusion equation; another leads to an entirely new diffusion equation. |
| format | Article |
| id | doaj-art-022a07db8c334a94aa51fc76d9b51df2 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-022a07db8c334a94aa51fc76d9b51df22025-08-20T03:06:24ZengMDPI AGMathematics2227-73902025-03-01137108410.3390/math13071084Convergence of Limiting Cases of Continuous-Time, Discrete-Space Jump Processes to Diffusion Processes for Bayesian InferenceAaron Lanterman0School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USAJump-diffusion algorithms are applied to sampling from Bayesian posterior distributions. We consider a class of random sampling algorithms based on continuous-time jump processes. The semigroup theory of random processes lets us show that limiting cases of certain jump processes acting on discretized spaces converge to diffusion processes as the discretization is refined. One of these processes leads to the familiar Langevin diffusion equation; another leads to an entirely new diffusion equation.https://www.mdpi.com/2227-7390/13/7/1084Markov chain Monte CarloMetropolis–HastingsGibbs samplingpattern theory |
| spellingShingle | Aaron Lanterman Convergence of Limiting Cases of Continuous-Time, Discrete-Space Jump Processes to Diffusion Processes for Bayesian Inference Mathematics Markov chain Monte Carlo Metropolis–Hastings Gibbs sampling pattern theory |
| title | Convergence of Limiting Cases of Continuous-Time, Discrete-Space Jump Processes to Diffusion Processes for Bayesian Inference |
| title_full | Convergence of Limiting Cases of Continuous-Time, Discrete-Space Jump Processes to Diffusion Processes for Bayesian Inference |
| title_fullStr | Convergence of Limiting Cases of Continuous-Time, Discrete-Space Jump Processes to Diffusion Processes for Bayesian Inference |
| title_full_unstemmed | Convergence of Limiting Cases of Continuous-Time, Discrete-Space Jump Processes to Diffusion Processes for Bayesian Inference |
| title_short | Convergence of Limiting Cases of Continuous-Time, Discrete-Space Jump Processes to Diffusion Processes for Bayesian Inference |
| title_sort | convergence of limiting cases of continuous time discrete space jump processes to diffusion processes for bayesian inference |
| topic | Markov chain Monte Carlo Metropolis–Hastings Gibbs sampling pattern theory |
| url | https://www.mdpi.com/2227-7390/13/7/1084 |
| work_keys_str_mv | AT aaronlanterman convergenceoflimitingcasesofcontinuoustimediscretespacejumpprocessestodiffusionprocessesforbayesianinference |