# Problem with Deterministic variable

**URL:** <https://discourse.pymc.io/t/problem-with-deterministic-variable/7041>\
**Category:** Questions\
**Created:** [March 19, 2021, 1:13pm UTC](https://discourse.pymc.io/t/problem-with-deterministic-variable/7041 "2021-03-19T13:13:48Z")\
**Posts on this page:** 8\
**Page:** 1

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**Author:** ![Francisco](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/francisco/32/3803_2.png) [@Francisco](https://discourse.pymc.io/u/Francisco)\
**Post date:** [March 19, 2021, 1:13pm UTC](https://discourse.pymc.io/t/problem-with-deterministic-variable/7041/1 "2021-03-19T13:13:48Z")

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Hello, I am very new in bayesian statistics and pymc3.  
I try with this very simple model

with pm.Model() as modelo\_complacencia:  
μ = pm.Uniform(‘μ’ , lower = 1, upper= 15)  
σ = pm.Uniform(‘σ’, lower = 1, upper= 15)  
P0 = pm.Normal(‘P0’, mu=μ, sd=σ, observed=data)  
IPVI = pm.Deterministic(‘PVI’, get\_pvi( P0))  
trace\_g = pm.sample(10)  
az.plot\_trace(trace\_g)

with

def get\_pvi(x):  
return 1.5497/np.log10(45.22/x)

data=np.array([ 9.4634, 9.8030, 9.0072, 9.4574, 9.8042,9.0752, 9.7246, 9.9534, 9.2020, 9.8305, 9.9323, 9.2103, 9.8232, 9.7856, 9.0838, 9.9306, 9.7179, 8.9507, 9.7838, 9.4283, 8.8593, 9.8523, 9.5175, 8.9576, 9.9520, 9.4569, 9.0570, 10.1093, 9.5680, 9.1668, 10.0123, 9.4289, 9.1801, 10.1137, 9.5103, 9.2803, 10.2759, 9.4823, 9.3829, 10.3293, 9.6556, 9.6288, 10.4406, 9.6630, 9.6831, 10.5126, 9.6760, 9.7955, 10.4225, 9.5551, 9.6265, 10.2659, 9.3821, 9.7273, 10.1402, 9.3808, 9.6738, 10.4288, 9.4218, 10.0775, 10.3577, 9.6004, 10.1041, 10.2955, 9.5451, 10.2484, 10.3395, 9.5534, 10.2460, 10.1394, 9.4752, 10.3348, 10.2022, 9.5235, 10.4362, 10.1432, 9.4596, 10.5102,  
10.1962, 9.7203, 10.7773, 10.3343, 9.9001, 10.8562, 10.3759, 10.0302, 11.0552, 10.2961, 9.8981, 10.8033, 10.0477, 9.7508, 10.6555, 9.9330, 9.7585, 10.5959 ])

and this message appears

anaconda3/lib/python3.8/site-packages/arviz/stats/density\_utils.py:770: UserWarning: Something failed when estimating the bandwidth. Please check your data warnings.warn(“Something failed when estimating the bandwidth. Please check your data”)

Could yo please help me to understand and solve this problem?

Thanks in advance

Francisco

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**Author:** ![ckrapu](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/ckrapu/32/1366_2.png) [@ckrapu](https://discourse.pymc.io/u/ckrapu)\
**Post date:** [March 19, 2021, 1:55pm UTC](https://discourse.pymc.io/t/problem-with-deterministic-variable/7041/2 "2021-03-19T13:55:24Z")

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`IPVI` is always the same because it’s a deterministic function of observed data. Arviz is trying to calculate bin edges for a histogram somewhere but since all samples of `IPVI` are the same, the left bin edge and right bin edge are identical, so the bandwidth (measured as left minus right) is zero. In short, declaring IPVI as a deterministic doesn’t really make sense - you can compute its value outside of PyMC3. Otherwise, if `P0` is not observed, then this would be a reasonable thing to do.

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**Author:** ![Francisco](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/francisco/32/3803_2.png) [@Francisco](https://discourse.pymc.io/u/Francisco)\
**Post date:** [March 19, 2021, 1:58pm UTC](https://discourse.pymc.io/t/problem-with-deterministic-variable/7041/3 "2021-03-19T13:58:49Z")

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Chris Krapu,

Thank you very much for yor reply!!! IPVI is a function of P0, as P0 is a random variable, IPVI should be a random variable also… How can I define it?

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**Author:** ![Francisco](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/francisco/32/3803_2.png) [@Francisco](https://discourse.pymc.io/u/Francisco)\
**Post date:** [March 19, 2021, 2:17pm UTC](https://discourse.pymc.io/t/problem-with-deterministic-variable/7041/4 "2021-03-19T14:17:06Z")

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I could define the model in this way

with pm.Model() as modelo\_complacencia:  
μ = pm.Uniform(‘μ’ , lower = 1, upper= 15)  
σ = pm.Uniform(‘σ’, lower = 1, upper= 15)  
P0 = pm.Normal(‘P0’, mu=μ, sd=σ, observed=data)  
IPVI = pm.Deterministic(‘IPVI’, get\_pvi(μ))  
trace\_g = pm.sample(10)  
az.plot\_trace(trace\_g)

But I think in this model IPVI is a function of the mean value of the prior parameter, Is that OK? I would like to IPVI as a function of a posteriori mean parameter

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**Author:** ![ckrapu](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/ckrapu/32/1366_2.png) [@ckrapu](https://discourse.pymc.io/u/ckrapu)\
**Post date:** [March 19, 2021, 4:25pm UTC](https://discourse.pymc.io/t/problem-with-deterministic-variable/7041/5 "2021-03-19T16:25:24Z")

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Yes! You’ve got it now. That should work better and it also makes sense from a modeling perspective.

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**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:** [March 19, 2021, 6:42pm UTC](https://discourse.pymc.io/t/problem-with-deterministic-variable/7041/6 "2021-03-19T18:42:10Z")

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It will be a function of the p

> [@Francisco](#):
>
> But I think in this model IPVI is a function of the mean value of the prior parameter, Is that OK? I would like to IPVI as a function of a posteriori mean parameter

It will be a function of the posterior `mu` value, since during `pm.sample` you are getting samples of the posterior `mu`

If your `get_pvi` is a vectorized function, you can do this much faster by calling `get_pvi(trace['mu'])` after your sampling is over.

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<div class="post-metadata">

**Author:** ![Francisco](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/francisco/32/3803_2.png) [@Francisco](https://discourse.pymc.io/u/Francisco)\
**Post date:** [March 22, 2021, 10:52pm UTC](https://discourse.pymc.io/t/problem-with-deterministic-variable/7041/7 "2021-03-22T22:52:05Z")

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Ricardo ! Thanl you very much

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**Author:** ![Francisco](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/francisco/32/3803_2.png) [@Francisco](https://discourse.pymc.io/u/Francisco)\
**Post date:** [March 22, 2021, 10:52pm UTC](https://discourse.pymc.io/t/problem-with-deterministic-variable/7041/8 "2021-03-22T22:52:32Z")

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Dear Chris, Thank you!!!