Questions tagged [markov-chains]
Questions that deal with modeling and simulating random processes which switch between states under the Markov assumptions.
64
questions
0
votes
1answer
54 views
Stationary Distribution of Markov Chain [closed]
I'm trying to compute the stationary distribution of the following Markov chain:
$$P=\left(
\begin{array}{cc}
p_{11} & p_{12} \\
p_{21} & p_{22} \\
\end{array}
\right)$$
I know you have to ...
0
votes
1answer
100 views
DiscreteMarkovProcess: preparing the transition matrix and unexpected negative results
I would like to implement a Markov process.
It consists on a walk on a one-dimensional lattice, with nodes spaced $\epsilon$ from $-2$ to $2$.
The transition probabilities for $x \neq y$ are as ...
0
votes
0answers
52 views
Unexpected PDF in `FirstPassageTimeDistribution`
I am new to Markov Processes, and while learning the discrete Markov chain with the following matrix $$P=\begin{bmatrix}\frac{1}{3} & \frac{2}{3} & 0 & 0 \\ \frac{1}{2} & \frac{1}{2} &...
3
votes
1answer
84 views
Graphing Markov chains / decision trees
I'm looking to graph a simple one-way Markov chain, which is effectively a decision tree with transitions probabilities. One way I've got this working in here in an MWE, here's a simple Markov chain ...
0
votes
0answers
15 views
Why the `ReachabilityProbability` of `DiscreteMarkovProcess` does not work with non-numeric parameters?
Most properties of Markov Processes work with non-numeric parameters, but this stops being true for ReachabilityProbability For example
...
15
votes
1answer
926 views
Metropolis-Hastings Algorithm - Significantly slower than Python
I would like to code a Metropolis Hasting algorithm and thought I would get the general scheme of things going with a toy example.
I think I got it running but my Mathematica code runs significantly ...
1
vote
2answers
61 views
How to add the weights to the transition graph of a Markov chain?
The following working program uses
Graph and Markov Chain
...
4
votes
2answers
127 views
Compute the stationary distribution of a large transition matrix
I am doing some simulations for simple random walks on directed random graphs. From a graph of n vertices, I get a n by ...
6
votes
2answers
318 views
Generate an ε-machine graph from transition probability matrices
I am trying to generate this type of graphic:
see Fig.1a from https://arxiv.org/abs/0905.3587.
This process is associated with two transition matrices
$$ T^{(0)} = \begin{pmatrix}
0&p&0\\
1&...
1
vote
2answers
210 views
How to convert a weighted, directed graph into a discrete Markov transition matrix
Suppose that I have matrix matT1 at time t and matT2 at time t+1:
...
2
votes
1answer
51 views
Mathematica demonstration for Markov convergence tracking effect on input distributions in 2D (or 3D)
Is there a mathematica demo that demonstrates the convergence of Markov chains in 2 dimensions, and possibly 3, as follows?
In 2 dimensions, start with the interval determined by $x + y = 1$ for ...
0
votes
1answer
46 views
Expression with Boole
Let us have an expression for example, this:
2 (-1 + p) (3 - 4 p + 2 p^2) Boole[\[FormalX] == 1] - 9 (1 - 2 p + p^2) Boole[\[FormalX] == 2] ...
For the whole ...
4
votes
3answers
451 views
Slow computation of recursive sequences
I want to investigate the asymptotic behavior of the following recursive system:
...
0
votes
1answer
28 views
Problem with solving a system of equations based on a matrix
I am trying to solve a system of equations based on a matrix in order to find the "stationary" matrix. the code I've written should break the matrix down into a system of equations such that some ...
4
votes
0answers
133 views
4
votes
1answer
239 views
The probability of reaching the absorbing states from a particular transient state?
Can I use the data available from MarkovProcessProperties to compute the probability of reaching each of the absorbing states from a particular transient state?
In an earlier post, kglr showed a ...
0
votes
1answer
113 views
Finding Steady States that Meet Additional Constraints
I've written a function that returns the steady state given a regular, column-stochastic matrix. I want to use it to solve a larger problem, finding steady states that satisfy certain conditions.
The ...
0
votes
1answer
115 views
How to simulate a Markov chain from the output of two other Markov chains?
I have a Markov chain defined by the output of two other Markov chains as time passes. (i.e., Z = X + Y).
How do I program such a Markov chain in Mathematica?
5
votes
1answer
114 views
22
votes
3answers
2k views
Efficient way to simulate thousands of Markov chains
I am currently trying to simulate relaxation of a protein population while maintaining the stochastic properties of the system. For this, I used a Markov chain to describe the temporal evolution of ...
8
votes
4answers
243 views
Constructing higher order transition probability matrix
Recently I asked a question here about how to construct a transition probability matrix given the following list:
...
6
votes
3answers
381 views
7
votes
2answers
493 views
How to make a cow smaller (in BubbleChart3D plot)
I've been using random walk Metropolis to sample from the (unnormalised distribution) which is defined as $p(r)\propto e^{-100 r}$, where $r$ is the perpendicular distance of a point in 3D space from ...
3
votes
1answer
372 views
Metropolis-Hastings Algorithm Problem
I've been trying to implement the Metropolis-Hastings algorithm for a while but there seems to be something weird going on.
This algorithm does not need as much of the statistics to understand, and ...
5
votes
1answer
171 views
1
vote
1answer
334 views
Deriving 68% confidence level for each parameter after MCMC
I used the MCMC package https://github.com/joshburkart/mathematica-mcmc to find the best parameters for model of Massive Gravity. Now I need to find the confidence 68% for each of those parameters and ...
