Webinar: Some Outstanding Challenges when Solving ODEs in a Bayesian context

This post is by Eric.

This Wednesday, at 12 pm ET, Charles Margossian is stopping by to talk to us about solving ODEs using Bayesian methods. You can register here.

If you want to get a feel for the types of issues he will be discussing, take a look at his (and Andrew’s) recent case study: “Bayesian Model of Planetary Motion: exploring ideas for a modeling workflow when dealing with ordinary differential equations and multimodality.”

Abstract

Many scientific models rely on differential equation-based likelihoods. Some unique challenges arise when fitting such models with full Bayesian inference. Indeed as our algorithm (e.g. Markov chain Monte Carlo) explores the parameter space, we must solve, not one, but a range of ODEs whose behaviors can change dramatically with different parameter values. I’ll present two examples where this phenomenon occurs: a classical mechanics problem where the speed of the solver differs for different parameter values; and a pharmacology example, wherein the ODE behaves in a stiff manner during the warmup phase but becomes non-stiff during the sampling phase. We’ll then have a candid discussion about the difficulties that arise when developing a modeling workflow with ODE-based models and brainstorm some ideas on how to move forward.

The video is now available here.

8 Comments

1. Funko says:

Such a simple ODE makes such problems? Unbelievable Oo

2. Andrew says:

Funko:

Oh, yeah, statistical computing is much harder than you might think! That’s a key motivation of our workflow paper.

3. Dan Bowman says:

No big deal, but there’s a typo in the LaTeX of the equations of motion given in the case study. The second equation should be for the time derivative of momentum (i.e., p). At any rate, thanks for writing it up. It looks quite interesting on an initial skimming and I look forward to reading it in detail.

4. Nick Patterson says:

Could this be related to phase change or chaos? It’s well known that planetary motion under Newtonian
gravitation can be chaotic, and I would expect that the qualitative behavior could sometimes be sensitive
to small changes in parameter values. You could easily imagine that would make an MCMC difficult to implement.

• Funko says:

I believe the N-body problem becomes chaotic for n>2, while the problem at hand looks at n=2.

5. Robert Goldman says:

Drat. Saw this announcement just too late. Is there a recording by any chance?

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