# Censoring a truncated distribution

**URL:** <https://discourse.pymc.io/t/censoring-a-truncated-distribution/13261>\
**Category:** v5\
**Created:** [November 9, 2023, 8:39am UTC](https://discourse.pymc.io/t/censoring-a-truncated-distribution/13261 "2023-11-09T08:39:40Z")\
**Posts on this page:** 8\
**Page:** 1

<div class="post-metadata">

**Author:** ![alaz](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/alaz/32/7376_2.png) [@alaz](https://discourse.pymc.io/u/alaz)\
**Post date:** [November 9, 2023, 8:39am UTC](https://discourse.pymc.io/t/censoring-a-truncated-distribution/13261/1 "2023-11-09T08:39:41Z")

</div>

Hello,

I’m trying to implement a right-censored model. However, I need the distribution which will be censored to be a normal distribution left-truncated at zero. I’m stuck with the following error.

```auto
NotImplementedError: LogCDF method not implemented for truncated_normal_rv{0, (0, 0, 0, 0), floatX, False}

```

What I understand is that there’s no `logcdf` defined for the truncated normal, but I saw a merged pull request [here](https://github.com/pymc-devs/pymc/pull/6690), and it seems that `logcdf` is in fact implemented?

# Censoring a truncated distribution

Following is a prior predictive illustration:

```auto
import pymc as pm
import arviz as az
import numpy as np
from copy import copy

```

```auto
with pm.Model() as m:
    a_normal = pm.Normal("n", 1, 1)
    normal_dist = pm.Normal.dist(mu=1.0, sigma=1.0)
    truncated_normal = pm.Truncated("truncated_normal", normal_dist, lower=0)
    truncated_normal_dist = pm.Truncated.dist(normal_dist, lower=0)
    cs_normal = pm.Censored("cs_n", normal_dist, lower=0, upper=3)
    cs_truncated_normal = pm.Censored("cs_tn", truncated_normal_dist, lower=None, upper=3)

with m:
    idata = pm.sample_prior_predictive(samples=10000)

az.plot_dist(idata.prior.stack(samples=("chain", "draw")).n, color='k', label="the normal")
az.plot_dist(idata.prior.stack(samples=("chain", "draw")).truncated_normal, color='b', label="lower-truncated at 0")
az.plot_dist(idata.prior.stack(samples=("chain", "draw")).cs_tn, color='r', label="truncated-censored")
az.plot_dist(idata.prior.stack(samples=("chain", "draw")).cs_n, color='g', label="non-truncated-censored")

```

Which will output:

 ![image](https://canada1.discourse-cdn.com/flex036/uploads/pymc3/original/2X/a/a982126b7d784c28c71b1f2ee0cbc6632610ce9e.png)

So, I can’t use a normal distribution (black) and censor it from both sides (green), what I need is a truncated distribution (blue) to be right-censored (red).

# Generate Data

```python
N = 1 # one trial is enough to illustrate the problem
mu, sigma = 1, 2
upper_bounds = np.random.randint(0, 3, N)
y = np.random.normal(loc=mu, scale=sigma, size=N)

def right_censor(y, upper_bounds):
    cy = copy(y)
    censor_index = cy >= upper_bounds
    cy[censor_index] = upper_bounds[censor_index]
    return cy

cy = right_censor(y, upper_bounds)

print(y, upper_bounds, cy)

```

# Inference model

```python
with pm.Model() as m1:
    mu = pm.Normal("mu", 0, 1)
    sigma = pm.Normal("sigma", 0, 1)
    normal_ = pm.Normal.dist(mu, sigma)
    trunc_normal = pm.Truncated.dist(normal_, lower=0)
    censored = pm.Censored("censored", trunc_normal, lower=None, upper=upper_bounds, observed=cy)

```

# Error

Following gives the error.

```auto
with m1:
    idata_m1 = pm.sample()

```

```auto
NotImplementedError: LogCDF method not implemented for truncated_normal_rv{0, (0, 0, 0, 0), floatX, False}

```

- The watermark:

Last updated: Thu Nov 09 2023

Python implementation: CPython  
Python version : 3.11.6  
IPython version : 8.16.1

scipy : 1.11.3  
arviz : 0.16.1  
pytensor : 2.13.1  
pymc : 5.9.0  
numpy : 1.25.2  
matplotlib: 3.8.0  
pandas : 2.1.1

Watermark: 2.4.3

# Question

So I want to ask:

- Is this the correct approach? Is this error really because the `logcdf` is not implemented, or is there a user error in model creation part?
- What may be a workaround if it’s not implemented yet? What would you suggest?

---

<div class="post-metadata">

**Author:** ![ricardoV94](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/ricardov94/32/5775_2.png) [@ricardoV94](https://discourse.pymc.io/u/ricardoV94)\
**Post date:** [November 9, 2023, 10:30am UTC](https://discourse.pymc.io/t/censoring-a-truncated-distribution/13261/2 "2023-11-09T10:30:02Z")

</div>

TruncatedNormal is a specialized distribution. The PR you saw implemented logcdf for all the other non-specialized cases, but leaves TruncatedNormal still without a logcdf. I’ll open an issue to add it.

