Statistical comparison of Hidden Markov Models via Fragment Analysis
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912353910521856 |
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| author | Hernandez-Suarez, Carlos M. Montesinos-López, Osval A. |
| author_facet | Hernandez-Suarez, Carlos M. Montesinos-López, Osval A. |
| contents | Standard practice in Hidden Markov Model (HMM) selection favors the candidate with the highest full-sequence likelihood, although this is equivalent to making a decision based on a single realization. We introduce a \emph{fragment-based} framework that redefines model selection as a formal statistical comparison. For an unknown true model $\mathrm{HMM}_0$ and a candidate $\mathrm{HMM}_j$, let $μ_j(r)$ denote the probability that $\mathrm{HMM}_j$ and $\mathrm{HMM}_0$ generate the same sequence of length~$r$. We show that if $\mathrm{HMM}_i$ is closer to $\mathrm{HMM}_0$ than $\mathrm{HMM}_j$, there exists a threshold $r^{*}$ -- often small -- such that $μ_i(r)>μ_j(r)$ for all $r\geq r^{*}$. Sampling $k$ independent fragments yields unbiased estimators $\hatμ_j(r)$ whose differences are asymptotically normal, enabling a straightforward $Z$-test for the hypothesis $H_0\!:\,μ_i(r)=μ_j(r)$. By evaluating only short subsequences, the procedure circumvents full-sequence likelihood computation and provides valid $p$-values for model comparison. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21046 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Statistical comparison of Hidden Markov Models via Fragment Analysis Hernandez-Suarez, Carlos M. Montesinos-López, Osval A. Methodology Statistics Theory 62M05, 62F03, 62F12 Standard practice in Hidden Markov Model (HMM) selection favors the candidate with the highest full-sequence likelihood, although this is equivalent to making a decision based on a single realization. We introduce a \emph{fragment-based} framework that redefines model selection as a formal statistical comparison. For an unknown true model $\mathrm{HMM}_0$ and a candidate $\mathrm{HMM}_j$, let $μ_j(r)$ denote the probability that $\mathrm{HMM}_j$ and $\mathrm{HMM}_0$ generate the same sequence of length~$r$. We show that if $\mathrm{HMM}_i$ is closer to $\mathrm{HMM}_0$ than $\mathrm{HMM}_j$, there exists a threshold $r^{*}$ -- often small -- such that $μ_i(r)>μ_j(r)$ for all $r\geq r^{*}$. Sampling $k$ independent fragments yields unbiased estimators $\hatμ_j(r)$ whose differences are asymptotically normal, enabling a straightforward $Z$-test for the hypothesis $H_0\!:\,μ_i(r)=μ_j(r)$. By evaluating only short subsequences, the procedure circumvents full-sequence likelihood computation and provides valid $p$-values for model comparison. |
| title | Statistical comparison of Hidden Markov Models via Fragment Analysis |
| topic | Methodology Statistics Theory 62M05, 62F03, 62F12 |
| url | https://arxiv.org/abs/2504.21046 |