# Detail: Bayes (Multinomial) Instantiated Model

This page describes **Bayes (multinomial) instantiated models** in the
**Instantiated Model** box. These are **discrete Bayesian networks that have been
estimated on a dataset**, starting from a Bayes parametric model.

```{figure} ../../_static/images/tetrad-interface/box-by-box/bayes-im.png
:name: tetrad-bayes-instantiated-model-screenshot
:alt: Bayes Instantiated Model

Bayes (Multinomial) Instantiated Model
```

An instantiated Bayes model consists of:

- A **graph structure** over discrete variables.
- A collection of **multinomial conditional probability tables (CPTs)** with
  concrete probability values.
- Optionally, summary quantities such as the **log-likelihood** or **BIC** for a
  particular dataset.

## How Bayes instantiated models are created

1. In the **Parametric Model** box, create a **Bayes (multinomial)** model whose
   structure and state spaces match your discrete graph and data.
2. In the **Estimator** box, select:
   - The Bayes parametric model, and
   - A discrete dataset (from the *Data* box).
3. Run an appropriate estimator (e.g., maximum likelihood or a Bayesian
   estimator).  
   The output is a **fitted Bayes model**.
4. Save or send this result to the **Instantiated Model** box, where it appears
   as a Bayes instantiated model.

Each instantiated model is tied to the dataset and estimator that produced it.

## Instantiated Model box layout (Bayes)

When you select a Bayes instantiated model in the Instantiated Model box, the
main panel typically shows:

- A list of variables with their **state spaces**.
- For each variable:
  - The **parent set**.
  - The **estimated CPT** for \(P(X \mid 	ext{Parents}(X))\), with one row per
    parent configuration and one column per child state.
- Optional summary information, such as:
  - Log-likelihood or average log-likelihood on the data.
  - Penalty-based scores (e.g., BIC) if your setup computes them.

The entries in the CPTs are now **fixed, estimated probabilities**, not free
parameters as in the parametric model view.

## Typical uses

Bayes instantiated models are useful when you want to:

- **Inspect fitted CPTs** to see how the data support various conditional
  relationships.
- **Simulate new discrete datasets** from the fitted Bayesian network
  (via the *Simulation* box).
- **Compare multiple fitted Bayes models** using the *Compare* box,
  for example by BIC or predictive performance.

## Tips

- Make sure the **state labels** and ordering in the data and parametric model
  agree; otherwise estimation can silently misalign probabilities.
- If you fit the same Bayes parametric model to multiple datasets, keep each
  instantiated model separate and use descriptive names indicating the dataset
  and estimator.