1. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Introduction to Probabilistic Models for Bioinformatics
Igor Bogicevic (igor.bogicevic@sbgenomics.com)
July 3, 2011
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G E N O M I C S, LLC
Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

2. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Short introduction to Bioinformatics
Bioinformatics is the application of statistics and computer science to the field of
molecular biology.
EVEN BRIDGES
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

3. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Short introduction to Bioinformatics
Bioinformatics is the application of statistics and computer science to the field of
molecular biology.
Major research efforts in the field include sequence alignment, gene finding,
genome assembly, drug design, drug discovery, protein structure alignment,
protein structure prediction, prediction of gene expression and protein-protein
interactions, genome-wide association studies and the modeling of evolution.
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

4. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Short introduction to Bioinformatics
Bioinformatics is the application of statistics and computer science to the field of
molecular biology.
Major research efforts in the field include sequence alignment, gene finding,
genome assembly, drug design, drug discovery, protein structure alignment,
protein structure prediction, prediction of gene expression and protein-protein
interactions, genome-wide association studies and the modeling of evolution.
At the current moment, given the enormous volumes of sequenced data, one of
the biggest challenges is not producing, but actually understanding the data.
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

5. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
What are the Probabilistic Models?
There are 2 basic definitions:
EVEN BRIDGES
G E N O M I C S, LLC
Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

6. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
What are the Probabilistic Models?
There are 2 basic definitions:
Statistical analysis tool that estimates, on the basis of past (historical) data, the
probability of an event occurring again.
Probabilistic model is a system that simulates the object under the consideration
and produces different outcomes with different probabilities.
EVEN BRIDGES
G E N O M I C S, LLC
Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

7. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
What are the Probabilistic Models?
There are 2 basic definitions:
Statistical analysis tool that estimates, on the basis of past (historical) data, the
probability of an event occurring again.
Probabilistic model is a system that simulates the object under the consideration
and produces different outcomes with different probabilities.
Simple example - rolling a die.
EVEN BRIDGES
G E N O M I C S, LLC
Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

8. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
What are the Probabilistic Models?
There are 2 basic definitions:
Statistical analysis tool that estimates, on the basis of past (historical) data, the
probability of an event occurring again.
Probabilistic model is a system that simulates the object under the consideration
and produces different outcomes with different probabilities.
Simple example - rolling a die.
A bit more relevant example - random sequence model in DNA .
Biological sequences are strings from a finite alphabet of residues, most
commonly either four nucleotides, or twenty amino acids.
Imagine that a residue a occurs with probability qa , if protein or DNA sequence is
denoted x1 ...xn , then probability of the whole sequence is:
n
Y
qx1 qx2 ...qxn = qxi
i=1
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G E N O M I C S, LLC
Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

9. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Sequence Alignment
Sequence alignment is a way of arranging the sequences of DNA, RNA, or protein
to identify regions of similarity that may be a consequence of functional,
structural, or evolutionary relationships between the sequences.
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G E N O M I C S, LLC
Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

10. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Sequence Alignment
Sequence alignment is a way of arranging the sequences of DNA, RNA, or protein
to identify regions of similarity that may be a consequence of functional,
structural, or evolutionary relationships between the sequences.
A variety of computational algorithms have been applied to the sequence
alignment problem, i.e. dynamic programming, heuristic algorithms, probabilistic
methods.
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G E N O M I C S, LLC
Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

11. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Sequence Alignment
Sequence alignment is a way of arranging the sequences of DNA, RNA, or protein
to identify regions of similarity that may be a consequence of functional,
structural, or evolutionary relationships between the sequences.
A variety of computational algorithms have been applied to the sequence
alignment problem, i.e. dynamic programming, heuristic algorithms, probabilistic
methods.
Common formats for representing alignments are FASTA and GenBank format
EVEN BRIDGES
G E N O M I C S, LLC
Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

12. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
EVEN BRIDGES
G E N O M I C S, LLC
Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

13. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Pairwise Alignment
Pairwise sequence alignment methods are used to find the best-matching
piecewise (local) or global alignments of two query sequences.
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G E N O M I C S, LLC
Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

14. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Pairwise Alignment
Pairwise sequence alignment methods are used to find the best-matching
piecewise (local) or global alignments of two query sequences.
The three primary methods of producing pairwise alignments are dot-matrix
methods, dynamic programming, and word methods.
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

15. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Pairwise Alignment
Pairwise sequence alignment methods are used to find the best-matching
piecewise (local) or global alignments of two query sequences.
The three primary methods of producing pairwise alignments are dot-matrix
methods, dynamic programming, and word methods.
Needleman-Wunsch algorithm (Global Alignment)
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

16. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Pairwise Alignment
Pairwise sequence alignment methods are used to find the best-matching
piecewise (local) or global alignments of two query sequences.
The three primary methods of producing pairwise alignments are dot-matrix
methods, dynamic programming, and word methods.
Needleman-Wunsch algorithm (Global Alignment)
Smith-Waterman algorithm (Local Alignment)
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

17. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Pairwise Alignment
Pairwise sequence alignment methods are used to find the best-matching
piecewise (local) or global alignments of two query sequences.
The three primary methods of producing pairwise alignments are dot-matrix
methods, dynamic programming, and word methods.
Needleman-Wunsch algorithm (Global Alignment)
Smith-Waterman algorithm (Local Alignment)
FASTA/BLAST Algorithms (k-tuple heuristic methods, often combined with
dynamic models)
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

18. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Pairwise Alignment
Pairwise sequence alignment methods are used to find the best-matching
piecewise (local) or global alignments of two query sequences.
The three primary methods of producing pairwise alignments are dot-matrix
methods, dynamic programming, and word methods.
Needleman-Wunsch algorithm (Global Alignment)
Smith-Waterman algorithm (Local Alignment)
FASTA/BLAST Algorithms (k-tuple heuristic methods, often combined with
dynamic models)
Gap Penalities - modeling a cost of a gap in matched sequences (linear, affine,
etc.)
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

19. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Example - Smith-Waterman: A matrix H is built as follows:
H(i, 0) = 0, 0 ≤ i ≤ m
H(0, j) = 0, 0 ≤ j ≤ n
if ai = bj then w (ai , bj ) = w (match)
or if ai ! = bj then w (ai , bj ) = w (mismatch)
8 9
>
> 0 >
>
H(i − 1, j − 1) + w (ai , bj ) Match/Mismatch
< =
H(i, j) = max , 1 ≤ i ≤ m, 1 ≤ j ≤ n
> H(i − 1, j) + w (ai , −)
> Deletion >
>
H(i, j − 1) + w (−, bj ) Insertion
: ;
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

20. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Sequence 1 = ACACACTA, Sequence 2 = AGCACACA
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

21. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Sequence 1 = ACACACTA, Sequence 2 = AGCACACA
w(match) = +2
w(a,-) = w(-,b) = w(mismatch) = -1
− A C A C A C T A
0 1
B− 0 0 0 0 0 0 0 0 0C
BA 0 2 1 2 1 2 1 0 2C
B C
BG 0 1 1 1 1 1 1 0 1C
B C
BC 0 0 3 2 3 2 3 2 1C
B C
H=B
BA 0 2 2 5 4 5 4 3 4C
C
BC 0 1 4 4 7 6 7 6 5C
B C
BA 0 2 3 6 6 9 8 7 8C
B C
@C 0 1 4 5 8 8 11 10 9A
A 0 2 3 6 7 10 10 10 12
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

22. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Sequence 1 = ACACACTA, Sequence 2 = AGCACACA
w(match) = +2
w(a,-) = w(-,b) = w(mismatch) = -1
− A C A C A C T A
0 1
B− 0 0 0 0 0 0 0 0 0C
BA 0 2 1 2 1 2 1 0 2C
B C
BG 0 1 1 1 1 1 1 0 1C
B C
BC 0 0 3 2 3 2 3 2 1C
B C
H=B
BA 0 2 2 5 4 5 4 3 4C
C
BC 0 1 4 4 7 6 7 6 5C
B C
BA 0 2 3 6 6 9 8 7 8C
B C
@C 0 1 4 5 8 8 11 10 9A
A 0 2 3 6 7 10 10 10 12
In the example, the highest value corresponds to the cell in position (8,8). The
walk back corresponds to (8,8), (7,7), (7,6), (6,5), (5,4), (4,3), (3,2), (2,1),
(1,1), and (0,0)
Sequence 1 = A-CACACTA, Sequence 2 = AGCACAC-A EVEN BRIDGES
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

23. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Multiple Sequence Alignment Models
A multiple sequence alignment (MSA) is a sequence alignment of three or more
biological sequences, commonly protein, DNA, or RNA.
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

24. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Multiple Sequence Alignment Models
A multiple sequence alignment (MSA) is a sequence alignment of three or more
biological sequences, commonly protein, DNA, or RNA.
We usually want to do multiple alignments to find a homologous sequences that
point to a shared evolutionary origins that can be used for further phylogenetic
analysis.
Progressive Alignment Methods - constructing succession of a pairwise alignment.
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

25. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Multiple Sequence Alignment Models
A multiple sequence alignment (MSA) is a sequence alignment of three or more
biological sequences, commonly protein, DNA, or RNA.
We usually want to do multiple alignments to find a homologous sequences that
point to a shared evolutionary origins that can be used for further phylogenetic
analysis.
Progressive Alignment Methods - constructing succession of a pairwise alignment.
Hidden Markov Models - representation of MSA as DAG, observed states are
individual alignment columns and the hidden states represent the presumed
ancestral sequence.
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

26. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
EVEN BRIDGES
G E N O M I C S, LLC
Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

27. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
What is Phylogenetics?
Phylogenetics is the study of evolutionary relatedness among groups of organisms
(e.g. species, populations), which is discovered through molecular sequencing
data and morphological data matrices.
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

28. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
What is Phylogenetics?
Phylogenetics is the study of evolutionary relatedness among groups of organisms
(e.g. species, populations), which is discovered through molecular sequencing
data and morphological data matrices.
Evolution is regarded as a branching process, whereby populations are altered
over time and may speciate into separate branches, hybridize together, or
terminate by extinction. This may be visualized in a phylogenetic tree.
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

29. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
What is Phylogenetics?
Phylogenetics is the study of evolutionary relatedness among groups of organisms
(e.g. species, populations), which is discovered through molecular sequencing
data and morphological data matrices.
Evolution is regarded as a branching process, whereby populations are altered
over time and may speciate into separate branches, hybridize together, or
terminate by extinction. This may be visualized in a phylogenetic tree.
Ernst Haeckel’s recapitulation theory (”ontogeny recapitulates phylogeny”) is a
hypothesis that in developing from embryo to adult, animals go through stages
resembling or representing successive stages in the evolution of their remote
ancestors.
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

30. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Building Phylogenetic Trees
Phylogenetic trees among a nontrivial number of input sequences are constructed
using computational phylogenetics methods.
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

31. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Building Phylogenetic Trees
Phylogenetic trees among a nontrivial number of input sequences are constructed
using computational phylogenetics methods.
Common method is to search for maximum likelihood, often within a Bayesian
Framework, and apply an explicit model of evolution to phylogenetic tree
estimation.
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

32. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Building Phylogenetic Trees
Phylogenetic trees among a nontrivial number of input sequences are constructed
using computational phylogenetics methods.
Common method is to search for maximum likelihood, often within a Bayesian
Framework, and apply an explicit model of evolution to phylogenetic tree
estimation.
Identifying the optimal tree using many of these techniques is NP-hard, so
heuristic search and optimization methods are used in combination with
tree-scoring functions to identify a reasonably good tree that fits the data.
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

33. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Building Phylogenetic Trees
Phylogenetic trees among a nontrivial number of input sequences are constructed
using computational phylogenetics methods.
Common method is to search for maximum likelihood, often within a Bayesian
Framework, and apply an explicit model of evolution to phylogenetic tree
estimation.
Identifying the optimal tree using many of these techniques is NP-hard, so
heuristic search and optimization methods are used in combination with
tree-scoring functions to identify a reasonably good tree that fits the data.
They do not necessarily accurately represent the species evolutionary history as
the data on which they are based is noisy; the analysis can be confounded by
horizontal gene transfer, hybridisation between species that were not nearest
neighbors on the tree before hybridisation takes place, convergent evolution, and
conserved sequences.
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

34. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
EVEN BRIDGES
G E N O M I C S, LLC
Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

35. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Other Models
Transformational Grammars (Chomsky Hierarchy)
RNA Structure Analysis Models (RNA contains the interactions - rather than
preserving the sequence)
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics

36. Short introduction to Bioinformatics
What are the Probabilistic Models?
Sequence Alignment
Pairwise Alignment
Multiple Sequence Alignment Models
What is Phylogenetics?
Building Phylogenetic Trees
Other Models
Conctact Us
Contact Us
We are Hiring!
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Igor Bogicevic (igor.bogicevic@sbgenomics.com) Introduction to Probabilistic Models for Bioinformatics