Abstract
Hidden Markov Models (HMMs) can be used to solve a variety of problems from facial recognition and language translation to animal movement characterization and gene discovery. With such problems, we have a sequence of observations that we are not certain is correct—we are not sure our observations accurately reveal the corresponding sequence of actual states, which are hidden—but we do know some important probabilities that will help us. In this chapter, we will develop the probability theory and algorithms for two types of problems that HMMs can solve—calculate the probability that a particular sequence of observations occurs and determine the most likely corresponding sequence of hidden states. The chapter will end with a collection of research projects appropriate for undergraduates.
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References
B10NUMB3R5: the database of useful biological numbers. http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=105336&ver=2
Centers for Disease Control and Prevention: 2–20 years: girls stature-for-age and weight-for-age percentiles. https://www.cdc.gov/growthcharts/data/set2clinical/cj41c072.pdf
Cerulo, L., Ceccarelli, M., Di Penta, M., Canfora, G.: A hidden Markov model to detect coded information islands. In: Source Code Analysis and Manipulation (SCAM) IEEE 13th International Working Conference on Source Code Analysis and Manipulation: 157–166. https://doi.org/10.1109/SCAM.2013.6648197 (2013)
Durbin, R., Eddy, S.R., Krogh, A., Mitchison, G.: Biological Sequence Analysis. Cambridge University Press, Cambridge (1998)
Eddy, S.R.: What is a hidden Markov model? Nat Biotechnol. 22(10), 1315–6 (2004) https://doi.org/10.1038/nbt1004-1315
Fosler-Lussier, E.: Markov models and hidden Markov models: a brief tutorial. International Computer Science Inst. http://di.ubi.pt/~jpaulo/competence/tutorials/hmm-tutorial-1.pdf
Gardiner-Garden, M., Frommer, M. CpG islands in vertebrate genomes. J. Mol. Biol. 196, 261–282 (1987)
Huson, D.: Chapter 8: Markov chains and hidden Markov models. In course: Algorithms in Bioinformatics University of Tübingen. https://ab.inf.uni-tuebingen.de/teaching/ss08/gbi/script/chapter08-hmms.pdf
Langrock, R., King, R., Matthiopoulos, J., Thomas, L., Fortin, D., Morales, J.M.: Flexible and practical modeling of animal telemetry data: hidden Markov models and extensions. Ecology, 93:2336–2342 (2012)
Lyngsø, R.: “Hidden Markov models.” http://www.stats.ox.ac.uk/~mcvean/DTC/STAT/Lectures/Weds_wk2/hidden_markov_models.pdf
Morales, J.M., Haydon, D.T., Frair, J.L., Holsinger, K.E., Fryxell, J.M.: Extracting more out of relocation data: building movement models as mixtures of random walks. Ecology 85:2436–2445 (2004)
NetLogo home page. https://ccl.northwestern.edu/netlogo/
Stamp, M.: A revealing introduction to hidden Markov models. https://www.cs.sjsu.edu/~stamp/RUA/HMM.pdf
Shiflet, A.: Accessing Chromosome 19 data. AccessingChr19Data.pdf in https://ics.wofford-ecs.org/files/HMM.zip
Shiflet, A.: Possible transition matrices for samples within and not within CpG islands. ProbabilitiesHumanPN.txt in https://ics.wofford-ecs.org/files/HMM.zip
Shiflet, A.: Transition matrix and other data from Hudson. ProbabilitiesHumanV.txt in https://ics.wofford-ecs.org/files/HMM.zip
Shiflet, A.: Telemetry program telemetry.nlogo in NetLogo. telemetry.nlogo in https://wofford-ecs.org/files/HMM.zip
Shiflet, A. Using a NetLogo program. UsingNetLogo.pdf in https://ics.wofford-ecs.org/files/HMM.zip
Shiflet, A., Shiflet, G. Introduction to Computational Science: Modeling and Simulation for the Sciences, 2nd ed., Princeton University Press (2014)
Shiflet, A., Shiflet, G. NetLogo agent-based files. https://ics.wofford-ecs.org/agent/NetLogo
Stanke, M.: Markov chains and hidden Markov models, Free University of Berlin. http://www.mi.fu-berlin.de/wiki/pub/ABI/HiddenMarkovModelsWS13/script.pdf
Sungkaworn, T., Jobin, M.L., Burnecki, K., Weron, A., Lohse, M.J., Calebiro, D.: Single-molecule imaging reveals receptor-G protein interactions at cell surface hot spots. Nature 550(7677) 543–547 (2017)
UCSC Genome Browser. https://genome.ucsc.edu/cgi-bin/hgGateway
Acknowledgements
Our thanks go to the Fulbright Specialist Program, University “Magna Græcia” of Catanzaro, and Wofford College for funding the Shiflets’ visit to the university and to the National Computational Science Institute Blue Waters Student Internship Program for funding Dmitriy Kaplun’s internship.
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Shiflet, A.B., Shiflet, G.W., Cannataro, M., Guzzi, P.H., Zucco, C., Kaplun, D.A. (2020). What Are the Chances?—Hidden Markov Models. In: Callender Highlander, H., Capaldi, A., Diaz Eaton, C. (eds) An Introduction to Undergraduate Research in Computational and Mathematical Biology. Foundations for Undergraduate Research in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-33645-5_8
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