Issue/873 embedded laplace#874
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| The Laplace approximation is especially useful if $p(\theta)$ is | ||
| multivariate normal and $p(y \mid \phi, \theta)$ is | ||
| log-concave. Stan's embedded Laplace approximation is restricted to | ||
| have multivariate normal prior $p(\theta)$ and ... likelihood |
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add here the restrictions for the likelihood
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There are two kinds of restrictions:
- what the user can do without breaking Stan, i.e. the operations in the likelihood need to support higher-order autodiff.
- what the user should do to insure the approximation is reliable.
I'll assume you have the first in mind.
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Yes, I was thinking the first as a restriction. For the second one we can say which kind of likelihood are more likely to work, ie, log concave and maybe near log concave
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I made some edits to use the statistical terms correctly. In the end of first section, it would be good to tell the constraints on the likelihood function and I left there three dots. |
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@charlesm93 I started to fill in some of the boilerplate we have in our functions reference. Those comments and things are actually useful for building the index page |
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@WardBrian In the doc, what are the |
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The unnormalized versions, which correspond to propto=true in the C++. For these functions they may be equivalent, but for technical reasons they still need to exist. If they don’t do anything we could remove the documentation, but it would be less consistent with others then |
| <!-- real; laplace_marginal; (function ll_function, tuple(...), vector theta0, function K_function, tuple(...)); --> | ||
| \index{{\tt \bfseries laplace\_marginal }!{\tt (function ll\_function, tuple(...), vector theta0, function K\_function, tuple(...)): real}|hyperpage} | ||
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| `real` **`laplace_marginal`**`(function ll_function, tuple(...), vector theta0, function K_function, tuple(...))`<br>\newline |
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Can we call theta0 theta_init? I just think it sounds more clear
| * `hessian_block_size`: the size of the blocks, assuming the Hessian | ||
| $\partial \log p(y \mid \theta, phi) \ \partial \theta$ is block-diagonal. | ||
| The structure of the Hessian is determined by the dependence structure of $y$ | ||
| on $\theta$. By default, the Hessian is treated as diagonal |
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We should note where that if Hessian block size is not 1 or N then theta needs to be divisible by the Hessian block size
| ``` | ||
| matrix K_function(...) | ||
| ``` | ||
| There is no type restrictions for the variadic arguments. The variables $\phi$ |
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I think moreso from the section it's not clear how this is related to the k function
| The only restriction is that this function returns a positive-definite matrix | ||
| with size $n \times n$ where $n$ is the size of $\theta$. The signature is: | ||
| ``` | ||
| matrix K_function(...) |
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Can we call this covariance_function?
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does the pdf build? I had to go through the file and change the |
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how do I add the section on the embedded Laplace approximation in the reference manual? I made edits to |
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@charlesm93 that is the correct place to add it for it to show up in the pdf, you should separately add it to the _quarto.yml in the folder above |
…ev/docs into issue/873-embeddedLaplace
…tional and (ii) helper functions allow for a prior mean.
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I updated the docs to reflect two ongoing changes:
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@charlesm93 I have a few changes here if you want to merge them. I mostly updated some wording and added the tuple for the laplace options |
| differentiation (AD). Most functions in Stan support higher-order AD. | ||
| The exceptions are functions with specialized calls for reverse-mode AD, and | ||
| these are higher-order functions (algebraic solvers, differential equation | ||
| solvers, and integrators), the marginalization function for hidden Markov |
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Based on the discussion in issue stan-dev/math#3280, at least integrate_1d should work (Steve is fixing this)
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Just as a reminder for @charlesm93 @avehtari @SteveBronder: The next release is scheduled for approximately one month away (will likely be May 11th or May 18th). It would be great to finish this API documentation and provide at least one runnable case study! |
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@charlesm93 I merged this! I think it looks good so far and I'd like to make sure we have docs for the next release. We can always make new branches for new docs when needed. |
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Sorry for not checking this earlier. I'll check it this week and before the next release |
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Submission Checklist
<<{ since VERSION }>>Summary
Documentation for suite of functions for the embedded Laplace approximation. Starting a PR to allow easy file comparison and will fill in the details soon.
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