# 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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### 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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### 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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### 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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### 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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### 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 ...
451 views

### Slow computation of recursive sequences

I want to investigate the asymptotic behavior of the following recursive system: ...
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### 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 ...
133 views

### Fit Markov Chain

Assume a simple Markov Chain with the transition matrix ...
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 ...
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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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### 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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### Plotting absorbing state probabilities from state 1

I have the following transition matrix: ...
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 ...
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: ...
381 views

### Constructing transition probability matrix

I have the following list: ...
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### 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 ...
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 ...
171 views

### FindShortestPath in Markov Transition Matrix

So I have a part of transition matrix like this. ...
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 ...
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 ...
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### 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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### 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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Observe: ...
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### 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 ...
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 <...
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: ...
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### 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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### 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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### 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 ...
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, ...
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### 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 ...
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 ...
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 $i$...
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 ...
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... ...
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### 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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### 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 ...
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 ...
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: ...
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### 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: ...