# Model with a loop - scan conversion

**URL:** <https://discourse.pymc.io/t/model-with-a-loop-scan-conversion/17538>\
**Category:** v5\
**Tags:** modeling\
**Created:** [January 25, 2026, 8:49pm UTC](https://discourse.pymc.io/t/model-with-a-loop-scan-conversion/17538 "2026-01-25T20:49:04Z")\
**Posts on this page:** 1\
**Showing post:** 2

<div class="post-metadata">

**Author:** ![jessegrabowski](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/jessegrabowski/32/5010_2.png) [@jessegrabowski](https://discourse.pymc.io/u/jessegrabowski)\
**Post date:** [January 25, 2026, 11:33pm UTC](https://discourse.pymc.io/t/model-with-a-loop-scan-conversion/17538/2 "2026-01-25T23:33:49Z")

</div>

Hey hey

You’re on the right track, but your mental model of what pytensor is is wrong. Amusingly, [my very first post on this forum](https://discourse.pymc.io/t/state-space-models-in-pymc/9146) made the same mistake, so you’re in good company.

Pytensor works by making a graph of symbolic computation. When you do e.g. `z = x + y`, `z` is not a number, it’s a set of instructions describing how `x`, `y`, and `z` are related. You build a computation up bit by bit, using and re-using these computational graphs. When you call `pytensor.function`, you signal that you’re done build and you want to do actual numeric computation from the inputs to the outputs.

So, your proximate error is caused because you are passing _symbolic values_ like `alpha` to your _compiled function_, which is done with symbolic stuff and is now ready for numeric values.

But the ultimately error is that you shouldn’t be doing anything with `pytensor.function` in the context of a pymc model. PyMC is going to compile some function itself, and it can’t see into or use your compiled function. But you don’t need this – instead, you need to keep everything symbolic from start to finish. For example:

```py
import pytensor 
import pytensor.tensor as pt
import numpy as np
import pymc as pm

n = 100
temp_data = np.random.normal(size=(n, ))

with pm.Model() as model:
    alpha = pm.Normal("alpha", mu=2.5, sigma=0.5)
    t_eq = pm.Normal("t_eq", mu=-1.5, sigma=0.5)
    s0 = pm.Normal("s0", mu=100, sigma=20)
    rho0 = pm.TruncatedNormal("rho0", mu=0.5, sigma=0.3, lower=-1, upper=1)
    sigma = pm.TruncatedNormal("sigma", mu=8, sigma=3, lower=0, upper=15)

    temps = pm.Data('temps', temp_data)

    def scan_step(previous_level, alpha, temps, t_eq):
        return previous_level + alpha * (temps - t_eq)
    
    sea_levels = pytensor.scan(scan_step,
                               outputs_info = s0,
                               sequences = temps,
                               non_sequences = [alpha, t_eq],
                               return_updates=False)
    
    hay_stds_diag = pt.eye(n)
    
    sigma_ar_1 = sigma **2 / (1 - rho0** 2)
    powers = pt.arange(1, n+1)
    cov_matrix_hay = sigma_ar_1 * rho0 ** pt.abs(pt.sub.outer(powers, powers)) + hay_stds_diag
    
    sea_level_hat = pm.MvNormal(name='sea_levels',
                                mu=sea_levels,
                                cov=cov_matrix_hay)

```

Some other issues though:

You seem to be computing an AR(1) model twice, once in the mean, then again in the covariance. It seems like you’re mixing a model defined once as a generative model (the AR(1) scan) and a likelihood (the MvNormal with AR(1) covariance matrix)

Using a big covariance matrix to define the observed variable will end up being really slow compared to using pm.AR. You’re essentially making a Gaussian Process by hand. Using a GP would give you access to approximations that could speed things up (like HSGP)

Nitpick: What you call “likelihood” isn’t a likelihood. It’s a symbolic random variable that generates draws from your model. You can check that `pm.draw(likelihood)` does not give back evaluations of the likelihood function. This distribution will be used to compute the likelihood term during estimation, but it’s not there yet.

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_[View the full topic](https://discourse.pymc.io/t/model-with-a-loop-scan-conversion/17538)._