APPLICATION OF DISCRETE HIDDEN MARKOV MODELS IN ANALYZING BLOOD TYPE INHERITANCE PATTERNS

DOI: https://doi.org/10.30598/barekengvol20iss2pp1501–1512
Keywords: Blood type inheritance, Discrete Hidden Markov Model

Abstract

This research investigates the application of a Discrete Hidden Markov Model (DHMM) to analyze inheritance patterns of ABO blood types. Leveraging the DHMM’s ability to model systems with hidden states, the study aims to improve the understanding of blood type inheritance dynamics in populations. The model employs six hidden states representing ABO genotypes (IAIA, IAi, IBIB, IBi, IAIB, and ii) and four observable states corresponding to blood type phenotypes (A, B, AB, and O). The transition and emission matrices followed Mendelian inheritance principles using population allele frequencies, whereas the initial probabilities were computed under Hardy-Weinberg Equilibrium (HWE) assumptions, with parameters calibrated to Indonesian blood type distributions. As a case study, we calculated the likelihood of observing phenotype A across five consecutive generations. Using the forward-backward algorithm, the probability of this sequence was calculated as 19%. The Viterbi algorithm further identified the most probable sequence of hidden genotypes, revealing a transition from the heterozygous IAi to the homozygous IAIA genotype over the five generations. One iteration of the Baum-Welch algorithm improved model accuracy, increasing log-likelihood from -1.661 to 0. Our results demonstrate the DHMM’s efficacy in decoding complex inheritance dynamics and provide a foundation for future population genetics research.

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Published
2026-01-26
How to Cite
[1]
N. Hayati, E. Sulistyono, and A. S. Anggraeni, “APPLICATION OF DISCRETE HIDDEN MARKOV MODELS IN ANALYZING BLOOD TYPE INHERITANCE PATTERNS”, BAREKENG: J. Math. & App., vol. 20, no. 2, pp. 1501–1512, Jan. 2026.
Issue
Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
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Articles

Copyright (c) 2026 Nahrul Hayati, Eko Sulistyono, Andini Setyo Anggraeni

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