# Parameter estimation and model inadequacy

**URL:** <https://discourse.julialang.org/t/parameter-estimation-and-model-inadequacy/69407>\
**Category:** Statistics\
**Tags:** turing, bayesian-inference, differentialequation\
**Created:** [October 8, 2021, 1:36am UTC](https://discourse.julialang.org/t/parameter-estimation-and-model-inadequacy/69407 "2021-10-08T01:36:03Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![GregCoyle](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gregcoyle/32/29663_2.png) [@GregCoyle](https://discourse.julialang.org/u/GregCoyle)\
**Post date:** [October 8, 2021, 1:36am UTC](https://discourse.julialang.org/t/parameter-estimation-and-model-inadequacy/69407/1 "2021-10-08T01:36:03Z")

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Are there any packages associated with Bayesian inference that provide methods to take on model inadequacy, AKA structural error, model bias, etc.? I’m particularly interested in applications to Bayesian parameter estimation and uncertainty quantification in systems of differential equations. [Brynjarsdottir and O’Hagan, 2014](http://www.tonyohagan.co.uk/academic/pdf/simmach.pdf) give a good overview of the issue and its importance for scientific simulators to which I am referring. For a more recent treatment, see [Sargsyan, et al., 2018](https://www.osti.gov/servlets/purl/1529284). Thanks in advance if you have any suggestions.

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**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [October 8, 2021, 10:13am UTC](https://discourse.julialang.org/t/parameter-estimation-and-model-inadequacy/69407/2 "2021-10-08T10:13:37Z")

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Yes, take a look at [[2012.07244] Bayesian Neural Ordinary Differential Equations](https://arxiv.org/abs/2012.07244)

Code examples in [https://diffeqflux.sciml.ai/dev/examples/BayesianNODE\_NUTS/](https://diffeqflux.sciml.ai/dev/examples/BayesianNODE_NUTS/)

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**Author:** ![GregCoyle](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gregcoyle/32/29663_2.png) [@GregCoyle](https://discourse.julialang.org/u/GregCoyle)\
**Post date:** [October 8, 2021, 3:51pm UTC](https://discourse.julialang.org/t/parameter-estimation-and-model-inadequacy/69407/3 "2021-10-08T15:51:46Z")

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Very cool, thanks for these! I’m curious to see how these methods compare to the “non-intrusive PCE” approach described in Sargsyan.