markov-chains

问题 i've been trying the last couple days to convert this js script to python code. My implementation (blindfull cp mostly, some minor fixes here and there) so far: import random class markov: memory = {} separator = ' ' order = 2 def getInitial(self): ret = [] for i in range(0, self.order, 1): ret.append('') return ret def breakText(self, txt, cb): parts = txt.split(self.separator) prev = self.getInitial() def step(self): cb(prev, self.next) prev.shift()#Javascript function. prev.append(self

问题 Generic formulation I have a dataset consisting of a sequence of points with 12 features each. I am interested in detecting an event in this data. In the training data I know the moments the event occurred. When the event occurs I can see an observable pattern in the sequence of points before the event. The pattern is formed from about 300 consecutive points. I am interested in detecting when the event occurred in a infinite sequence of points. The analysis happens post factum. I am not

问题 The following source code is from a book. Comments are written by me to understand the code better. #================================================================== # markov(init,mat,n,states) = Simulates n steps of a Markov chain #------------------------------------------------------------------ # init = initial distribution # mat = transition matrix # labels = a character vector of states used as label of data-frame; # default is 1, .... k #----------------------------------------------

问题 i have a sequence of 1/0's indicating if patient is in remission or not, assume the records of remission or not were taken at discrete times, how can i check the markov property for each patient, then summarize the findings, that is the assumption that the probability of remission for any patient at any time depends only if the patient had remission the last time/not remission last time(same as thing as saying probability of remission for any patient at any time depends only if the patient

问题 i have a sequence of 1/0's indicating if patient is in remission or not, assume the records of remission or not were taken at discrete times, how can i check the markov property for each patient, then summarize the findings, that is the assumption that the probability of remission for any patient at any time depends only if the patient had remission the last time/not remission last time(same as thing as saying probability of remission for any patient at any time depends only if the patient

问题 I have a Markov chain given as a large sparse scipy matrix A . (I've constructed the matrix in scipy.sparse.dok_matrix format, but converting to other ones or constructing it as csc_matrix are fine.) I'd like to know any stationary distribution p of this matrix, which is an eigenvector to the eigenvalue 1 . All entries in this eigenvector should be positive and add up to 1, in order to represent a probability distribution. This means I want any solution for the system (A-I) p = 0 , p.sum()=1

问题 I have a Markov chain given as a large sparse scipy matrix A . (I've constructed the matrix in scipy.sparse.dok_matrix format, but converting to other ones or constructing it as csc_matrix are fine.) I'd like to know any stationary distribution p of this matrix, which is an eigenvector to the eigenvalue 1 . All entries in this eigenvector should be positive and add up to 1, in order to represent a probability distribution. This means I want any solution for the system (A-I) p = 0 , p.sum()=1

问题 Consider the Markov chain with state space S = {1, 2} , transition matrix and initial distribution α = (1/2, 1/2) . Simulate 5 steps of the Markov chain (that is, simulate X 0 , X 1 , . . . , X 5 ). Repeat the simulation 100 times. Use the results of your simulations to solve the following problems. Estimate P(X 1 = 1|X 0 = 1) . Compare your result with the exact probability. My solution: # returns Xn func2 <- function(alpha1, mat1, n1) { xn <- alpha1 %*% matrixpower(mat1, n1+1) return (xn) }

问题 Maze I have a maze as shown above(use the link) and state 3 contains prize while state 7 contains shock. a mouse can be placed in any state from 1 to 9 randomly and it move through the maze uniformly at random Pi denote the probability that mouse reaches state 3 before state 7, given that AIM started in compartment i. how to compute Pi for ∈ {1,2,3,4,5,6,7,8,9}. 回答1: Let Px be the probability that the game ends in position 3 if it starts in position x . We know that P3=1 and P7=0 If you start

问题 Let's use the dataset from this question: dat<-data.frame(replicate(20,sample(c("A", "B", "C","D"), size = 100, replace=TRUE))) Then we can build the transition matrix and the markov chain: # Build transition matrix trans.matrix <- function(X, prob=T) { tt <- table( c(X[,-ncol(X)]), c(X[,-1]) ) if(prob) tt <- tt / rowSums(tt) tt } trans.mat <- trans.matrix(as.matrix(dat)) attributes(trans.mat)$class <- 'matrix' # Build markovchain library(markovchain) chain <- new('markovchain',