Questions tagged [markov-chains]

Questions that deal with modeling and simulating random processes which switch between states under the Markov assumptions.

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Error in Metropolis-Hastings with three states?

I wanted to create a simple example of the Metropolis-Hastings algorithm as a sanity check but the check failed and the results do not line up. I have a vector of energies $\vec E=(E_1,E_2,E_3)$ and ...
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0 votes
1 answer
58 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 ...
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  • 341
0 votes
1 answer
111 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 ...
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0 votes
0 answers
54 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} &...
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  • 101
3 votes
1 answer
107 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 ...
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  • 857
15 votes
1 answer
973 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 ...
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1 vote
2 answers
70 views

How to add the weights to the transition graph of a Markov chain?

The following working program uses Graph and Markov Chain ...
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  • 896
4 votes
2 answers
170 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 ...
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  • 1,261
6 votes
2 answers
337 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&...
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  • 517
1 vote
2 answers
245 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: ...
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  • 4,391
2 votes
1 answer
52 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 ...
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  • 1,004
0 votes
1 answer
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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 ...
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4 votes
3 answers
463 views

Slow computation of recursive sequences

I want to investigate the asymptotic behavior of the following recursive system: ...
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0 votes
1 answer
30 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 ...
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4 votes
0 answers
140 views

Fit Markov Chain

Assume a simple Markov Chain with the transition matrix ...
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  • 387
4 votes
1 answer
261 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 ...
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  • 2,595
0 votes
1 answer
147 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 ...
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  • 101
0 votes
1 answer
116 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?
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5 votes
1 answer
119 views

Plotting absorbing state probabilities from state 1

I have the following transition matrix: ...
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  • 2,595
22 votes
3 answers
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 ...
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  • 1,002
8 votes
4 answers
258 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: ...
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  • 2,696
6 votes
3 answers
426 views

Constructing transition probability matrix

I have the following list: ...
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  • 2,696
7 votes
2 answers
527 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 ...
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  • 3,077
3 votes
1 answer
401 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 ...
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5 votes
1 answer
178 views

FindShortestPath in Markov Transition Matrix

So I have a part of transition matrix like this. ...
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  • 117
1 vote
1 answer
354 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 ...
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4 votes
1 answer
221 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 ...
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0 votes
1 answer
82 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: ...
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1 vote
0 answers
120 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: ...
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1 vote
0 answers
42 views

What's going on with this FirstPassageTimeDistribution performance quirk?

Observe: ...
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  • 25k
5 votes
0 answers
709 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 ...
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  • 831
4 votes
0 answers
208 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 <...
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  • 17.6k
2 votes
1 answer
111 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: ...
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  • 2,283
1 vote
0 answers
85 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 ...
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7 votes
0 answers
78 views

Problem/bug with `RandomVariate` and `FirstPassageTimeDistribution`?

...
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1 vote
0 answers
262 views

Training Hidden Markov Models using Mathematica

I have created a Hidden Markov Process with an initial probability vector, emission and transmission matrices. ...
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1 vote
0 answers
388 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 ...
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  • 409
1 vote
1 answer
248 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, ...
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4 votes
1 answer
135 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 ...
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  • 183
1 vote
0 answers
353 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 ...
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  • 1,542
-1 votes
2 answers
170 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 $i$...
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2 votes
1 answer
247 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 ...
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0 votes
2 answers
176 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... ...
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  • 341
2 votes
0 answers
101 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; ...
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1 vote
0 answers
118 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 ...
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  • 3,077
4 votes
2 answers
668 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 ...
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  • 3,077
1 vote
1 answer
851 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: ...
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  • 7,661
3 votes
3 answers
229 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: ...
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  • 596
2 votes
1 answer
577 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 ...
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  • 1,095
0 votes
1 answer
457 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 ...
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