[kalman_2] Update code and descriptions#907
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Pull request overview
This PR updates the kalman_2 lecture to better align the math, narrative timing, and code implementation of the Kalman filter with the intended worker model, addressing clarifications raised in issue #904.
Changes:
- Aligns the observation equation with the text by setting the measurement matrix to exclude direct dependence on effort (
G = [g, 0]) and clarifies independence/initial-belief variance vs. standard deviation notation. - Reorders Kalman-filter bookkeeping to record beliefs before incorporating the current observation (consistent with conditioning on (y^{t-1})), and adjusts arrays/loop indexing accordingly.
- Improves figure metadata/captions and narrative explanations around simulation initial conditions and learning experiments.
Co-authored-by: Copilot Autofix powered by AI <175728472+Copilot@users.noreply.github.com>
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Hi @longye-tian, I think this is ready to be merged. Please let me know if there is anything else you would like to add! |
| In particular, we want to compute all of the objects in an "innovation representation". | ||
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| ## An Innovations Representation | ||
| ## An innovations representation |
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Maybe here we should use An innovation representation or An innovation's representation.
What do you think?
Best,
Longye
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Many thanks @longye-tian! Innovations representation is a standard term in timeseries analysis (I know it is a bit strange!)
(See e.g., https://www.stat.berkeley.edu/~bartlett/courses/153-fall2010/lectures/10.pdf)
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Thanks @HumphreyYang!
I see, shall we use the term The innovations representation instead of An innovations representation to match your referenced document?
Best,
Longye
| ax[0].set_title(r'$\mathbb{E}[y_t]$ over time') | ||
| ax[0].set_xlabel('time') | ||
| ax[0].set_ylabel(r'$\mathbb{E}[y_t| y^{t-1}]$') | ||
| ax[0].set_title(r'$\mathbb{E}[y_t| y^{t-1}]$ over time') |
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According to the style guide qe-fig-003 No matplotlib embedded titles, should we delete the title and descibe those figures inline?
Best,
Longye
| axs[i].set_title(f'Time Step {t+1}') | ||
| axs[i].set_xlabel(r'$h_{{{}}}$'.format(str(t+1))) | ||
| axs[i].set_ylabel(r'$u_{{{}}}$'.format(str(t+1))) | ||
| axs[i].set_title(f'Time Step {t}') |
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same stye guide comment here
longye-tian
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Many thanks @HumphreyYang !
They all looks good to me. Just some minor comments see above.
Best,
Longye
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Many thanks @longye-tian for the detailed check! I left out those two cases intentionally. Personally, I think it would be a bit unclear if we don’t use subplot titles for figures with multiple subplots. For instance, if we remove the Please let me know what you think between those two cases! If this makes sense, I can update the style guide accordingly (CC @mmcky and @jstac)! Without subplot titles: With subplot titles: |
This PR closes #904 and makes a few improvements beyond it.
Hi @longye-tian, this PR resolves #904, and thanks for raising those issues!