# Initial evaluation of model at starting point failed, when attempting to use truncated model

**URL:** <https://discourse.pymc.io/t/initial-evaluation-of-model-at-starting-point-failed-when-attempting-to-use-truncated-model/16066>\
**Category:** version agnostic\
**Created:** [November 4, 2024, 6:25pm UTC](https://discourse.pymc.io/t/initial-evaluation-of-model-at-starting-point-failed-when-attempting-to-use-truncated-model/16066 "2024-11-04T18:25:17Z")\
**Posts on this page:** 8\
**Page:** 1

<div class="post-metadata">

**Author:** ![astro\_student](https://avatars.discourse-cdn.com/v4/letter/a/edb3f5/32.png) [@astro\_student](https://discourse.pymc.io/u/astro_student)\
**Post date:** [November 4, 2024, 6:25pm UTC](https://discourse.pymc.io/t/initial-evaluation-of-model-at-starting-point-failed-when-attempting-to-use-truncated-model/16066/1 "2024-11-04T18:25:17Z")

</div>

I am new to PyMC, and I am attempting to estimate the parameters of a [Generalized Extreme Value distribution](https://www.pymc.io/projects/examples/en/latest/case_studies/GEV.html#id27) for my dataset. My data has been truncated artificially, and so I would like to use a truncated version of this distribution. I am able to estimate parameters for the GEV distribution for my data without truncation, but I am having trouble making the distribution truncated.

The following DOES work, without truncation:

```auto
data = read_in_data() # a numpy array of floats
basic_model = pm.Model()
with basic_model: 
    # Priors 
    mu = pm.Uniform("mu", lower = 1300, upper = 1500)
    sigma = pm.Uniform("sigma", lower = 90, upper = 150)
    xi = pm.TruncatedNormal("chi", mu=0, sigma=0.4, lower=-0.7, upper=0.7)   
    # Estimation
    gev = pmx.GenExtreme("gev", mu=mu, sigma=sigma, xi=xi, observed=data)
    gev_idata = pm.sample()

```

However, I believe my data comes from a truncated GEV distribution. My attempt to use a truncated GEV distribution, after reading the documentation [here](https://www.pymc.io/projects/docs/en/v5.4.0/api/distributions/generated/pymc.Truncated.html) is as follows:

```auto
data = read_in_data() # a numpy array of floats
basic_model = pm.Model()
with basic_model: 
    # Priors 
    mu = pm.Uniform("mu", lower = 1300, upper = 1500)
    sigma = pm.Uniform("sigma", lower = 90, upper = 150)
    xi = pm.TruncatedNormal("xi", mu=0, sigma=0.4, lower=-0.7, upper=0.7)   
    # Estimation
    gev_full = pmx.GenExtreme.dist(mu=mu, sigma=sigma, xi=xi)
    gev = pm.Truncated("gev", gev_full, upper=2000, lower = None, observed=z_ions)
    gev_idata = pm.sample()

```

I get the error:

```auto
SamplingError: Initial evaluation of model at starting point failed!
Starting values:
{'mu_interval__': array(-0.53549444), 'sigma_interval__': array(-0.41259799), 'xi_interval__': array(0.48288129)}

Logp initial evaluation results:
{'mu': -1.46, 'sigma': -1.43, 'xi': -1.18, 'gev': -inf}
You can call `model.debug()` for more details.

```

I’ve got this error many times before, without using the truncated distribution, and never understood why it was trying to evaluate starting values of the parameters outside the distributions I specified. I see that it’s giving an infinite value of the `gev` distribution which is why it is erroring out, but I don’t understand why. In the past, just playing around with the priors for some reason fixed this error, but I can’t seem to find a set of priors that works in this case.

I assume I’m making a rookie mistake in implementing the truncated distribution.  
How can I implement a truncated GEV distribution? Thank you so much in advance!

---

<div class="post-metadata">

**Author:** ![cluhmann](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/cluhmann/32/3083_2.png) [@cluhmann](https://discourse.pymc.io/u/cluhmann)\
**Post date:** [November 4, 2024, 6:59pm UTC](https://discourse.pymc.io/t/initial-evaluation-of-model-at-starting-point-failed-when-attempting-to-use-truncated-model/16066/2 "2024-11-04T18:59:20Z")

</div>

Welcome!

You can simply specify valid starting values for your model parameters. This can either be done on a per-parameter basis:

```python
with pm.Model() as basic_model: 
    # Priors 
    mu = pm.Uniform("mu", lower = 1300, upper = 1500, initval=1400)
    sigma = pm.Uniform("sigma", lower = 90, upper = 150, initval=120)
    xi = pm.TruncatedNormal("xi", mu=0, sigma=0.4, lower=-0.7, upper=0.7, initval=0)
    # Estimation
    gev_full = pmx.GenExtreme.dist(mu=mu, sigma=sigma, xi=xi)
    gev = pm.Truncated("gev", gev_full, upper=2000, lower = None, observed=[1400])
    gev_idata = pm.sample(init="adapt_diag")

```

Or you can do it all in one go when calling `pm.sample()`:

```python
with basic_model:
    gev_idata = pm.sample(init="adapt_diag", initvals={"mu":1400, "sigma":120, "xi":0})

```

In both cases note I have changed the default initialization routine to `init="adapt_diag"`. This is because the default (`init="jitter+adapt_diag"`) will jitter the starting values and thus can still end up in invalid parts of the parameter space.

