implement blocked gibbs sampling for Bayesian inference in linear Gaussian SSM using JSL

[murphyk]

Implement blocked gibbs sampling for Bayesian inference in linear Gaussian SSM .
In the "E step", use the Jax SSM library for forwards-filtering backwards-sampling.
In the "M step", sample from the parameter posteriors assuming conjugate priors.

Some details can be found in this paper
A. Wills, T. B. Schön, F. Lindsten, and B. Ninness, “Estimation of Linear Systems using a Gibbs Sampler,” IFAC proc. vol., vol. 45, no. 16, pp. 203–208, Jul. 2012, doi: 10.3182/20120711-3-be-2027.00297. [Online]. Available: https://linkinghub.elsevier.com/retrieve/pii/S1474667015379520

[calvintanama]

Hi, can I work on this one?

[murphyk]

Hi @calvintanama . Sure, please feel free to work on this.
See sec 12.3.7 of vol 2 for some details.
Note: you need to solve #678 first!

[murphyk]

See the PySSM library for relevant code.
Please try to replicate some of their examples.

[calvintanama]

Hi @murphyk. Since you have mentioned, that I need to solve #678 first, should I make separate PR for #678 and this issue and work on that one first?

[murphyk]

On Thu, Mar 10, 2022 at 9:09 PM calvintanama ***@***.***> wrote: Hi @murphyk <https://github.com/murphyk>. Since you have mentioned, that I need to solve #678 <#678> first, should I make separate PR for #678 <#678> and this issue and work on that one first?

Yes

[murphyk]

Concretely the goal should be to replicate the functionality and examples of this paper

C. Strickland, R. Burdett, K. Mengersen, and R. Denham, “PySSM: A Python Module for Bayesian Inference of Linear Gaussian State Space Models,” J. Stat. Softw., vol. 57, pp. 1–37, Apr. 2014, doi: 10.18637/jss.v057.i06. [Online]. Available: https://www.jstatsoft.org/article/view/v057i06. [Accessed: Mar. 11, 2022]

[murphyk]

See also

@misc{helske2021bssm,
title={bssm: Bayesian Inference of Non-linear and Non-Gaussian State Space Models in R},
author={Jouni Helske and Matti Vihola},
year={2021},
url={https://arxiv.org/abs/2101.08492},
eprint={2101.08492},
archivePrefix={arXiv},
primaryClass={stat.CO}
}

[calvintanama]

Hi @murphyk thanks for the literature! For the issue #678 I tried to implement Durbin-Koopman sampling from [1] (https://www.jstor.org/stable/4140605) using modification of Jarociński [2] (https://www.sciencedirect.com/science/article/pii/S0167947315001176?via%3Dihub#tb000005). I made an assumption, that the matrix R_t in [1] is identity matrix because in the current implementation of LDS it is not needed to specify one.
I tried to test my implementation using LGSSM from TensorFlow Probability as you have mentioned, but somehow I can not get the equivalent LGSSM object of LDS (.sample() method resulting different numbers). Here is my code https://colab.research.google.com/drive/1NgA8-7qDviN-ID-PtWqL0jIPjNKBdhXQ?usp=sharing
My questions:

1. Am I going into expected direction?
2. How should I handle PRNG?

[xinglong-li]

I've completed issue #678 and I'd like to continue work on this series of tasks ;)

[murphyk]

Hi @xinglong-li Yes, please go for it. If you use conjugate priors, it should be easy to do (as you know :)