odemodeling-package: The 'odemodeling' package

In jtimonen/odemodeling: Building, fitting, and validating Bayesian ODE models in 'Stan'

The 'odemodeling' package

Description

Building and fitting ordinary differential equation (ODE) models with different numerical solvers in 'Stan'. Designed for efficient validation of the accuracy of numerical solvers in the Bayesian context. Using Pareto-smoothed importance sampling (PSIS) and its diagnostics. The package is based on the R6 object oriented system and uses cmdstanr as the interface to 'Stan'.

Creating a model

• Declare model data, parameters, and other variables using stan_array(), stan_dim(), stan_matrix(), stan_param(), stan_transform(), stan_vector_array(), and stan_vector().

• Create an OdeModel model using ode_model().

Using different ODE solvers

• See odesolvers for constructors that create objects of class OdeSolver.

Fitting a model

• Sample the posterior or prior distribution of the model parameters, and generate corresponding ODE solutions using the ⁠$sample()⁠ method of the OdeModel class.

• See methods of the OdeModelMCMC class for studying the returned object.

Additional simulation of ODE systems

• See the ⁠$gqs()⁠ method of the OdeModelMCMC and OdeModel classes.

• See methods of the OdeModelGQ class for studying the returned object.

• See compare_odefits for functions to compare different ODE model simulations and fits.

Importance sampling for reliable and efficient inference in Bayesian ODE models

Our proposed workflow is to

1. Select an initial ODE solver M.

2. Sample the parameter posterior using MCMC with M as the ODE solver.

3. Compute certain metrics using a more accurate solver M∗.

4. Increase the accuracy of M∗ and repeat Step 3 until the metrics converge. If the Pareto-k metric converges to a value larger than 0.7, increase the accuracy of M and go back to Step 2.

5. Compute any posterior estimates using final importance weights. See Timonen et al. (2022) below.

The algorithm can be used to validate the reliability, and correct the errors of a given method M, which can be for example a software default. On the other hand, a smart initial selection of M can provide speed gains compared to often rather conservatively set software defaults, while still maintaining reliability of the inferences.

We generally recommend selecting M initially so that sampling is as fast as possible. For example, for non-adaptive ODE solvers, one can first try using the smallest sensible number of steps that does not result in immediate failure. Selecting a good M is more difficult in the case of adaptive solvers. We have observed that tolerances on the order of 1e-4 to 1e-3 generally work well.

See the reliability() method of the OdeModelMCMC class.

Tutorial

See the tutorial vignette.

Author(s)

Maintainer: Juho Timonen [e-mail] (ORCID)

References

1. Timonen, J., Siccha, N., Bales, B., Lähdesmäki, H., & Vehtari, A. (2023). An importance sampling approach for reliable and efficient inference in Bayesian ordinary differential equation models. Stat, 12(1), e614. https://onlinelibrary.wiley.com/doi/full/10.1002/sta4.614

jtimonen/odemodeling documentation built on Sept. 15, 2024, 4:29 a.m.