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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How to run a for loop for RandomFunction in order to take an aggregate of trajectories to approximate the steady state?

I am trying to approximate the steady state for the given rate matrix: By using the ContinuousMarkovProcess function and the RandomFunction process. I want to implement some sort of for loop system ...
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1 vote
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How to find periodic steady state of symbolic matrix in Mathematica?

I am currently trying to recreate results in a paper where I solve for the periodic steady state of the following rate matrix: Where epsilon is some force parameter, I have found the left and right ...
• 27
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How to solve a Markov transition matrix using Mathematica?

I need some help in working out how to solve this problem. I have a transition matrix of size $4\times4$ at time $t=0$ - call it $A$ I also have another transition matrix at time $t= 10$ - call it $B$ ...
• 9
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Any luck estimating a multivariate hidden Markov process?

I am having problems using EstimatedProcess to estimate a multivariate HiddenMarkovProcess. I'm following the work of a paper, so I know this method is feasible. In brief, given 2 economic variables: ...
• 1
108 views

Optimization of a Markov сhain with symbolic transition rate

I am trying to work on 1D random walk that can move to left, right or stay with probabilities $p_i$,$q_i$,$r_i$ that changes with the site $i$. I am trying to simulate this by using a recurrence ...
• 160
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Which model behind SequencePredictorFunction?

Is the SequencePredictorFunction based on Hidden Markov Model? If so, how does the model estimate the number of hidden states?
1k views

Diffusion probabilistic model in deep generative modeling

Diffusion Models (http://proceedings.mlr.press/v37/sohl-dickstein15.html and https://arxiv.org/abs/2006.11239) are generative models gaining popularity in the community of deep generative modeling, ...
• 835
160 views

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 ...
126 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 ...
• 437
137 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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1 vote
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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: ...
• 6,263
75 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 ...
• 1,698
60 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 ...
482 views

Slow computation of recursive sequences

I want to investigate the asymptotic behavior of the following recursive system: ...
38 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 ...
• 802
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Fit Markov Chain

Assume a simple Markov Chain with the transition matrix ...
• 407
345 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 ...
• 2,705
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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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1 vote
136 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?
136 views

Plotting absorbing state probabilities from state 1

I have the following transition matrix: ...
• 2,705
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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 ...
• 1,022
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Constructing higher order transition probability matrix

Recently I asked a question here about how to construct a transition probability matrix given the following list: ...
• 3,116
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Constructing transition probability matrix

I have the following list: ...
• 3,116
677 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 ...
• 3,167
530 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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FindShortestPath in Markov Transition Matrix

So I have a part of transition matrix like this. ...
• 127
1 vote
387 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 ...
236 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 ...
87 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
134 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
44 views

Observe: ...
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794 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 ...
• 841
212 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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130 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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1 vote
95 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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1 vote
293 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
419 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 ...
• 439
1 vote
283 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, ...
• 11
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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 ...
• 183
1 vote
361 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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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 $i$...