---

<div class="post-metadata">

**Author:** ![astro\_student](https://avatars.discourse-cdn.com/v4/letter/a/edb3f5/32.png) [@astro\_student](https://discourse.pymc.io/u/astro_student)\
**Post date:** [November 4, 2024, 8:58pm UTC](https://discourse.pymc.io/t/initial-evaluation-of-model-at-starting-point-failed-when-attempting-to-use-truncated-model/16066/3 "2024-11-04T20:58:11Z")

</div>

Thank you so much for the help!  
I attempted to do as you suggested, and replaced the sampling line with (using values that I know these parameters should be very close to):

```auto
gev_idata = pm.sample(init="adapt_diag", initvals={"mu":1440, "sigma":125, "xi":0.03})

```

However, I still get the same error:

```auto
SamplingError: Initial evaluation of model at starting point failed!
Starting values:
{'mu_interval__': array(0.84729786), 'sigma_interval__': array(0.), 'xi_interval__': array(-0.28185115)}

Logp initial evaluation results:
{'mu': -1.56, 'sigma': -1.39, 'xi': -1.16, 'gev': -inf}
You can call `model.debug()` for more details.

```

I don’t understand how it can be picking initial values that aren’t allowed given the priors. For instance, my prior on `mu` is a uniform distribution between 1300 and 1500, yet if I am interpreting the output correctly it is trying to use 0.84729786 as the initial value for `mu`.

---

<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 4, 2024, 9:22pm UTC](https://discourse.pymc.io/t/initial-evaluation-of-model-at-starting-point-failed-when-attempting-to-use-truncated-model/16066/4 "2024-11-04T21:22:56Z")

</div>

The value you’re seeing is on the unconstrained transformed scale, note the ` __interval__ ` suffix

---

<div class="post-metadata">

**Author:** ![astro\_student](https://avatars.discourse-cdn.com/v4/letter/a/edb3f5/32.png) [@astro\_student](https://discourse.pymc.io/u/astro_student)\
**Post date:** [November 4, 2024, 9:36pm UTC](https://discourse.pymc.io/t/initial-evaluation-of-model-at-starting-point-failed-when-attempting-to-use-truncated-model/16066/5 "2024-11-04T21:36:35Z")

</div>

Ok, I see, thank you. I guess regardless of that though, it’s still giving me the `SamplingError`. Do you have any thoughts as to why?

---

<div class="post-metadata">

**Author:** ![cluhmann](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/cluhmann/32/3083_2.png) [@cluhmann](https://discourse.pymc.io/u/cluhmann)\
**Post date:** [November 4, 2024, 10:26pm UTC](https://discourse.pymc.io/t/initial-evaluation-of-model-at-starting-point-failed-when-attempting-to-use-truncated-model/16066/6 "2024-11-04T22:26:06Z")

</div>

> [@astro\_student](#):
>
> I don’t understand how it can be picking initial values that aren’t allowed given the priors.

“It” hasn’t picked any parameter values. It is (now) using the parameter values you have supplied. and the model parameter values are not the problem. The error message tells you the (log) probability of each model parameter and they are all fine. However, the probability of `gev` is `-inf` (i.e., impossible according to your model/parameter values). Because `gev` is an observed variable (rather than a model parameter), this suggests that one or more observations are inconsistent with your model and the starting parameter values. This could happen, for example, if any of your observations are `>2000` (straying outside the interval specified for the truncation transform). But there could be other reasons as well.

---

<div class="post-metadata">

**Author:** ![astro\_student](https://avatars.discourse-cdn.com/v4/letter/a/edb3f5/32.png) [@astro\_student](https://discourse.pymc.io/u/astro_student)\
**Post date:** [November 4, 2024, 10:42pm UTC](https://discourse.pymc.io/t/initial-evaluation-of-model-at-starting-point-failed-when-attempting-to-use-truncated-model/16066/7 "2024-11-04T22:42:50Z")

</div>

Thank you so much! You’re right, the issue is that my dataset does have a few values past 2000. I didn’t realize that would give `inf` values for the truncated distribution. I still want the distribution they are theoretically drawn from to cap at 2000, but that’s an issue with my data not PyMC. Thanks again for your help in pointing this out!

---

<div class="post-metadata">

**Author:** ![cluhmann](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/cluhmann/32/3083_2.png) [@cluhmann](https://discourse.pymc.io/u/cluhmann)\
**Post date:** [November 4, 2024, 11:34pm UTC](https://discourse.pymc.io/t/initial-evaluation-of-model-at-starting-point-failed-when-attempting-to-use-truncated-model/16066/8 "2024-11-04T23:34:23Z")

</div>

> [@astro\_student](#):
>
> I didn’t realize that would give `inf` values for the truncated distribution.

This has nothing to do with the trucation transformation per se. The probability of any “impossible” observation is zero, so `logp==ln(0)==-inf`. This is most commonly seen when feeding parameters that try to move model parameters outside where the associated distributions have support. This is a bit of a contrived example, but it illustrates that you don’t need any explicit transformations:

```python

with pm.Model() as model: 
    # hyper parameter will almost certainly be negative
    sigma = pm.Normal("sigma", mu=-1000, sigma=1)
    # half normal has support on R+ and the observed data
    # is consistent with this support
    # but the negative sigma makes the positive observation "impossible"
    obs = pm.HalfNormal("obs", sigma=sigma, observed=[1])
    pm.sample()

```