Bayesian Model Comparison for Isthmian Script Language Affiliation

1. -Author: Dr. Chem Vatho (PhD in Phonetics, University of Cologne: 2022-25)
2. -Submission for Posdoctoral position: Research Proposal for VolkswagenStiftung Project
3. -Project: Exploring an unknown language in an unknown writing system: The Isthmus script
4. -Institution: University of Cologne, Department of Linguistics
5. -Led by: Dr. Svenja Bonmann

A computational approach to evaluating competing language family hypotheses for the undeciphered Isthmian (Epi-Olmec) script using Bayesian phonotactic analysis.

Overview

The Isthmian script (also called Epi-Olmec) is an undeciphered writing system from ancient Mesoamerica (500 BCE – 500 CE). Despite several long inscriptions, including La Mojarra Stela 1 (~535 signs) and the Tuxtla Statuette (~75 signs), the linguistic affiliation remains contested.

This project implements a Bayesian model comparison framework that evaluates statistical patterns in the script against typological expectations from candidate language families—without requiring proposed sign readings.

The Problem

Vonk (2020) demonstrated that the Isthmian corpus is too small for unique decipherment:

qW = distinct signs / total attestations ≈ 160/700 ≈ 0.23 >> 0.1 (threshold)

This means traditional sign-value decipherment cannot discriminate between language families. Both Mixe-Zoquean (Justeson & Kaufman 1993) and Huastecan (Vonk 2020) readings can be made to fit the data.

Our Approach

Instead of assigning phonetic values, we analyze distributional features:

• Segment length statistics (using MS20 as boundary marker)
• Positional entropy (initial/final sign distributions)
• Bigram transition probabilities
• Frequency concentration patterns

These features are compared against phonotactic priors derived from Proto-Mixe-Zoquean and Proto-Huastecan reconstructions.

Key Findings

Preliminary Results (Exploratory)

Language Family	Log Evidence	Rank
Proto-Mixe-Zoquean	−44.41	1
Proto-Huastecan	−49.61	2

⚠️ Important Caveat: These results use hypothetical priors, not empirically-derived corpus statistics. The analysis is exploratory and requires validation.

Critical Methodological Issue: What Does MS20 Mark?

The validity of the analysis depends on interpreting MS20 (the most frequent sign). Our comparison with Maya script reveals:

Feature	Maya Script	Isthmian Script
Word boundary marker	NONE	MS20 (disputed)
Visual word unit	Glyph block	Unknown
Script type	Logosyllabic (deciphered)	Logosyllabic (assumed)

Key insight: Maya (the only deciphered Mesoamerican script) has no boundary marker. MS20 is therefore either:

1. A unique Isthmian innovation, OR
2. Serves a different purpose than word boundaries

The segment length analysis (~5 signs/segment) supports the word-boundary hypothesis but does not prove it.

Repository Contents

├── README.md                               # This file
├── isthmian_bayesian_with_maya_comparison.ipynb  # Main analysis notebook (Google Colab)
├── Research_Proposal_With_Maya.docx        # Full research proposal document
│
└── data/
    ├── sign_sequences.csv                  # Complete sign sequences (576 tokens)
    ├── verified_isthmian_frequencies.csv   # Verified frequencies from R52/R53
    ├── corpus_statistics.csv               # Summary statistics
    ├── isthmus_unigram_counts.csv          # Sign frequency counts
    ├── isthmus_bigram_counts.csv           # Sign pair frequencies
    ├── isthmus_segments_cleaned.csv        # MS20-delimited segments
    ├── real_proto_mixe_zoquean.csv         # Proto-MZ lexical data
    ├── real_proto_huastecan.csv            # Proto-Huastecan lexical data
    └── real_sign_inventory_r53.csv         # Sign inventory from R53

Data Files Description

File	Description	Rows	Key Columns
sign_sequences.csv	Token-level sign data	576	text_id, column, sign_token, is_boundary_MS20
verified_isthmian_frequencies.csv	Official counts from R52/R53	9	sign, count, source
corpus_statistics.csv	Summary metrics	32	category, metric, value
isthmus_unigram_counts.csv	Sign frequencies	~170	token, count, prob_mle
isthmus_bigram_counts.csv	Sign pair frequencies	~400	bigram, count

Corpus Overview

Text	Tokens	MS20 Boundaries	Date
La Mojarra Stela 1	403	35	156 CE
Feldspar Mask	86	0	Unknown
Tuxtla Statuette	59	9	162 CE
Ceramic Mask	23	0	Unknown
Chiapa de Corzo	5	1	36 BCE
Total	576	45	—

Note: The Feldspar Mask and Ceramic Mask contain NO MS20 boundary markers, which is significant for interpreting MS20's function.