> <https://github.com/pymc-devs/pymc/issues/7003>
>
> \### Description
> 
> We implemented the logcdf for the general Truncated cases in …https://github.com/pymc-devs/pymc/pull/6690, but TruncatedNormal is its own distribution and doesn't have a logcdf currently implemented.
> 
> We should refactor the logcdf function added in that PR so that we can call it from the logcdf of TruncatedNormal as well as the general Truncated (no point in duplicating the code)
> 
> Reported in https://discourse.pymc.io/t/censoring-a-truncated-distribution/13261

---

<div class="post-metadata">

**Author:** ![ricardoV94](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/ricardov94/32/5775_2.png) [@ricardoV94](https://discourse.pymc.io/u/ricardoV94)\
**Post date:** [November 9, 2023, 12:38pm UTC](https://discourse.pymc.io/t/censoring-a-truncated-distribution/13261/3 "2023-11-09T12:38:09Z")

</div>

As silly as it may be that means you can use a StudentT with large fixed nu, to get what you want. That will behaves basically like a Normal, except the likelihood could be a bit slower.

---

<div class="post-metadata">

**Author:** ![alaz](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/alaz/32/7376_2.png) [@alaz](https://discourse.pymc.io/u/alaz)\
**Post date:** [November 21, 2023, 9:47am UTC](https://discourse.pymc.io/t/censoring-a-truncated-distribution/13261/4 "2023-11-21T09:47:09Z")

</div>

Thank you very much for your answers Ricardo. I tried your solution and it works. As I try to replicate the prior part with `pm.StudentT` I got another error.

```auto
with pm.Model() as m2:
    n = pm.Normal("n", 3, 1)
    sT_nu_fixed = pm.ConstantData("sT_nu_fixed", 100)
    sT = pm.StudentT("sT", nu=sT_nu_fixed, mu=3, sigma=1)
    sT_d = pm.StudentT.dist(nu=sT_nu_fixed, mu=3, sigma=1, shape=1) # error without shape argument
    sT_t = pm.Truncated("sT_t", sT_d, lower=2)
    sT_c = pm.Censored("sT_c", sT_d, lower=2, upper=5)
    sT_t_d = pm.Truncated.dist(sT_d, lower=2, shape=1)
    # st_t_c = pm.Censored("sT_t_c", sT_t_d, lower=None, upper=5) # this line gives truncation error
    idata_m2 = pm.sample_prior_predictive(samples=15_000)

```

This code block above gives following errors:

- ValueError: Nonzero only supports non-scalar arrays. → If `pm.StudentT.dist` has no shape argument.
- TruncationError: Truncation did not converge in 10000 steps → when I use that second censored distribution (`st_t_c`)

But it works when it’s in another model:

```auto
with pm.Model() as m2_1:
    # repeat as in m2
    sT_nu_fixed = pm.ConstantData("sT_nu_fixed", 100)
    sT = pm.StudentT("sT", nu=sT_nu_fixed, mu=3, sigma=1)
    sT_d = pm.StudentT.dist(nu=sT_nu_fixed, mu=3, sigma=1, shape=1) # error without shape argument
    sT_t_d = pm.Truncated.dist(sT_d, lower=2)
    st_t_c = pm.Censored("sT_t_c", sT_t_d, lower=None, upper=5)
    idata_m2_1 = pm.sample_prior_predictive(samples=15_000)

```

and plotting:

```auto
az.plot_dist(idata_m2.prior.stack(samples=("chain", "draw")).n, color='m', label="n")
az.plot_dist(idata_m2.prior.stack(samples=("chain", "draw")).sT, color='k', label="sT")
az.plot_dist(idata_m2.prior.stack(samples=("chain", "draw")).sT_t, color='b', label="truncated-sT")
az.plot_dist(idata_m2.prior.stack(samples=("chain", "draw")).sT_c, color='g', label="censored-sT")
az.plot_dist(idata_m2_1.prior.stack(samples=("chain", "draw")).sT_t_c, color='r', label="censored-truncated-sT");

```

returns:  
 ![image](https://canada1.discourse-cdn.com/flex036/uploads/pymc3/original/2X/5/5d7d193f859f1d904b931f778e918c73882c57b9.png)

The inference part works fine:

```auto
with pm.Model() as m3:
    sigma = pm.Exponential("sigma", 1)
    mu = pm.Normal("mu", 3, 1)
    sT_nu_fixed = pm.ConstantData("sT_nu_fixed", 100)
    sT_d = pm.StudentT.dist(nu=sT_nu_fixed, mu=mu, sigma=sigma, shape=2)
    sT_t = pm.Truncated.dist(sT_d, lower=0)
    censored = pm.Censored("censored", sT_t, lower=None, upper=[3, 5], observed=[1, 3])
    idata_m3 = pm.sample()

