Paper: Charles Lindsey Bayesian Statistics SciPy paper 2023

[cdlindsey]

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[cdlindsey]

I added some more python code snippets that should be instructive.

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[jderekito]

Hello, Please let me know if there is anything further needed on my part. Thank you Derek

On Tue, Jun 27, 2023 at 5:04 PM Charles David Lindsey < @.***> wrote:

@.**** commented on this pull request.

In papers/charles_lindsey/bayes_noresample.rst https://github.com/scipy-conference/scipy_proceedings/pull/832#discussion_r1244417130 :

+ +With these assumptions, as the sample size :math:n\to\infty the quadratic approximation for :math:\log \pi(\boldsymbol{\theta}\vert {\bf x}) becomes more accurate. At the posterior mode :math:{\boldsymbol \theta}={\widehat{\boldsymbol \theta}}, :math:\log \pi(\boldsymbol{\theta}\vert {\bf x}) is maximized and :math:0=S({\boldsymbol \theta})\vert_{{\boldsymbol \theta}={\widehat{\boldsymbol \theta}}}. + +Given this, we can exponentiate the approximation to get + +.. math:: +

• \pi(\boldsymbol{\theta}\vert {\bf x}) \approx \pi(\widehat{\boldsymbol \theta}\vert{\bf x}) \exp(\frac{1}{2} (\boldsymbol{\theta} - \widehat{\boldsymbol \theta} )^T H(\widehat{\boldsymbol \theta}) (\boldsymbol{\theta} - \widehat{\boldsymbol \theta} ))

• +So for large :math:n, the posterior distribution of :math:{\boldsymbol \theta} is approximately proportional to a multivariate normal density with mean :math:\widehat{\boldsymbol{\theta}} and covariance :math:-H(\widehat{\boldsymbol{\theta}})^{-1}.

• +.. math::

• {\boldsymbol \theta} \vert x \approx_D N(\widehat{\boldsymbol{\theta}}, -H(\widehat{\boldsymbol{\theta}})^{-1})

• +Another caveat for this result is that the prior should be proper, or at least lead to a proper posterior. Our asymptotic results are depending on probabilities integrating to 1.

Yes. I just added a sentence.

— Reply to this email directly, view it on GitHub https://github.com/scipy-conference/scipy_proceedings/pull/832#discussion_r1244417130, or unsubscribe https://github.com/notifications/unsubscribe-auth/ABJIIQVQZTFRZFO4S3XXFGTXNNKGBANCNFSM6AAAAAAYZDEPRQ . You are receiving this because you were mentioned.Message ID: @.***>

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Reference check summary (note 'MISSING' DOIs are suggestions that need verification):

OK DOIs

- 10.1080/00031305.1992.10475842 is OK
- 10.1038/s41586-020-2649-2 is OK
- 10.1038/s41592-019-0686-2 is OK
- 10.2307/2286009 is OK

MISSING DOIs

- 10.4135/9781412961288.n455 may be a valid DOI for title: Teoria statistica delle classi e calcolo delle probabilita
- 10.1002/9781118723203 may be a valid DOI for title: Practical Methods of Optimization
- 10.25080/majora-92bf1922-011 may be a valid DOI for title: statsmodels: Econometric and statistical modeling with python

INVALID DOIs

- None

[cbcunc]

@cdlindsey would you please address the missing DOIs above?

[jderekito]

@jderekito does this paper have your final review approval?

@cdlindsey I can see the revisions, and it looks good to me. Thanks for letting me help out.

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[deniederhut]

@scoobies check references

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Reference check summary (note 'MISSING' DOIs are suggestions that need verification):

OK DOIs

- 10.1080/00031305.1992.10475842 is OK
- 10.1038/s41586-020-2649-2 is OK
- 10.1038/s41592-019-0686-2 is OK
- 10.2307/2286009 is OK

MISSING DOIs

- 10.4135/9781412961288.n455 may be a valid DOI for title: Teoria statistica delle classi e calcolo delle probabilita
- 10.1002/9781118723203 may be a valid DOI for title: Practical Methods of Optimization
- 10.25080/majora-92bf1922-011 may be a valid DOI for title: statsmodels: Econometric and statistical modeling with python

INVALID DOIs

- None