I oftenly see articles tackling regression-problems with nonlinear parameters but i rarely see someone dwelling into the issues with this in bayesian inference.

As an example: A Bayesian Approach to Media Mix Modeling by Michael Johns & Zhenyu Wang

Where the adstock and saturation transformations are nonlinear w.r.t parameters. How far can we stretch this, i mean can we actually model for e.g an multiplicative counterpart of the model proposed in the article with nonlinear parameters and compute it within an resonable time with e.g the NUTS-sampler or is an non mcmc-package preferred which deploys SVI when tackling these complex nonlinearities?

What kind of issues have people been expriencing w.r.t this using pymc?

Hi! I think, as always, depends on the model and the data . I have worked a simulated example where I show the inference steps Media Effect Estimation with PyMC: Adstock, Saturation & Diminishing Returns - Dr. Juan Camilo Orduz In practice, it has also worked with real-data as long as one has concrete assumptions on the data generating process.

For more complex models @lucianopaz has certainly much more experience

thanks for cc:ing.

yeah of course it depends alot on the data and how complex the model is. What would be nice to see is an example of someone that managed to stretch this way further performing bayesian inference on an highly nonlinear very complex model with the NUTS-sampler in pymc. Most people i´ve seen that worked on very complex models with potentially large datasets tend to choose SVI from what i´ve seen. Btw, i pm:ed you about your article.

An additional recent and relevant reference is Bayesian Media Mix Models: Modelling changes in marketing effectiveness over time - PyMC Labs