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Installation

You can install BioMarkovChains from the julia REPL. Press ] to enter pkg mode, and enter the following:

]add BioMarkovChains

If you are interested in the cutting edge of the development, please check out the main branch to try new features before release.

Create a BioMarkovChain of DNA

using BioSequences, BioMarkovChains

seq = dna"CCTCCCGGACCCTGGGCTCGGGAC"

BioMarkovChain(seq)

BioMarkovChain of DNA alphabet and order 1:
  - Transition Probability Matrix -> Matrix{Float64}(4 × 4):
   0.0     1.0     0.0     0.0
   0.0     0.5     0.2     0.3
   0.25    0.125   0.625   0.0
   0.0     0.6667  0.3333  0.0
  - Initial Probabilities -> Vector{Float64}(4 × 1):
   0.087   0.4348  0.3478  0.1304

Note that, sometimes the dinucleotides transition do not harbor important biological meaning, whereas trinucleotides or codons are, in fact, the building block of proteins. Therefore, sometimes the transition model we want to build is usually a second-order Markov chain, that represents the possible transitions of a trinucleotide.

A very nice nice property of the transition probability matrix is that the n-step transition probability matrix ${\mathcal{M}}^n=({\mathcal{m}}_{ij}(n))$, that is the $n$th power of $\mathcal{M}$ represents $i\hspace{0.33em}\to j$ transitions in n steps. We can also have higher order transition models as:

BioMarkovChain(seq, 2)

BioMarkovChain of DNA alphabet and order 2:
  - Transition Probability Matrix -> Matrix{Float64}(4 × 4):
   0.0     0.5     0.2     0.3
   0.05    0.475   0.325   0.15
   0.1562  0.3906  0.4156  0.0375
   0.0833  0.375   0.3417  0.2
  - Initial Probabilities -> Vector{Float64}(4 × 1):
   0.087   0.4348  0.3478  0.1304