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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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: ...
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2
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2
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104
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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 ...
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49
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2
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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?
17
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2
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957
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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, ...
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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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111
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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 ...
- 427
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126
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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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57
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Unexpected PDF in `FirstPassageTimeDistribution`
I am new to Markov Processes, and while learning the discrete Markov chain with the following matrix $$P=\begin{bmatrix}\frac{1}{3} & \frac{2}{3} & 0 & 0 \\ \frac{1}{2} & \frac{1}{2} &...
- 101
3
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1
answer
226
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Graphing Markov chains / decision trees
I'm looking to graph a simple one-way Markov chain, which is effectively a decision tree with transitions probabilities. One way I've got this working in here in an MWE, here's a simple Markov chain ...
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Metropolis-Hastings Algorithm - Significantly slower than Python
I would like to code a Metropolis Hasting algorithm and thought I would get the general scheme of things going with a toy example.
I think I got it running but my Mathematica code runs significantly ...
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2
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How to add the weights to the transition graph of a Markov chain?
The following working program uses
Graph and Markov Chain
...
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4
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Compute the stationary distribution of a large transition matrix
I am doing some simulations for simple random walks on directed random graphs. From a graph of n vertices, I get a n by ...
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6
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2
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389
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Generate an ε-machine graph from transition probability matrices
I am trying to generate this type of graphic:
see Fig.1a from https://arxiv.org/abs/0905.3587.
This process is associated with two transition matrices
$$ T^{(0)} = \begin{pmatrix}
0&p&0\\
1&...
- 561
1
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2
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369
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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 ...
- 1,596
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60
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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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473
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Slow computation of recursive sequences
I want to investigate the asymptotic behavior of the following recursive system:
...
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35
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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 ...
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145
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4
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329
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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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330
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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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131
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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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133
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Plotting absorbing state probabilities from state 1
I have the following transition matrix:
...
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22
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3
answers
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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 ...
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4
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303
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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:
...
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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 ...
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3
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1
answer
455
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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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1
answer
190
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FindShortestPath in Markov Transition Matrix
So I have a part of transition matrix like this.
...
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1
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376
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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
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1
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231
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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 ...
- 631
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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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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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4
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212
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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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121
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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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93
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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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283
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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 ...
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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 ...
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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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2
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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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1
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253
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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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2
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181
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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 ...
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