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Log Riemann Zeta plus Zipf distribution #28
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I would also appreciate being able to evaluate the zeta function in Stan because I am trying to fit a piecewise distribution and it is needed to ensure smoothness at the breakpoint. Is there any way I can do this?
- Stan needs to wrap it from Boost http://www.boost.org/doc/libs/1_66_0/libs/math/doc/html/math_toolkit/zetas/zeta.html…On Tue, Feb 20, 2018 at 11:25 AM, Quentin Read ***@***.***> wrote: I would also appreciate being able to evaluate the zeta function in Stan because I am trying to fit a piecewise distribution and it is needed to ensure smoothness at the breakpoint. Is there any way I can do this? — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#28 (comment)>, or mute the thread <https://github.com/notifications/unsubscribe-auth/ADOrqtgi7MHBu-NVtO78-gDTn2M4RkzSks5tWvIVgaJpZM4FTDfv> .
Looks like someone conveniently worked out the form of the derivative:
https://proofwiki.org/wiki/Derivative_of_Riemann_Zeta_Function
If you try to just use the templated form from Boost, it'll autodiff their iterative definition of
zetarather than implementing the approximate autodiff. The latter's usually more stable, though we've gotten many workable results from the former.Reacted by Luiz Max Carvalho
From @bob-carpenter on February 12, 2014 18:9
It'd be nice to have the Zipf distribution in Stan:
See: http://mathworld.wolfram.com/ZipfDistribution.html
The pmf is involves the Riemann zeta function, which is available from Boost:
http://www.boost.org/doc/libs/1_55_0/libs/math/doc/html/math_toolkit/zetas/zeta.html
so we could add it directly with auto-diff. But auto-diffing these numerical
approximations to functions isn't ideal.
Plus, we really need
log_zetafor Stan, and then we'd want a direct schemefor evaluating both
and
See also, this paper by Choudhury (1995), which is what the Mathworld page cites: https://www.jstor.org/stable/52768?seq=1#page_scan_tab_contents
Copied from original issue: stan-dev/stan#551