# How to use costum logliklihood function effectively using pm.DensityDist

**URL:** <https://discourse.pymc.io/t/how-to-use-costum-logliklihood-function-effectively-using-pm-densitydist/14282>\
**Category:** General\
**Created:** [April 18, 2024, 10:45am UTC](https://discourse.pymc.io/t/how-to-use-costum-logliklihood-function-effectively-using-pm-densitydist/14282 "2024-04-18T10:45:36Z")\
**Posts on this page:** 9\
**Page:** 1

<div class="post-metadata">

**Author:** ![Mahak\_Singh\_Chauhan](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/mahak_singh_chauhan/32/8062_2.png) [@Mahak\_Singh\_Chauhan](https://discourse.pymc.io/u/Mahak_Singh_Chauhan)\
**Post date:** [April 18, 2024, 10:45am UTC](https://discourse.pymc.io/t/how-to-use-costum-logliklihood-function-effectively-using-pm-densitydist/14282/1 "2024-04-18T10:45:36Z")

</div>

In the following code I want to use pm.DensityDist. The parameter B, T, var is the known data which uploaded from directory.

where  
B is a 2D matrix  
T is 1D array  
var is 1D array.

**mp or model is unknown parameter I want to estimate.**

I have following questions:

1. What value/parameter should I pass in “observed” of pm.DensityDist
2. How can I make this code faster as the size of B and T is quite large.

pymc. **version** = ‘5.13.0’

```auto
with basic_model:
    mp = pm.Normal("mp",mu=0, sigma=1, shape=N)
    
    def logp(model, B, T, var):            
        
        NG=len(T)

        data_cal = np.dot(B, model);
        
        data_residuals= data_cal - T;
        cov_m=1/(var)*np.identity(NG);
        factor= -0.5 * np.dot(np.dot(data_residuals.T,covd),data_residuals)
    
        return factor

    loglike = pm.DensityDist('loglike', B, T, var, logp=logp, observed=?)
    trace=pm.sample(100,progressbar=True)

```

Thank you!

---

<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:** [April 18, 2024, 10:55am UTC](https://discourse.pymc.io/t/how-to-use-costum-logliklihood-function-effectively-using-pm-densitydist/14282/2 "2024-04-18T10:55:12Z")

</div>

First things off, the logp must be implemented with PyTensor variables and operations.

If you don’t know what `observed` should be, it probably means you don’t have a typical random variable that is being observed. Instead you can use `pm.Potential` with the logp (which still has to be defined with PyTensor variables and operations)

Before continuing with either approach, is there a generative model that you can define instead with pure PyMC building blocks? This looks like some sort of linear regression?

---

<div class="post-metadata">

**Author:** ![Mahak\_Singh\_Chauhan](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/mahak_singh_chauhan/32/8062_2.png) [@Mahak\_Singh\_Chauhan](https://discourse.pymc.io/u/Mahak_Singh_Chauhan)\
**Post date:** [April 18, 2024, 11:10am UTC](https://discourse.pymc.io/t/how-to-use-costum-logliklihood-function-effectively-using-pm-densitydist/14282/3 "2024-04-18T11:10:35Z")

</div>

Thank you for your kind reply.

Yes, you are right. This is like a linear regression. I have the matrix B and need to find some coefficients (a: 1D array) which can fit the the “T” by minimizing error ||T - B\*a||.

I am new to pymc just trying to learn how can I solve this problem effectively. Kindly suggest if there is another method for this particular problem within the Bayesian framework which I can use.

Thank you!

---

<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:** [April 18, 2024, 11:35am UTC](https://discourse.pymc.io/t/how-to-use-costum-logliklihood-function-effectively-using-pm-densitydist/14282/4 "2024-04-18T11:35:20Z")

</div>

I suggest browsing :

> **[PyMC Example Gallery](https://www.pymc.io/projects/examples/en/latest/gallery.html#generalized-linear-models)**
>
> Introductory: General Overview Simple Linear Regression General API quickstart Library Fundamentals: Distribution Dimensionality PyMC and PyTensor Using Data Containers How to: Prior and Posterior ...

