我想在实施隐藏马尔可夫方法以根据 SNP 基因型数据分配祖先时寻求帮助。鉴于我有一个这样生成的转换矩阵：
states <- c("A1","A2","A3","A4","A5","A6","A7","A8") # Define the names of the states
A1 <- c(0.9,0.1,0.1,0.1,0.1,0.1,0.1,0.1) # Set the probabilities of switching states, where the previous state was "A1"
A2 <- c(0.1,0.9,0.1,0.1,0.1,0.1,0.1,0.1) # Set the probabilities of switching states, where the previous state was "A2"
A3 <- c(0.1,0.1,0.9,0.1,0.1,0.1,0.1,0.1) # Set the probabilities of switching states, where the previous state was "A3"
A4 <- c(0.1,0.1,0.1,0.9,0.1,0.1,0.1,0.1) # Set the probabilities of switching states, where the previous state was "A4"
A5 <- c(0.1,0.1,0.1,0.1,0.9,0.1,0.1,0.1) # Set the probabilities of switching states, where the previous state was "A5"
A6 <- c(0.1,0.1,0.1,0.1,0.1,0.9,0.1,0.1) # Set the probabilities of switching states, where the previous state was "A6"
A7 <- c(0.1,0.1,0.1,0.1,0.1,0.1,0.9,0.1) # Set the probabilities of switching states, where the previous state was "A7"
A8 <- c(0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.9) # Set the probabilities of switching states, where the previous state was "A8"
thetransitionmatrix <- matrix(c(A1,A2,A3,A4,A5,A6,A7,A8), 8, 8, byrow = TRUE) # Create an 8 x 8 matrix
rownames(thetransitionmatrix) <- states
colnames(thetransitionmatrix) <- states
thetransitionmatrix # Print out the transition matrix
A1 A2 A3 A4 A5 A6 A7 A8
A1 0.9 0.1 0.1 0.1 0.1 0.1 0.1 0.1
A2 0.1 0.9 0.1 0.1 0.1 0.1 0.1 0.1
A3 0.1 0.1 0.9 0.1 0.1 0.1 0.1 0.1
A4 0.1 0.1 0.1 0.9 0.1 0.1 0.1 0.1
A5 0.1 0.1 0.1 0.1 0.9 0.1 0.1 0.1
A6 0.1 0.1 0.1 0.1 0.1 0.9 0.1 0.1
A7 0.1 0.1 0.1 0.1 0.1 0.1 0.9 0.1
A8 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.9
发射矩阵是 n 个 8x4 矩阵的列表，其中 n 等于数据中 SNP/行的数量。例如，对于 3 个 SNP/行的 8 个样本 (A1-A8) 的以下数据：
A1 A2 A3 A4 A5 A6 A7 A8
T T T T T T T C
T C T T T T T C
A A A G G A A A
列表中的矩阵 1 将是
A C G T
A1 0 0 0 1/7
A2 0 0 0 1/7
A3 0 0 0 1/7
A4 0 0 0 1/7
A5 0 0 0 1/7
A6 0 0 0 1/7
A7 0 0 0 1/7
A8 0 1 0 0
由于第 1 行中有 7 个样本具有 T，因此每个样本的概率为 1/7。由于只有 A8 拥有 C，因此将 C 分配给 A8 的概率为 100%。对于第 3 行，输出应为
A C G T
A1 1/6 0 0 0
A2 1/6 0 0 0
A3 1/6 0 0 0
A4 1/2 0 0 0
A5 1/2 0 0 0
A6 1/6 0 0 0
A7 1/6 0 0 0
A8 1/6 0 0 0
使用上述转换矩阵和发射矩阵列表，我希望在任何等位基因序列上实现维特比算法。我目前拥有的代码无法为每一行使用不同的发射矩阵
viterbi <- function(sequence, transitionmatrix, emissionmatrix)
# This carries out the Viterbi algorithm.
# Adapted from "Applied Statistics for Bioinformatics using R" by Wim P. Krijnen, page 209
# ( cran.r-project.org/doc/contrib/Krijnen-IntroBioInfStatistics.pdf )
{
# Get the names of the states in the HMM:
states <- rownames(theemissionmatrix)
# Make the Viterbi matrix v:
v <- makeViterbimat(sequence, transitionmatrix, emissionmatrix)
# Go through each of the rows of the matrix v (where each row represents
# a position in the DNA sequence), and find out which column has the
# maximum value for that row (where each column represents one state of
# the HMM):
mostprobablestatepath <- apply(v, 1, function(x) which.max(x))
# Print out the most probable state path:
prevnucleotide <- sequence[1]
prevmostprobablestate <- mostprobablestatepath[1]
prevmostprobablestatename <- states[prevmostprobablestate]
startpos <- 1
for (i in 2:length(sequence))
{
nucleotide <- sequence[i]
mostprobablestate <- mostprobablestatepath[i]
mostprobablestatename <- states[mostprobablestate]
if (mostprobablestatename != prevmostprobablestatename)
{
print(paste("Positions",startpos,"-",(i-1), "Most probable state = ", prevmostprobablestatename))
startpos <- i
}
prevnucleotide <- nucleotide
prevmostprobablestatename <- mostprobablestatename
}
print(paste("Positions",startpos,"-",i, "Most probable state = ", prevmostprobablestatename))
}
# the viterbi() function requires a second function makeViterbimat():
makeViterbimat <- function(sequence, transitionmatrix, emissionmatrix)
# This makes the matrix v using the Viterbi algorithm.
# Adapted from "Applied Statistics for Bioinformatics using R" by Wim P. Krijnen, page 209
# ( cran.r-project.org/doc/contrib/Krijnen-IntroBioInfStatistics.pdf )
{
# Change the sequence to uppercase
sequence <- toupper(sequence)
# Find out how many states are in the HMM
numstates <- dim(transitionmatrix)[1]
# Make a matrix with as many rows as positions in the sequence, and as many
# columns as states in the HMM
v <- matrix(NA, nrow = length(sequence), ncol = dim(transitionmatrix)[1])
# Set the values in the first row of matrix v (representing the first position of the sequence) to 0
v[1, ] <- 0
# Set the value in the first row of matrix v, first column to 1
v[1,1] <- 1
# Fill in the matrix v:
for (i in 2:length(sequence)) # For each position in the DNA sequence:
{
for (l in 1:numstates) # For each of the states of in the HMM:
{
# Find the probabilility, if we are in state l, of choosing the nucleotide at position in the sequence
statelprobnucleotidei <- emissionmatrix[l,sequence[i]]
# v[(i-1),] gives the values of v for the (i-1)th row of v, ie. the (i-1)th position in the sequence.
# In v[(i-1),] there are values of v at the (i-1)th row of the sequence for each possible state k.
# v[(i-1),k] gives the value of v at the (i-1)th row of the sequence for a particular state k.
# transitionmatrix[l,] gives the values in the lth row of the transition matrix, xx should not be transitionmatrix[,l]?
# probabilities of changing from a previous state k to a current state l.
# max(v[(i-1),] * transitionmatrix[l,]) is the maximum probability for the nucleotide observed
# at the previous position in the sequence in state k, followed by a transition from previous
# state k to current state l at the current nucleotide position.
# Set the value in matrix v for row i (nucleotide position i), column l (state l) to be:
v[i,l] <- statelprobnucleotidei * max(v[(i-1),] * transitionmatrix[,l])
}
}
return(v)
}