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If the threshold is zero and you integrate $\psi$ out of the posterior, the second model becomes a probit model. Gibbs samplers actually estimate the $\psi$ parameters, but that is not a good idea (if you can avoid it) for Hamiltonian Monte Carlo samplers such as Stan. A Stan program with a probit log-likelihood would be data { int<lower = 0> N; ...

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It's been three years, but I believe this might be the approach mentioned in the comments by @twiecki. It uses a truncated Dirichlet Process Mixture Model to detect multiple change points without any prior knowledge of their number. I have tried to disassemble their implementation and re-implement it on my own, so take the following with a grain of salt. ...

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The book has been ported to PyMC3. The updated example of the Price is Right model can be found here: https://render.githubusercontent.com/view/ipynb?commit=be1faee30c4eb6bef4c049b6e11499db144c5697&enc_url=...

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My original comment misunderstood the nature of your problem. Indeed, it is correct that PyMC cannot model systems where the observed variable is deterministic. That was a bit of a surprise to me, but the article that you link provides a good reason why that is the case. Now, for your problem: Given that we cannot directly observe the sum-of-products $Y$ as ...

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Meanwhile, other papers related to Bayesian RNNs have been published. For example, Bayesian Recurrent Neural Networks and Bayesian Recurrent Neural Network Models for Forecasting and Quantifying Uncertainty in Spatial-Temporal Data.

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The BayesianTools R package (disclaimer: I am one of the authors) allows specifying arbitrary priors, and there is a function createPriorDensity for summarising the posterior as a new prior. The limitation of this is that we currently only implement a multivariate normal density estimator, so you will have a loss of information if your posterior is not ...

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