`multinomial_dirichlet_inputs` should handle categorical/string data

[williambdean]

Summary

The multinomial_dirichlet_inputs helper is currently an identity function that doesn't process data, but the documentation suggests it can handle raw categorical data like string labels.

Current Behavior

from conjugate.helpers import multinomial_dirichlet_inputs

# This is what the helper actually does:
counts = [5, 3, 8, 2]
inputs = multinomial_dirichlet_inputs(counts)
# Returns: {'x': [5, 3, 8, 2]}  # Just wraps in dict

# This does NOT work despite documentation suggesting it:
responses = ['Excellent', 'Good', 'Fair', 'Good', 'Excellent']
inputs = multinomial_dirichlet_inputs(responses)
# Returns: {'x': ['Excellent', 'Good', 'Fair', 'Good', 'Excellent']}
# This will FAIL when passed to the model!

Documentation Shows Different Usage

From docs/examples/raw-data-workflow.md:

responses = ['Excellent', 'Good', 'Fair', 'Good', ...]
inputs = multinomial_dirichlet_inputs(responses)  # Implied to work

# But then manually counts anyway:
from collections import Counter
counts = Counter(responses)
response_counts = [responses.count(cat) for cat in categories]

This contradicts the "automatic extraction" promise of the helpers module.

Expected Behavior

The helper should optionally accept categorical data and convert to counts:

# Option 1: Auto-detect and count unique values
responses = ['A', 'B', 'A', 'C', 'B', 'A']
inputs = multinomial_dirichlet_inputs(responses)
# Returns: {'x': [3, 2, 1]}  # Counts for A, B, C

# Option 2: Specify categories explicitly for ordering
inputs = multinomial_dirichlet_inputs(responses, categories=['A', 'B', 'C'])
# Returns: {'x': [3, 2, 1]}

Suggested Fix

def multinomial_dirichlet_inputs(x, *, categories=None):
    """Extract sufficient statistics for multinomial_dirichlet model.
    
    Args:
        x: Either counts array or categorical observations (strings/labels)
        categories: If x contains categorical data, specify category order.
                   If None and x contains non-numeric data, auto-detect categories.
    
    Returns:
        Dict with key 'x' containing counts for each category
    """
    if categories is not None:
        # Convert categorical to counts
        x_list = list(x)
        x = [x_list.count(cat) for cat in categories]
    elif hasattr(x, '__iter__') and len(x) > 0:
        # Auto-detect if first element is string-like
        first = next(iter(x))
        if isinstance(first, str):
            from collections import Counter
            counts = Counter(x)
            x = list(counts.values())
    
    return {"x": x}

Alternative

If the helper should remain simple, update documentation to clearly show:

1. Helper only accepts pre-counted arrays
2. Show manual counting as the expected pattern

Also Affects

• categorical_dirichlet_inputs - same issue