# Detail: Bayes (Multinomial) Parametric Model

This page describes the **Bayes (multinomial)** model type in the **Parametric Model** and
**Instantiated Model** boxes. These models represent **discrete Bayesian networks** where each
variable has a finite set of states and is parameterized by **multinomial conditional probability
tables (CPTs)**.

```{figure} ../../_static/images/tetrad-interface/box-by-box/bayes-pm.png
:name: tetrad-bayes-pm-screenshot
:alt: Bayes (Multinomial) Parametric Model

Bayes (Multinomial) Parametric Model
```

## When to use Bayes models

Use the Bayes model family when:

- All variables in the model are **discrete** (categorical with a small number of levels), and
- You want a **Bayesian network** parameterization with CPTs of the form  
  \( P(X \mid 	ext{Parents}(X)) \).

Typical examples include:

- Discrete simulations with known probability tables.
- Evaluating discrete search algorithms (e.g., BDe/BDeu-style scores).
- Teaching or demos of small Bayesian networks.

## Main panel layout

When you select a Bayes parametric model, the main panel typically shows:

- A list of variables and their **state spaces**.
- For each variable:
  - The set of **parent configurations**.
  - A CPT editor with the **probabilities of the child states** for each parent configuration.
- Controls to:
  - Normalize probabilities in a row.
  - Copy/paste rows or tables.
  - Optionally randomize or reset CPTs.

(In an instantiated model, you will additionally see fit-related information, such as log-likelihood
on a dataset, when available.)

## Typical workflow

1. **Create a Bayes parametric model**
   - Start from a discrete graph in the *Graph* box (all variables discrete).
   - In the *Parametric Model* box, choose **New → Bayes (multinomial)** to build CPTs with a default
     parameterization (often uniform or lightly perturbed).

2. **Edit CPTs**
   - Select each variable and edit its CPT rows to reflect your prior knowledge or simulation design.
   - Make sure each row sums to 1; use the normalization tools if provided.

3. **Estimate from data (optional)**
   - Pass the Bayes parametric model to the *Estimator* box and fit the CPTs from discrete data
     using maximum likelihood or Bayesian estimators (depending on what your setup supports).

4. **Use in Simulation or Compare**
   - Use the fitted or hand-specified Bayes model in the *Simulation* box to generate discrete data.
   - Use *Compare* to evaluate search algorithms that attempt to recover the structure or parameters.

## Tips and caveats

- Keep the **number of parents per node modest**, as CPT size grows exponentially with the number of
  parents.
- Ensure that the **state labels in the model match the data** exactly (including spelling and
  capitalization) before attempting estimation.
- If you have mixed discrete/continuous data, consider the **Hybrid (conditional Gaussian)**
  model family instead of pure Bayes.