This is the most beginner one: [GLM: Linear regression — PyMC 5.13.1 documentation](https://www.pymc.io/projects/docs/en/stable/learn/core_notebooks/GLM_linear.html)

---

<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:** [April 18, 2024, 11:37am UTC](https://discourse.pymc.io/t/how-to-use-costum-logliklihood-function-effectively-using-pm-densitydist/14282/5 "2024-04-18T11:37:02Z")

</div>

You’ll notice none of those examples implement CustomDist, they always use PyMC building blocks. That’s definitely what we would recommend for 99.999% of users and 100% of beginner ones

---

<div class="post-metadata">

**Author:** ![Mahak\_Singh\_Chauhan](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/mahak_singh_chauhan/32/8062_2.png) [@Mahak\_Singh\_Chauhan](https://discourse.pymc.io/u/Mahak_Singh_Chauhan)\
**Post date:** [April 18, 2024, 11:54am UTC](https://discourse.pymc.io/t/how-to-use-costum-logliklihood-function-effectively-using-pm-densitydist/14282/6 "2024-04-18T11:54:38Z")

</div>

Thank you for your suggestion. Following one of the example, I have wrote the following code:

```auto
with basic_model:
    # Priors for the parameters
    mp = pm.Normal("mp",mu=0, sigma=1, shape=N)

    # Define linear model
    y_est = pt.tensor.dot(B,mp)

    # Define Normal likelihood
    pm.Normal("y", mu=y_est, sigma=cov_data, observed=T)

with basic_model:
    trc_ols = pm.sample(
        tune=5000,
        draws=500,
        chains=4,
        cores=4,
        init="advi+adapt_diag",
        n_init=50000,
    )

```

The size of B is 18965X1625.  
cov\_data is the measurement errors of T.

I have a decent computer and code is showing me more than 6 hours to complete. is it normal for this size of data? Can you please suggest where can I improve it? Just to begin with.

This is my last question regarding this post.

Thank you

---

<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:** [April 18, 2024, 12:06pm UTC](https://discourse.pymc.io/t/how-to-use-costum-logliklihood-function-effectively-using-pm-densitydist/14282/7 "2024-04-18T12:06:28Z")

</div>

1.6k features? That’s quite a lot. Probably a lot of redundancy in there?

You may need to do some feature engineering, or find more structured priors for `mp`. Also are you sure about `sigma` being fixed? That’s usually also inferred.

Besides that:

1. Do you get a warning about blas when you import PyMC? If so you should reinstall using the official instructions: [Installation — PyMC 5.13.1 documentation](https://www.pymc.io/projects/docs/en/stable/installation.html)
2. Do you have a CUDA GPU? Pick Numpyro as the sampler, so your GPU can crunch through that huge matmul: [Faster Sampling with JAX and Numba — PyMC example gallery](https://www.pymc.io/projects/examples/en/latest/samplers/fast_sampling_with_jax_and_numba.html)

---

<div class="post-metadata">

**Author:** ![Mahak\_Singh\_Chauhan](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/mahak_singh_chauhan/32/8062_2.png) [@Mahak\_Singh\_Chauhan](https://discourse.pymc.io/u/Mahak_Singh_Chauhan)\
**Post date:** [April 18, 2024, 12:15pm UTC](https://discourse.pymc.io/t/how-to-use-costum-logliklihood-function-effectively-using-pm-densitydist/14282/8 "2024-04-18T12:15:49Z")

</div>

Thanks again for your reply.

1. Yes, I have variance of data which I want to use in likelihood function through Diagonal covariance matrix,

2. I have installed pymc following the documentation you suggested. After importing the following libraries I do get some warnings:

```auto
import pymc as pm
import arviz as az
import pandas as pd
basic_model = pm.Model()
import pytensor as pt

```

```auto
WARNING (pytensor.configdefaults): g++ not detected! PyTensor will be unable to compile C-implementations and will default to Python. Performance may be severely degraded. To remove this warning, set PyTensor flags cxx to an empty string.
WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.

```

1. I have only workstation with capacity in attached file.

![PC](https://canada1.discourse-cdn.com/flex036/uploads/pymc3/original/2X/6/660aacebe21894bbc4b99008d4150dbeac21707b.png)

Thank you  
Regards

---

<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:** [April 18, 2024, 12:17pm UTC](https://discourse.pymc.io/t/how-to-use-costum-logliklihood-function-effectively-using-pm-densitydist/14282/9 "2024-04-18T12:17:32Z")

</div>

You are not installing correctly, or are not linking to the right environment (if on a jupyter notebook). Those warnings shouldn’t be there, and indicate you will have significant slow down on models that rely mostly on matmul like yours.