# Hidden Markov Model

The hidden Markov Ising model makes an Ising model, a binary graphical model from statistical physics, the emission distribution of a hidden Markov chain, so that a binary network's dependence structure is modeled directly as its state changes over time. Because the Ising normalizing constant grows exponentially with the number of nodes, fitting uses pseudolikelihood inside Baum-Welch reestimation, with results on the algorithm's validity, model identifiability and large-network consistency. Exogenous covariates extend it to a hidden Markov autologistic model, applied to a five-year sequence of weekly gun-death events across 3109 continental U.S. counties from 2021 to 2025, where it identifies state changes in gun violence activity.

The hidden Markov Ising model makes an Ising model, a binary graphical model from statistical physics, the emission distribution of a hidden Markov chain, so that a binary network's dependence structure is modeled directly as its state changes over time. Because the Ising normalizing constant grows exponentially with the number of nodes, fitting uses pseudolikelihood inside Baum-Welch reestimation, with results on the algorithm's validity, model identifiability and large-network consistency. Exogenous covariates extend it to a hidden Markov autologistic model, applied to a five-year sequence of weekly gun-death events across 3109 continental U.S. counties from 2021 to 2025, where it identifies state changes in gun violence activity.

Long-read DNA often carries frameshift errors, and aligning it to protein family profiles has meant either translating six reading frames or correcting errors first, both of which cost sensitivity. DUMMEST follows DUMMER's length-bias-free alignment idea and adds nucleotide-emitting indel states to the match, insert and delete states, approximating frameshifts with combinations of nucleotides and codons, with GPU-accelerated MMseqs2 multistage prefiltering. On simulated long reads it detects more alignments with greater average length, matches BATH in sensitivity, improves specificity under simulated sequencing artifacts, and runs 2–12× faster depending on dataset.

Long-read DNA often carries frameshift errors, and aligning it to protein family profiles has meant either translating six reading frames or correcting errors first, both of which cost sensitivity. DUMMEST follows DUMMER's length-bias-free alignment idea and adds nucleotide-emitting indel states to the match, insert and delete states, approximating frameshifts with combinations of nucleotides and codons, with GPU-accelerated MMseqs2 multistage prefiltering. On simulated long reads it detects more alignments with greater average length, matches BATH in sensitivity, improves specificity under simulated sequencing artifacts, and runs 2–12× faster depending on dataset.