# Use Kriging as forward model in Bayesian calibration

**URL:** <https://openturns.discourse.group/t/use-kriging-as-forward-model-in-bayesian-calibration/262>\
**Category:** Python usage\
**Created:** [January 6, 2023, 11:53am UTC](https://openturns.discourse.group/t/use-kriging-as-forward-model-in-bayesian-calibration/262 "2023-01-06T11:53:10Z")\
**Posts on this page:** 1\
**Showing post:** 13

<div class="post-metadata">

**Author:** ![josephmure](https://yyz2.discourse-cdn.com/free1/user_avatar/openturns.discourse.group/josephmure/32/114_2.png) [@josephmure](https://openturns.discourse.group/u/josephmure)\
**Post date:** [August 16, 2023, 12:01pm UTC](https://openturns.discourse.group/t/use-kriging-as-forward-model-in-bayesian-calibration/262/13 "2023-08-16T12:01:09Z")

</div>

Hi @elieso and sorry for the delay, I have not had time to browse the forum for a while.

If your Kriging model has output dimension 2, let’s say \boldsymbol{Y}(x) = (Y\_1(x), Y\_2(x))^T where x is the N\_d-dimensional input, then \boldsymbol{Y}(x) follows a bivariate normal distribution.

Therefore your conditional distribution is going to be defined with:

```auto
conditional = ot.Normal(2)

```

And your link function will need to output the parameters of a bivariate normal distribution.  
To see what these parameters are, use the `getParameterDescription` method:

```auto
conditional.getParameterDescription()

```

Output:

```auto
[mean_0,standard_deviation_0,mean_1,standard_deviation_1,R_1_0]

```

which are respectively the mean of Y\_1(x), the standard deviation of Y\_1(x), the mean of Y\_2(x), the standard deviation of Y\_2(x), and the correlation coefficient of Y\_1(x) and Y\_2(x) (with value 0 if they are independent which is by default the case when you do Kriging with multiple outputs).

---

_[View the full topic](https://openturns.discourse.group/t/use-kriging-as-forward-model-in-bayesian-calibration/262)._