```

Now my problem is solved, but I wanted to share those errors above, I could not make sense of them. Trying with another continuous distribution (VonMises) also returned the same error. Pasting the code below:

```auto
with pm.Model() as m4:
    vm = pm.VonMises("vm", mu=1, kappa=100)
    vm_dist = pm.VonMises.dist(mu=1, kappa=100, shape=1) # warning w/o shape argument ?
    vm_truncated = pm.Truncated("vm_truncated", vm_dist, lower=0.9)
    vm_truncated_dist = pm.Truncated.dist(vm_dist, lower=0.9)
    cs_vm = pm.Censored("cs_vm", vm_dist, lower=0.9, upper=1.2)
    # cs_vm_t = pm.Censored("cs_vm_t", vm_truncated_dist, lower=0, upper=3) # this gives error
    idata_m4 = pm.sample_prior_predictive(samples=10_000)
with pm.Model() as m5:
    vm = pm.VonMises("vm", mu=1, kappa=100)
    vm_dist = pm.VonMises.dist(mu=1, kappa=100, shape=1) # warning w/o shape argument ?
    vm_truncated_dist = pm.Truncated.dist(vm_dist, lower=0.9)
    cs_vm_t = pm.Censored("cs_vm_t", vm_truncated_dist, lower=0, upper=1.2)
    idata_m5 = pm.sample_prior_predictive(samples=10_000)
az.plot_dist(idata_m4.prior.stack(samples=("chain", "draw")).vm, color='k', label="vm")
az.plot_dist(idata_m4.prior.stack(samples=("chain", "draw")).vm_truncated, color='b', label="truncated-vm")
az.plot_dist(idata_m4.prior.stack(samples=("chain", "draw")).cs_vm, color='r', label="non-truncated-censored-vm")
az.plot_dist(idata_m5.prior.stack(samples=("chain", "draw")).cs_vm_t, color='g', label="truncated-censored-sT")

```

---

<div class="post-metadata">

**Author:** ![ricardoV94](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/ricardov94/32/5775_2.png) [@ricardoV94](https://discourse.pymc.io/u/ricardoV94)\
**Post date:** [November 21, 2023, 10:01am UTC](https://discourse.pymc.io/t/censoring-a-truncated-distribution/13261/5 "2023-11-21T10:01:23Z")

</div>

Can you share a fully reproducible example with the StudentT? Also, what version of PyMC are you using? Using the latest would be the best

---

<div class="post-metadata">

**Author:** ![alaz](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/alaz/32/7376_2.png) [@alaz](https://discourse.pymc.io/u/alaz)\
**Post date:** [November 21, 2023, 12:17pm UTC](https://discourse.pymc.io/t/censoring-a-truncated-distribution/13261/6 "2023-11-21T12:17:04Z")

</div>

I think running m2 without commenting that line should produce the error. I was running on pymc 5.9.0, now updated to 5.9.2 but it persists. Following block should be fully reproducible:

```auto
import pymc as pm
with pm.Model() as m2:
    n = pm.Normal("n", 3, 1)
    sT_nu_fixed = pm.ConstantData("sT_nu_fixed", 100)
    sT = pm.StudentT("sT", nu=sT_nu_fixed, mu=3, sigma=1)
    sT_d = pm.StudentT.dist(nu=sT_nu_fixed, mu=3, sigma=1, shape=1) # error without shape argument
    sT_t = pm.Truncated("sT_t", sT_d, lower=2)
    sT_c = pm.Censored("sT_c", sT_d, lower=2, upper=5)
    sT_t_d = pm.Truncated.dist(sT_d, lower=2, shape=1)
    st_t_c = pm.Censored("sT_t_c", sT_t_d, lower=None, upper=5) # this line gives truncation error
    idata_m2 = pm.sample_prior_predictive(samples=15_000)

```

Python implementation: CPython  
Python version : 3.11.6  
IPython version : 8.17.2

numpy: 1.25.2  
pymc : 5.9.2  
arviz: 0.16.1

Watermark: 2.4.3

---

<div class="post-metadata">

**Author:** ![ricardoV94](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/ricardov94/32/5775_2.png) [@ricardoV94](https://discourse.pymc.io/u/ricardoV94)\
**Post date:** [November 22, 2023, 8:42am UTC](https://discourse.pymc.io/t/censoring-a-truncated-distribution/13261/7 "2023-11-22T08:42:45Z")

</div>

Thanks @alaz I could reproduce the problem with a simpler scenario. It has nothing to do with `Censored` but with identical `Truncated` distributions in the same model. You should see the problem go away if you change one of the parameters to be slightly different, like nu=100 in one of the truncated and nu=101 in the other.

I opened an issue in the PyMC repo: [Conflicts between multiple identical Truncated distributions · Issue #7024 · pymc-devs/pymc · GitHub](https://github.com/pymc-devs/pymc/issues/7024)

---

<div class="post-metadata">

**Author:** ![alaz](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/alaz/32/7376_2.png) [@alaz](https://discourse.pymc.io/u/alaz)\
**Post date:** [November 22, 2023, 8:56am UTC](https://discourse.pymc.io/t/censoring-a-truncated-distribution/13261/8 "2023-11-22T08:56:52Z")

</div>

Thank you very much!