# Multivariate model with censored data

**URL:** <https://discourse.pymc.io/t/multivariate-model-with-censored-data/5083>\
**Category:** Questions\
**Created:** [May 13, 2020, 6:45pm UTC](https://discourse.pymc.io/t/multivariate-model-with-censored-data/5083 "2020-05-13T18:45:39Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![sammosummo](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/sammosummo/32/96_2.png) [@sammosummo](https://discourse.pymc.io/u/sammosummo)\
**Post date:** [May 13, 2020, 6:45pm UTC](https://discourse.pymc.io/t/multivariate-model-with-censored-data/5083/1 "2020-05-13T18:45:39Z")

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I have multivariate censored (clipped) data, which I am currently modeling using

`y = pm.MvNormal(name="$Y$", mu=mu, cov=Sigma, observed=items, shape=items.shape)`

From [this example](https://docs.pymc.io/notebooks/censored_data.html) it seems like one simply has to add two terms to the log likelihood.

1. Number of samples at the lower bound multiplied by the log of MVNormal CDF.
2. Number of samples at the upper bound multiplied by the log of MVNormal CCDF.

Is this correct?

If so, how can I implement this efficiently in PyMC3? Is there are way of drawing the logcdf straight from ‘y’?

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**Author:** ![junpenglao](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/junpenglao/32/8_2.png) [@junpenglao](https://discourse.pymc.io/u/junpenglao)\
**Post date:** [May 13, 2020, 7:02pm UTC](https://discourse.pymc.io/t/multivariate-model-with-censored-data/5083/2 "2020-05-13T19:02:52Z")

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IIUC there is no close form expression of MvN CDF: [https://en.wikipedia.org/wiki/Multivariate\_normal\_distribution#Cumulative\_distribution\_function](https://en.wikipedia.org/wiki/Multivariate_normal_distribution#Cumulative_distribution_function)

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<div class="post-metadata">

**Author:** ![sammosummo](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/sammosummo/32/96_2.png) [@sammosummo](https://discourse.pymc.io/u/sammosummo)\
**Post date:** [May 13, 2020, 7:34pm UTC](https://discourse.pymc.io/t/multivariate-model-with-censored-data/5083/3 "2020-05-13T19:34:42Z")

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Well, so much for that project. Thanks!

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<div class="post-metadata">

**Author:** ![junpenglao](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/junpenglao/32/8_2.png) [@junpenglao](https://discourse.pymc.io/u/junpenglao)\
**Post date:** [May 14, 2020, 5:30am UTC](https://discourse.pymc.io/t/multivariate-model-with-censored-data/5083/4 "2020-05-14T05:30:15Z")

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High dimension stuff is difficult 😅