The normalized log2 ratios are assumed to be distributed as A copy number state is associated with each clone. In this Bayesian HMM algorithm, there are four states, defined as copy number loss state ( 1), copy number neutral state ( 2), single copy gain state ( 3), and amplification (multiple gain) state ( 4). Posterior inferences are made about the copy number gains and losses. Bayesian learning is used to identify genome-wide changes in copy number from the data. The intensity ratios are generated by hidden copy number states. The hidden Markov model accounts for the dependence between neighboring clones.
Guha et al., (2006) proposed a Bayesian statistical approach depending on a hidden Markov model (HMM) for analyzing array CGH data. These issues necessitate the use of efficient statistical algorithms characterizing the genomic profiles. There is also a dependence between the intensity ratios of neighboring clones. One main factor is contamination of the tumor samples with normal cells. The ratios typically shrink towards zero.
In real applications, even after accounting for measurement error, the log2 ratios differ considerably from the theoretical values. Loss of both copies, or a deletion would correspond to the value of -inf. Multiple copy gains or amplifications would have values of log2(4/2), log2(5/2). In an ideal situation, the log2 ratio of normal (copy-neutral) clones is log2(2/2) = 0, single copy losses is log2(1/2) = -1, and single copy gains is log2(3/2) = 0.58. Log2 intensity ratios of test to reference provide useful information about genome-wide profiles in copy number. The DNA fragments or "clones" of test and reference samples are hybridized to mapped array fragments. The small effective size translates into a high Monte Carlo standard error and broader credibility intervals.Array-based CGH is a high-throughput technique to measure DNA copy number change across the genome. While mixing and convergence is extremely efficient, as expected when dealing with generated data, we note that the regression parameters for the latent states are the worst performers. MCSE = Monte Carlo Standard Error, SE = Standard Error, Med = Median, ESS = Effective Sample Size. Hatx_t <- extract(stan.fit, pars = 'hatx_t')] Estimated parameters and hidden quantities. Zstar_t <- extract(stan.fit, pars = 'zstar_t')] Gamma_tk <- extract(stan.fit, pars = 'gamma_tk')] # launch_shinystan(stan.fit) # Extraction -Īlpha_tk <- extract(stan.fit, pars = 'alpha_tk')] # Chain 1, Iteration: 400 / 400 (Sampling) # Chain 1, Iteration: 360 / 400 (Sampling) # Chain 1, Iteration: 320 / 400 (Sampling) # Chain 1, Iteration: 280 / 400 (Sampling) # Chain 1, Iteration: 240 / 400 (Sampling) # Chain 1, Iteration: 201 / 400 (Sampling) # SAMPLING FOR MODEL 'iohmm-reg' NOW (CHAIN 1). # STARTING SAMPLER FOR MODEL 'iohmm-reg' NOW. # CHECKING DATA AND PREPROCESSING FOR MODEL 'iohmm-reg' NOW. # successful in parsing the Stan model 'iohmm-reg'.
#Foracasting using hidden markov model matlab code#
# TRANSLATING MODEL 'iohmm-reg' FROM Stan CODE TO C++ CODE NOW. Stan.model = './iohmm-reg/stan/iohmm-reg.stan' Options( mc.cores = parallel:: detectCores())
The authors acknowledge Google for financial support via the Google Summer of Code 2017 program.Īs with HMM, IOHMM involves two interconnected models, \[\begin_k\), one set per possible hidden state. The model is introduced only briefly, a more detailed mathematical treatment can be found in our literature review. 2016) for a fully Bayesian estimation of the model parameters and inference on hidden quantities, namely filtered state belief, smoothed state belief, jointly most probable state path and fitted output. The main goal is to produce public programming code in Stan (Carpenter et al.
This work aims at replicating the Input-Output Hidden Markov Model (IOHMM) originally proposed by Hassan and Nath (2005) to forecast stock prices.
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