4
votes
1answer
210 views
MCMC problem for Acoustic Scale Cosmology
I'm using this MCMC Mathematica package https://github.com/joshburkart/mathematica-mcmc to do a MCMC on number of different data sets for a problem. I'm almost done but I have one problem. Whenever I ...
0
votes
1answer
75 views
Evaluated To Non-Numerical Values Error using MCMC package Mathematica Via NIntegrate
I'm using this package https://github.com/joshburkart/mathematica-mcmc and am trying to evaluate the following:
...
1
vote
0answers
117 views
Error using MCMC package Mathematica Via NIntegrate
I'm using this package https://github.com/joshburkart/mathematica-mcmc and am trying to evaluate the following:
...
1
vote
0answers
42 views
5
votes
0answers
690 views
Estimate process parameters of geometric Brownian motion with a two-state Markov chain
I have the following sequence.
Consider a model that follows a geometric Brownian motion whose drift switches between two different regimes representing the up trend and down trend. The regime ...
4
votes
0answers
203 views
Why is this non-vectorized NDSolve faster than vectorized?
I'm trying to get a feeling for stochastic population models. A simple starting place is a birth-death process whose deterministic limit is the logistic equation. The idea is to model the probability <...
2
votes
1answer
107 views
Issue with EdgeLabels
I want to reproduce Shannon's telegraph Markov chain from A Mathematical Theory of Communication.
EdgeLabels isn't doing the trick here:
...
1
vote
0answers
81 views
Generalization of DiscreteMarkovProcess?
I am trying to create a Markov chain using the initial state of a probabilistic cellular automaton, that is a list of length 8, as the first argument of the function ...
7
votes
0answers
76 views
1
vote
0answers
242 views
Training Hidden Markov Models using Mathematica
I have created a Hidden Markov Process with an initial probability vector, emission and transmission matrices.
...
1
vote
0answers
373 views
Hidden Markov Model: emissions probabilities dependent on observable parameter
I need to fit an HMM where the emission probabilities (ep) are discrete and dependent on a known variable quantity. E.g.:
Imagine a daily time series of binary emissions ("1" or "2"). I suppose an ...
1
vote
1answer
246 views
Nonlinear Markov chain (numerical simulation)
Suppose you have a linear Markov process, and you can write it as
x(t+1) = Ax(t).
Here x is the vector of values, and A is the transition matrix. Since this is linear, it can be solved analytically, ...
4
votes
1answer
132 views
Use (network) graph as vertex
I have a Markov chain with graphs as the states. Basically how one network structure would evolve to another in the next period. To avoid confusion, I'll use the term "network" instead of "graph".
I ...
1
vote
0answers
349 views
What's the algorithm behind markov classifier in Classify function for text classification?
https://www.wolfram.com/mathematica/new-in-10/highly-automated-machine-learning/find-which-author-wrote-a-text.html
The above url show the use of Classify ...
-1
votes
2answers
166 views
Using Mathematica to calculate expected time to absorption [closed]
I am trying to solve a standard ETA on a birth-death process with $n$ states $\in \{0,\cdots,n-1\}$ where state $n-1$ is absorbing. Also $\mu_i$ is the expected time to absorption starting at state $i$...
2
votes
1answer
241 views
Part specification error with InterpolatingFunction when generating a Markov Modulated Poisson Process
I want to create a Markov Modulated Poisson Process, where the arrival rates created by the states of a ContinuousMarkovProcess are fed into an ...
0
votes
2answers
164 views
Question RE DiscreteMarkovProcess Graph Labels
I'm trying to label the arc's of my Markov chain with symbols like $\alpha$, $\beta$, etc., to show how the Markov chain looks abstractly.
So, I did this...
...
2
votes
0answers
96 views
What do the default shapes/colors in DiscreteMarkovProcess Graph mean?
In making markov chains, I know how to do that, but I am curious as to what the different colors, and shapes of the vertexes in the graph output mean.
as example;
...
1
vote
0answers
113 views
Fit a custom process to a data: inhomogeneous 2-state Markov chain
I would like to fit a custom process - a time inhomogeneous 2-state Markov chain, to data. The time inhomogeneity is a result of the transition probabilities varying sinusoidally through time with a ...
4
votes
2answers
630 views
Time inhomogeneous Markov Chain in Mathematica
I would like to create a discrete 2-state Markov process, where the switching probabilities in the transition matrix vary with time.
I can currently do the following, which creates a process with ...
1
vote
1answer
828 views
Code efficiency improvement needed solving problem 499 in Project Euler
I am trying to solve https://projecteuler.net/problem=499 by constructing a transition matrix and finding its steady state. Here is my code:
...
3
votes
3answers
228 views
Problem with a Markov's Matrix
I recently discovered the Markov process.
To simplify my work, I use the following code taken from the DiscreteMarkovProcess documentation:
...
2
votes
1answer
553 views
Where can I find a good tutorial for stochastic modeling using Mathematica?
I am a newbie in Mathematica and I aim to use Mathematica mostly for stochastic modeling (to develop and analyze models in evolutionary biology). Note that I am not necessarily a great mathematician ...
0
votes
1answer
441 views
My Baum-Welch algorithm is very slow. Is it due to Mathematica?
I've also posted this question here, since I'm not sure which community is more adequate for this type of question.
I've programmed imperatively the Baum-Welch algorithm for a 2 state hidden Markov ...
