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Update commonstatsmethods.md
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nucleosynthesis authored Dec 22, 2022
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Again, the resulting limit tree will contain the result. You can also save the chains using the option `--saveChain` which will then also be included in the output file.

Exclusion regions can be made from the posterior once an ordering principle is defined to decide how to grow the contour (there's infinite possible regions that contain 68% of the posterior pdf...)
Below is a simple example script which can be used to plot the posterior distribution from these chains and calculate the *smallest* such region. Note that in this example we are ignoring the burn-in (but you can add it by just editing `for i in range(mychain.numEntries()):` to `for i in range(200,mychain.numEntries()):` eg for a burn-in of 200.
Exclusion regions can be made from the posterior once an ordering principle is defined to decide how to grow the contour (there's infinite possible regions that contain 68% of the posterior pdf). Below is a simple example script which can be used to plot the posterior distribution from these chains and calculate the *smallest* such region. Note that in this example we are ignoring the burn-in (but you can add it by just editing `for i in range(mychain.numEntries()):` to `for i in range(200,mychain.numEntries()):` eg for a burn-in of 200.

```python
<details>
<summary><b>Show example script</b></summary>
<pre class="python"><code>
import ROOT

rmin = 0
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lu.Draw()

print " %g %% (%g %%) interval (target) = %g < r < %g "%(trueCL,CL,vl,vu)
```
</code></pre>
</details>

Running the script on the output file produced for the same datacard (including the `--saveChain` option) will produce the following output

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![](images/bayes2D.png)
## Computing Limits with toys
The `HybridNew` method is used to compute either the hybrid bayesian-frequentist limits popularly known as "CL<sub>s</sub> of LEP or Tevatron type" or the fully frequentist limits which are the current recommended method by the LHC Higgs Combination Group. Note that these methods can be resource intensive for complex models.
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