accuracy with 80% specificity compared to an annotated database. Copy-number variation detection Copy-number variations (CNVs) are an abundant form of genome structure variation in humans. A discrete-valued bivariate HMM (dbHMM) was used assigning chromosomal regions to seven distinct states: unaffected regions, deletions, duplications and four transition states. Solving this model using Baum-Welch demonstrated the ability to predict the location of CNV breakpoint to approximately 300 bp from micro-array experiments. This magnitude of resolution enables more precise correlations between different CNVs and across populations than previously possible, allowing the study of CNV population frequencies. It also demonstrated a direct inheritance pattern for a particular CNV. Implementations Accord.NET in C# ghmm C library with Python bindings that supports both discrete and continuous emissions. Jajapy Python library that implements Baum-Welch on various kind of Markov Models ( HMM, MC, MDP, CTMC, GOHMM and MGOHMM). HMMBase package for Julia. HMMFit function in the RHmm package for R. hmmtrain in MATLAB rustbio in Rust See also Viterbi algorithm Hidden Markov model EM algorithm Maximum likelihood Speech recognition Bioinformatics Cryptanalysis References External links A comprehensive review of HMM methods and software in bioinformatics – Profile Hidden Markov Models Early HMM publications by Baum: A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains An inequality with applications to statistical estimation for probabilistic functions of Markov processes and to a model for ecology Statistical Inference for Probabilistic Functions of Finite State Markov Chains The Shannon Lecture by Welch, which speaks to how the algorithm can be implemented efficiently: Hidden Markov Models and the Baum–Welch Algorithm, IEEE Information Theory Society Newsletter, Dec. 2003. An alternative to the Baum–Welch algorithm, the Viterbi Path Counting algorithm: Davis, Richard I. A.; Lovell, Brian C.; "Comparing and evaluating HMM ensemble training algorithms using train and test and condition number criteria", Pattern Analysis and Applications, vol. 6, no. 4, pp. 327–336, 2003. An Interactive Spreadsheet for Teaching the Forward-Backward Algorithm (spreadsheet and article with step-by-step walkthrough) Formal derivation of the Baum–Welch algorithm Implementation of the Baum–Welch algorithm Randomized algorithms Bioinformatics algorithms Markov models