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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401 views

Slow computation of recursive sequences

I want to investigate the asymptotic behavior of the following recursive system: ...
24 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 ...
99 views

Fit Markov Chain

Assume a simple Markov Chain with the transition matrix ...
166 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 ...
64 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 ...
84 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?
72 views

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 ...
188 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: ...
267 views

Constructing transition probability matrix

I have the following list: ...
291 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 ...
288 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 ...
154 views

FindShortestPath in Markov Transition Matrix

So I have a part of transition matrix like this. ...
217 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 ...
161 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 ...
58 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: ...
105 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: ...
39 views

Observe: ...
582 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 ...
172 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 <...
95 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: ...
77 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 ...
69 views

...
205 views

Training Hidden Markov Models using Mathematica

I have created a Hidden Markov Process with an initial probability vector, emission and transmission matrices. ...
333 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 ...
216 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, ...
109 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 ...
330 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 ...
152 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 $i$...
227 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 ...
128 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... ...
90 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; ...
107 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 ...
481 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 ...
712 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: ...
216 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: ...
512 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 ...
385 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 ...
358 views

Calculate the power spectral density of a Markov chain

I would like to calculate the symbolic power spectral density of a two state Markov process with a symbolic transition matrix characterised by two parameters. I have tried the code below, but it ...
229 views

Expectation of a composite Markov-Gamma distribution

In a model I have a discrete two-state first order Markov process, defined by a (2x2) transition matrix with two free parameters. If the first state occurs then the process outputs zero for that ...
144 views

Why am I getting wildly incorrect results from FirstPassageTimeDistribution with inexact transition matrix?

Working on some large systems using DiscreteMarkovProcess, I changed the transition matrix to machine precision vs using exact values, which sped things up handily. ...
389 views

State “i” goes to state “j”: list accessible states in a Markov-chain

I would like to have a code that given a state "i" in S, it give the set of states "j" which are accessible from "i". Is that possible in mathematica? My state space (S) is ...
275 views

Arranging “ranked” nodes of a graph symmetrically

I have Markov chains with a pair of absorbing states taken from the $n$-length strings formed from {"H","T"} for n at least 3 (...
314 views

How do I change the initial state of a discrete Markov process?

I have a simple Markov process defined with ...
1k views

How do I show the transition probabilities in a graph of a Markov process?

How do I get Graph to display the transition probabilities for a Markov process as labels on the graph's edges? The information is clearly present in the graph, but ...
279 views

Multiple Simulations of a Markov Chain

I am trying to create a simple series of Bernoulli bits whose probabilities follow a two-state Markov chain. ...
354 views

How to impose control over vertex-to-vertex Graph edges?

I’m working on a Markov Chain and hope there is a way to impose control over how Mathematica places edges to connect vertices in a Graph. My Markov Chain currently ...
207 views

random Poisson process over multiple variables (state vector) for chemical kinetics

Has anyone figured out how to coerce ContinuousMarkovProcess to work with a state vector, transition matrix, and rate (propensity) vector, and RandomFunction to return pairs of state vector and time, ...
I'm simulating a discrete time Markov process on a finite state space corresponding to a linear interval $(x_1, x_2, ..., x_N) \in X$, where each time step $t_i$ involves updating the state of some ...