Hidden Markov models in DNA sequence segmentation modeling Dr Darfiana Nur

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1 Hidden Markov model in DNA equence egmenaion modeling Dr Darfiana Nur Lecurer in Saiic School of Mahemaical and hyical Science The Univeriy of Newcale Auralia

2 Reearch inere Since Nonlinear ime erie modeling Ergodiciy/aionariy condiion Adapive eimaion in nonlinear ime erie model Since 999. Markov Chain Mone Carlo (MCMC) convergence diagnoic Since he end DNA equence analyi ASEARC Workhop

3 Reearch aciviie : Nonlinear TS and MCMC ublicaion: D.Nur K.L.Mengeren and R.C.Wolff (2005). hae Randomiaion : A Convergence Diagnoic for MCMC. Auralian and New Zealand Journal of Saiic Volume 47 Number 3 Sepember 2005 pp (5). D. Nur R.C.Wolff and K.L.Mengeren (200). hae Randomiaion : Numerical Reul of Higher Cumulan Behaviour. Compuaional Saiic and Daa Analyi 37/ R.C.Wolff D. Nur and K.L.Mengeren (200). Aemen of MCMC convergence : a ime erie and dynamical yem approach. roceeding of he h IEEE Workhop on Saiical Signal roceing. Singapore 6-8 Augu 200 pp D. Nur M.G.Nair and N.D.Yaawara (2008?) Efficien Eimaion in Smooh Threhold Auoregreive model. Acceped in Journ of Sa racice and Theory. Some conference paper Ongoing aciviy : Adapive eimaion in Smooh Threhold AR() model wih GARCHerror. Ongoing projec in collaboraion wih A/rof Yan-Xia Lin Univeriy of Wollongong ASEARC Workhop

4 Reearch aciviie : DNA equence modeling in 2007 Conference paper in 2007 : Seniiviy of prior in Bayeian analyi of DNA equence egmenaion. Inernaional Saiical Iniue Meeing 2007 Augu Libon orugal A rior eniiviy analyi for DNA equence egmenaion of he baceriophage lambda genome. The 9h ICC on Saiical Science 2007 December in Kuala Lumpur Malayia. Reearch collaboraion/ubmied publicaion D Nur D Allingham J. Roueau and K.L.Mengeren. Bayeian analyi of DNA equence egmenaion : A prior eniiviy analyi. Submied o Compuaional Saiic and Daa Analyi. R. McVinih K. Mengeren D. Nur J. Roueau and C. Guihenneuc. To be ubmied o Sa Compuing. Seniiviy of prior for raniion marix among egmen in Bayeian analyi of DNA equence egmenaion. Ongoing projec in collaboraion wih rof Mengeren QUT. Simulaion of Hidden Markov model for DNA equence egmenaion modeling. Ongoing projec in collaboraion wih rof Mengeren QUT and A/rof Yan-Xia Lin (UoW) ASEARC Workhop

5 Smooh Threhold AR() wih GARCH() error (wih Yan-Xia) X X ε h = θ X + θ X F = η h = ν + αε βh η ~ iid(0) ( ) X r + ε where i he obervaion a ime- ; 2 are parameer- coefficien; F(.) i a diribuion funcion;d i delay parameer; r i hrehold parameer and z i moohing parameer i GARCH() ε η θ θ Uually i aumed o be Gauian we would like o weaken he aumpion on η d z Applicaion : Finance hi model i imilar o Regime wiching model. Reference : Tong (990) Dijk Teravira and Frane (2002 Economeric Review) ASEARC Workhop

6 Smooh Threhold AR() wih GARCH() error arameer : ( θ θ ν α β 2 Le he diribuion of belong o D a cla of Lebegue deniie roblem of adapive eimaion of λ when f in D unknown Sep o prove when f i a ymmeric deniy: Impoe aumpion (eg regulariy) I he model LAQ or LAN? Wihin LAQ/LAN adapive eimaion i derived λ = ASEARC Workhop η ) '

7 DNA equence In Augu 2005 Nucleoide Sequence daabank conain more han 00Giga bae pair (bp) Hidden Markov model (HMM) Expecaion and Maximiaion (EM) algorihm Bayeian via MCMC (Gibb ampler) were inroduced for biological equence analyi in early 990. Bayeian compuaion via MCMC (Meropoli Haing Gibb ampler) Bayeian HMM for DNA equence : Segmenaion modeling Gene regulaory (idenifying TFBS) ASEARC Workhop

8 In more deail (color ~ae) ASEARC Workhop

9 Hidden Markov model ( HMM ) Conider a DNA equence y = { y y2... yn} a a realiaion of a random proce Y Y2... Y n where Y Є {acg }={234} =2...n and n repreen he lengh of equence. Suppoe ha here are a mo r ype of homogeneou egmen ype S a locaion wihin he DNA equence ha i S Є {2...r }. Example : inron7 of chimpanzee DNA daa he fir n=20 r = 2 egmen (black (ype ) red (ype 2)) -20 ggaagagc gcca aaaaagaga caccc ccc gcc acaaaag ggagaagg ggacg aaggac agagaga aacaggga ASEARC Workhop

10 Simulaion HMM : arameer and (Mengeren and Yan-Xia Lin) Aume ha raniion beween bae Y Y follow a firorder Markov chain where he choice of raniion marix i deermined by he hidden egmen ype S a locaion. Λ 4 x 4 bae raniion marice given he egmen ype k=2 r i=j=234 : = {... ( ) (2) ( r) } ( ( k ) ij k ) = ( ) Aume ha raniion beween egmen S follow a firorder Markov chain r x r raniion marice Λ= λ ) i=j=2 r ( ij S ASEARC Workhop

11 ASEARC Workhop HMM : arameer eimaion Auming ha Y and S follow independen dicree uniform diribuion he likelihood funcion for he model parameer given he oberved DNA equence y and he hidden egmen ype i The likelihood i diribued a a mulinomial Bayeian mehodology : poerior = prior x likelihood oible prior deniie : Dirichle; mixure Dirichle y y n r n r n y y y y Lik ) ( ) ( ) ( ) ( ) ( = = = = = Λ = Λ λ

12 ASEARC Workhop The imulaion reul : r = 2 Model λ I II III () λˆ ˆ) (λ e ) ˆ ( () e ˆ ()

13 Some plo ASEARC Workhop

14 DISCUSSION Any queion? CRICOS rovider 0009J