Tag Archives: ODE

Stan PK/PD Tutorial at the American Conference on Pharmacometrics, 8 Oct 2015

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Bill Gillespie, of Metrum, is giving a tutorial next week at ACoP:

This is super cool for us, because Bill’s not one of our core developers and has created this tutorial without the core development team’s help. Having said that, we’ve learned a lot from Bill and colleagues on our mailing lists as we were designing ODE solvers for Stan (an ongoing issue—see below for future plans).

Bill’s tutorial is up against a 2-day Monolix tutorial and a 2-day tutorial on R by Devin Pastoor, who’s also been active on our mailing lists recently.

Why Stan for PK/PD?

In case you’re wondering why people would use Stan for this instead of something more specialized like Monolix or NONMEM, it’s because of the modeling flexiblity provided by the Stan language and the effectiveness of NUTS for MCMC. So far, though, we’re in the hole in not having a stiff ODE solver in place. Or a good NONMEM-like event data language on top.

Maybe Bill will jump in with some other motivations.

What’s in Store for Stan’s ODE Solvers?

There’s been lots of behind-the-scenes activity on our ODE solvers—we’re really just getting burned in warmed up.

The next minor release of Stan (2.9) should stop the freezing issue when parameters wander into regions of parameter space that lead to stiff ODEs. And we’ve really sped up the Jacobian calculations when Michael Betancourt realized we were doing a lot of redundant calculation and he and I put a patch in to fix it. We should also allow user-defined control of absolute and relative tolerances.

Next, hopefully by Stan 2.10, we’ll have a stiff solver and maybe a way for users to supply analytic coupled-system gradients and Jacobians. Stay tuned. These new designs are largely being guided by Sebastian Weber and Wenping Wang at Novartis. And of course, by Michael Betancourt working out all the math and Daniel, Michael, and I working out the code with Sebastian’s and Wenping’s input.

We also need to evaluate how well variational inference works for ODE problems. Our early trials are very promising. Then we could replace the max marginal likelihood approach of NONMEM with a very speedy variational inference mechanism allowing much more general models.

There’s more in the works, but the above are the top of our to-do list.

Stan 2.5, now with MATLAB, Julia, and ODEs

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stanlogo-main

As usual, you can find everything on the

Drop us a line on the stan-users group if you have problems with installs or questions about Stan or coding particular models.

New Interfaces

We’d like to welcome two new interfaces:

The new interface home pages are linked from the Stan home page.

New Features

The biggest new feature is a differential equation solver (Runge-Kutta from Boost’s odeint with coupled sensitivities). We also added new cbind and rbind functions, is_nan and is_inf functions, a num_elements function, a mechanism to throw exceptions to reject samples with printed messages, and two new distributions, the Frechet and 2-parameter Pareto (both contributed by Alexey Stukalov).

Backward Compatibility

Stan 2.5 is fully backward compatible with earlier 2.x releases and will remain so until Stan 3 (which is not yet designed, much less scheduled).

Revised Manual

In addition to the ODE documentation, there is a new chapter on marginalizing discrete latent parameters with several example models, new sections on regression priors for coefficients and noise scale in ordinary, hierarchical, and multivariate settings, along with new chapters on all the algorithms used by Stan for MCMC sampling, optimization, and diagnosis, with configuration information and advice.

Preview of 2.6 and Beyond

Our plans for major features in the near future include stiff ODE solvers, a general MATLAB/R-style array/matrix/vector indexing and assignment syntax, and uncertainty estimates for penalized maximum likelihood estimates via Laplace approximations with second-order autodiff.

Release Notes

Here are the release notes.


v2.5.0 (20 October 2014)
======================================================================

New Features
----------------------------------------
* ordinary differential equation solver, implemented by coupling
  the user-specified system with its sensitivities (#771)
* add reject() statement for user-defined rejections/exceptions (#458)
* new num_elements() functions that applies to all containers (#1026)
* added is_nan() and is_inf() functions (#592)
* nested reverse-mode autodiff, primarily for ode solver (#1031)
* added get_lp() function to remove any need for bare lp__  (#470)
* new functions cbind() and rbind() like those in R (#787)
* added modulus function in a way tht is consistent with integer
  division across platforms (#577)
* exposed pareto_type_2_rng (#580)
* added Frechet distribution and multi_gp_cholesky distribution 
  (thanks to Alexey Stukalov for both)

Enhancements 
----------------------------------------
* removed Eigen code insertion for numeric traits and replaced
  with order-independent metaprogram (#1065)
* cleaned up error messages to provide clearer error context
  and more informative messages (#640)
* extensive tests for higher order autodiff in densities (#823)
* added context factory 
* deprecated lkj_cov density (#865)
* trying again with informational/rejection message (#223)
* more code moved from interfaces into Stan common libraries,
  including a var_context factory for configuration
* moved example models to own repo (stan-dev/example-models) and
  included as submodule for stan-dev/stan (#314)
* added per-iteration interrupt handler to BFGS optimizer (#768)
* worked around unused function warnings from gcc (#796)
* fixed error messages in vector to array conversion (#579, thanks
  Kevin S. Van Horn)
* fixed gp-fit.stan example to be as efficient as manual 
  version (#782)
* update to Eigen version 3.2.2 (#1087)

Builds
----------------------------------------
* pull out testing into Python script for developers to simplify
  makes
* libstan dependencies handled properly and regenerate
  dependencies, including working around bug in GNU 
  make 3.8.1 (#1058, #1061, #1062)

Bug Fixes
----------------------------------------
* deal with covariant return structure in functions (allows
  data-only variables to alternate with parameter version);  involved
  adding new traits metaprograms promote_scalar and
  promote_scalar_type (#849)
* fixed error message on check_nonzero_size (#1066)
* fix arg config printing after random seed generation (#1049)
* logical conjunction and disjunction operators short circuit (#593)
* clean up parser bug preventing variables starting with reserved
  names (#866)
* fma() function calls underlying platform fma (#667)
* remove upper bound on number of function arguments (#867)
* cleaned up code to remove compiler warnings (#1034)
* share likely() and unlikely() macros to avoid redundancy warnings (#1002)
* complete review of function library for NaN behavior and consistency
  of calls for double and autodiff values, with extensive
  documentation and extensive new unit tests for this and other,
  enhances NaN testing in built-in test functions (several dozen issues 
  in the #800 to #902 range)
* fixing Eigen assert bugs with NO_DEBUG in tests (#904)
* fix to makefile to allow builds in g++ 4.4 (thanks to Ewan Dunbar)
* fix precedence of exponentiation in language (#835)
* allow size zero inputs in data and initialization (#683)

Documentation
----------------------------------------
* new chapter on differential equation solver
* new sections on default priors for regression coefficients and
  scales, including hierarchical and multivariate based on
  full Cholesky parameterization
* new part on algorithms, which chapters on HMC/NUTS, optimization,
  and diagnostics
* new chapter on models with latent discrete parameters
* using latexmk through make for LaTeX compilation
* changed page numbers to beg contiguous throughout so page 
  numbers match PDF viewer page number
* all user-supplied corrections applied from next-manual issue
* section on identifiability with priors, including discussion of K-1
  parameterization of softmax and IRT
* new section on convergence monitoring
* extensive corrections from Andrew Gelman on regression models
  and notation
* added discussion of hurdle model in zero inflation section
* update built-in function doc to clarify several behaviors (#1025)