Getting Started

Option 1: Google Colab (Recommended)

1. Open isthmian_bayesian_with_maya_comparison.ipynb in Google Colab
2. Run all cells—no installation required
3. The notebook includes embedded data; no file uploads needed for basic analysis

Option 2: Local Installation

# Clone the repository
git clone https://github.com/[username]/isthmian-bayesian.git
cd isthmian-bayesian

# Create virtual environment
python -m venv venv
source venv/bin/activate  # On Windows: venv\Scripts\activate

# Install dependencies
pip install numpy scipy pandas matplotlib seaborn

Data Input Options

The notebook supports four data input methods:

Option	Description	Use Case
A	Upload CSV files	Use sign_sequences.csv from this repo
B	Parse PDF articles	Extract from Macri (2017) PDFs
C	Embedded sequences	Quick start, no uploads needed
D	Verified frequencies	Uses confirmed counts from R52/R53

Quick Start with Repository Data

# Load the sign sequences
import pandas as pd
df = pd.read_csv('data/sign_sequences.csv')

# Filter to non-eroded signs only
df_clean = df[df['is_eroded'] == 0]

# Get segment statistics
segments = df_clean.groupby('segment_id').size()
print(f"Mean segment length: {segments.mean():.2f}")
print(f"Number of segments: {len(segments)}")

Methodology

1. Feature Extraction

# Features extracted from Isthmian corpus
features = {
    'segment_length_mean': 5.06,    # Signs per MS20-delimited segment
    'segment_length_std': 4.12,     # Variance in segment length
    'final_entropy': 4.33,          # Uncertainty at segment-final position
    'initial_entropy': 5.12,        # Uncertainty at segment-initial position
    'bigram_entropy': 8.57,         # Predictability of sign transitions
}

2. Phonotactic Priors

Priors are derived from typological characteristics:

Feature	Proto-MZ Prior	Proto-Huastecan Prior
Segment length	μ=5.0, σ=1.5	μ=6.0, σ=2.0
Final entropy	μ=2.0, σ=0.5	μ=1.8, σ=0.4
Bigram entropy	μ=4.5, σ=1.0	μ=4.0, σ=1.0

3. Bayesian Model Comparison

Using Normal-Normal conjugacy:

P(H|Data) ∝ P(Data|H) × P(H)

Log Evidence = Σ [ -½ log(σ²_prior + σ²_obs) - (μ_obs - μ_prior)² / 2(σ²_prior + σ²_obs) ]

Bayes Factor interpretation (Kass & Raftery 1995):

• BF > 100: Decisive evidence
• BF 10-100: Strong evidence
• BF 3-10: Moderate evidence
• BF 1-3: Weak evidence

Limitations and Future Work

Current Limitations

1. Priors are hypothetical — derived from typological generalizations, not actual proto-lexicon statistics
2. MS20 interpretation uncertain — could mark words, phrases, or graphic units
3. Data incompleteness — current dataset is ~22% incomplete compared to R53 official counts
4. No validation — methodology not yet tested on known scripts

Proposed Validation

Test the methodology on Maya script (where the answer is known):

1. Treat Maya inscriptions as "undeciphered"
2. Apply the same Bayesian analysis
3. Check if it correctly identifies the language as Mayan

Research Questions

1. Can empirically-derived priors from proto-lexicon corpora improve discrimination?
2. Does Vonk's qW limitation extend to distributional methods?
3. What proportion of Isthmian signs are logographic vs. syllabic?

References

Primary Sources

• Justeson, J. S., & Kaufman, T. S. (1993). A decipherment of Epi-Olmec hieroglyphic writing. Science, 259(5102), 1703–1711.
• Houston, S. D., & Coe, M. D. (2003). Has Isthmian writing been deciphered? Mexicon, 25(6), 151–161.
• Vonk, T. (2020). Yet another "decipherment" of the Isthmian writing system. Unpublished manuscript.
• Macri, M. J. (2017a–d). Glyph Dwellers Reports 51–54. UC Davis.

Comparative Data

• Wichmann, S. (1995). The relationship among the Mixe-Zoquean languages. University of Utah Press.
• Kaufman, T., & Norman, W. (1984). An outline of Proto-Cholan phonology, morphology and vocabulary. In Phoneticism in Mayan hieroglyphic writing.

Methodology

• Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90(430), 773–795.

Contributing

Contributions are welcome! Please feel free to submit issues or pull requests for:

• Bug fixes in the analysis code
• Improved prior specifications
• Additional data sources
• Validation experiments

License

This project is licensed under the MIT License - see the LICENSE file for details.

Acknowledgments

This research is conducted as part of a postdoctoral proposal for the VolkswagenStiftung-funded project "Exploring an unknown language in an unknown writing system: The Isthmus script" at the University of Cologne.

Citation

If you use this code or methodology, please cite:

@software{isthmian_bayesian,
  author = {[Chem Vatho]},
  title = {Bayesian Model Comparison for Isthmian Script Language Affiliation},
  year = {2025},
  url = {https://github.com/chemvatho/isthmian-script}
}

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Note: This is exploratory research. The results should be interpreted as conditional conclusions dependent on unvalidated assumptions about the MS20 boundary marker and phonotactic priors.