# Example of Bayesian inference computation creating a model output at the mean of the parameter samples that is outside of the discrete posterior predictive support

**URL:** <https://uqworld.org/t/example-of-bayesian-inference-computation-creating-a-model-output-at-the-mean-of-the-parameter-samples-that-is-outside-of-the-discrete-posterior-predictive-support/726>\
**Category:** Case Studies\
**Tags:** inversion\
**Created:** [July 6, 2020, 1:53pm UTC](https://uqworld.org/t/example-of-bayesian-inference-computation-creating-a-model-output-at-the-mean-of-the-parameter-samples-that-is-outside-of-the-discrete-posterior-predictive-support/726 "2020-07-06T13:53:02Z")\
**Posts on this page:** 1\
**Showing post:** 3

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**Author:** ![olaf.klein](https://uqworld.org/user_avatar/uqworld.org/olaf.klein/32/468_2.png) [@olaf.klein](https://uqworld.org/u/olaf.klein)\
**Post date:** [July 14, 2020, 3:34pm UTC](https://uqworld.org/t/example-of-bayesian-inference-computation-creating-a-model-output-at-the-mean-of-the-parameter-samples-that-is-outside-of-the-discrete-posterior-predictive-support/726/3 "2020-07-14T15:34:24Z")

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Dear Paul,

thanks for your answer with this elaborated discussion and your suggestion to reparametrize the problem. I will apply this to my real world application.  
I view of your remark that the AIES MSMC samplers has less problems with the hyperbolic trench as other MCMC smaplers I would like to point out some observation that surprised me somehow:

Since I believed that the model output at the mean of the parameter samples would be in the discrete posterior predictive support if the numbers of steps became sufficiently large, I increased the value of `Solver.MCMC.Steps` up to 25,000, but could not observe this behavior. This behavior was still not observed after I increased `Solver.MCMC.Steps` even further to **250,000**. After more the 72 hours of computing time got I the following plots for the MCMC samples with a strange observation in the second plot, i.e. the one for X2:

![strange_mean_prediction_more_steps-fig-1](https://uqworld.org/uploads/default/original/1X/f969ef14c0250e548d1b2aae9e7df84d38a98b6f.png)

![strange_mean_prediction_more_steps-fig-2](https://uqworld.org/uploads/default/original/1X/a57df87c195d9020febe8850c5d7263c18ac41e7.png)

I try to figure out if this change of behavior for the samples for X2 at around step 110,000 can be a real result of the algorithm or if it may be an indication that there may be some well hidden error somewhere?  
What do you think?

Many thanks again

Greetings  
Olaf

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