Rendering Documentation with Jupytext + Myst-NB

Math Test

Let’s put some math here: \(e = mc^2\), and also

\[\begin{split} \begin{aligned} x^2 + y^2 & = 1 \\ x & = \cos(t) \\ y & = \sin(t). \end{aligned} \end{split}\]

Now let’s try a macro and an equation reference:

(1)\[ y_i = \xx_i'\bbe + \varepsilon_i. \]

If it works we should get (1).

Code Test

import numpy as np
x = np.array([1., 2., 3.])
x

array([1., 2., 3.])

Cross-Referencing Test

A review of particle filters is provided in Doucet and Johansen [3], but it does not discuss score and hessian calculations [5]. In addition, please see code.

References

1: Olivier Cappé and Eric Moulines. On the use of particle filtering for maximum likelihood parameter estimation. In 13th European Signal Processing Conference, 1–4. 2005.
2: Adrien Corenflos, James Thornton, George Deligiannidis, and Arnaud Doucet. Differentiable particle filtering via entropy-regularized optimal transport. In Marina Meila and Tong Zhang, editors, Proceedings of the 38th international conference on machine learning, volume 139 of Proceedings of machine learning research, 2100–2111. PMLR, 2021. URL: https://proceedings.mlr.press/v139/corenflos21a.html.
3: Arnaud Doucet and Adam M. Johansen. A tutorial on particle filtering and smoothing: Fifteen years later. In D. Crisan and B. Rozovsky, editors, Handbook of Nonlinear Filtering. Cambridge University Press, Cambridge, 2009.
4: N.J. Gordon, D.J. Salmond, and A.F.M. Smith. Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proceedings-F, 140(2):107–113, 1993. URL: https://digital-library.theiet.org/content/journals/10.1049/ip-f-2.1993.0015, doi:10.1049/ip-f-2.1993.0015.
5: G. Poyiadjis, A. Doucet, and S. S. Singh. Particle approximations of the score and observed information matrix in state space models with application to parameter estimation. Biometrika, 98(1):65–80, 2011. URL: https://academic.oup.com/biomet/article-lookup/doi/10.1093/biomet/asq062, doi:10.1093/biomet/asq062.