markov | 易学教程

PyMC: Parameter estimation in a Markov system

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问题 A Simple Markow Chain Let's say we want to estimate parameters of a system such that we can predict the state of the system at timestep t+1 given the state at timestep t. PyMC should be able to deal with this easily. Let our toy system consist of a moving object in a 1D world. The state is the position of the object. We want to estimate the latent variable/the speed of the object. The next state depends on the previous state and the latent variable the speed. # define the system and the data

Creating a matrix of arbitrary size where rows sum to 1?

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问题 My task is to create a program that simulates a discrete time Markov Chain, for an arbitrary number of events. However, right now the part I'm struggling with is creating the right stochastic matrix that will represent the probabilities. A right stochastic matrix is a matrix that has row entries that sum to 1. And for a given size, I kind of know how to write the matrix that does that, however, the problem is that I don't know how to do that for an arbitrary size. For example: here is my code

Understanding Markov Chain source code in R

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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 #----------------------------------------------

subseting dataframe conditions on factor(binary) column(vector in r language)

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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

subseting dataframe conditions on factor(binary) column(vector in r language)

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transition matrix for counts and proportions python

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问题 I have a matrix with the grades from a class for different years(rows for years and columns for grades). What I want is to build a transition matrix with the change between years. For instance, I want year t-1 on the y-axis and year t on the x-axis and then I want a transition matrix with the difference in the number of people with grade A between year t-1 and t, grade B between year t-1 and t, and so on. And then a second transition matrix with the proportions, for example: - Between year t

How can I obtain stationary distribution of a Markov Chain given a transition probability matrix

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问题 I'm trying to write mpow(P, 18) in vector form & matrix form. Can anyone help me with that? Also, I'm trying to find the stationary distribution of each state. Pi_0 = ? Pi_1 = ? Pi_2 = ? ... Pi_5 = ? Here is the code I've written: P <- matrix(c(0, 0, 0, 0.5, 0, 0.5, 0.1, 0.1, 0, 0.4, 0, 0.4, 0, 0.2, 0.2, 0.3, 0, 0.3, 0, 0, 0.3, 0.5, 0, 0.2, 0, 0, 0, 0.4, 0.6, 0, 0, 0, 0, 0, 0.4, 0.6), nrow = 6, ncol = 6, byrow = TRUE) mpow <- function(P, n) { if (n == 0) diag(nrow(P)) else if (n == 1) P else

PyMC: Parameter estimation in a Markov system

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A Simple Markow Chain Let's say we want to estimate parameters of a system such that we can predict the state of the system at timestep t+1 given the state at timestep t. PyMC should be able to deal with this easily. Let our toy system consist of a moving object in a 1D world. The state is the position of the object. We want to estimate the latent variable/the speed of the object. The next state depends on the previous state and the latent variable the speed. # define the system and the data true_vel = .2 true_pos = 0 true_positions = [.2 * step for step in range(100)] We assume that we have

Is there an elegant and efficient way to implement weighted random choices in golang? Details on current implementation and issues inside

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tl;dr: I'm looking for methods to implement a weighted random choice based on the relative magnitude of values (or functions of values) in an array in golang. Are there standard algorithms or recommendable packages for this? Is so how do they scale? Goals I'm trying to write 2D and 3D markov process programs in golang. A simple 2D example of such is the following: Imagine one has a lattice, and on each site labeled by index (i,j) there are n(i,j) particles. At each time step, the program chooses a site and moves one particle from this site to a random adjacent site. The probability that a site

How do Markov Chains work and what is memorylessness?

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问题 How do Markov Chains work? I have read wikipedia for Markov Chain, But the thing I don't get is memorylessness. Memorylessness states that: The next state depends only on the current state and not on the sequence of events that preceded it. If Markov Chain has this kind of property, then what is the use of chain in markov model? Explain this property. 回答1: You can visualize Markov chains like a frog hopping from lily pad to lily pad on a pond. The frog does not remember which lily pad(s) it