Kernel distributions
Bactrian operators sample from a kernel distribution from which a proposal is created.
The following kernel distributions are currently implemented, many of them propossed in Yang & Rodríguez (2013) and Thawornwattana et al (2018).
| Name | Distribution | Bactrian? |
|---|---|---|
| uniform | uniform distribution | no |
| normal | normal distribution | no |
| laplace | Laplace distribution | no |
| t4 | T-distribution with 4 degrees of freedom | no |
| cauchy | Cauchy distribution | no |
| bactrian_normal | normal distribution | yes |
| bactrian_laplace | Laplace distribution | yes |
| bactrian_triangle | triangle shaped distribution | yes |
| bactrian_uniform | uniform distribution | yes |
| bactrian_t4 | T-distribution with 4 degrees of freedom | yes |
| bactrian_cauchy | Cauchy distribution | yes |
| bactrian_box | box-shaped distribution | yes |
| bactrian_airplane | airplane distribution | yes |
| bactrian_strawhat | strawhat distribution | yes |
The default kernel distribution is the Bactrian normal distribution. This seems to perform well for a wide range of cases (see also BEAST 2 benchmark). So, there does not seem a compelling reason to switch – let me know if you know any.
References
Yang Z, Rodríguez CE. Searching for efficient Markov chain Monte Carlo proposal kernels. Proceedings of the National Academy of Sciences. 2013 Nov 26;110(48):19307-12. doi: 10.1073/pnas.1311790110).
Thawornwattana Y, Dalquen D, Yang Z. Designing simple and efficient Markov chain Monte Carlo proposal kernels. Bayesian Analysis. 2018;13(4):1037-63. doi: 10.1214/17-BA1084,