Questions tagged [transition-matrix]

A transition matrix is a square matrix used to describe the transitions of a Markov chain.

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How to map a sequence to a transition matrix

I have the following transition matrices, one for Maria and one for Anna: ...
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How to analyze a time series of categorical data?

I have some data that look like this: ...
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What are the transition functions for RNNs

From what I understand, the hidden states of RNNs are equivalent to the deterministic probability distribution over hidden states in for example a Hidden Markov Model. Thus, just as probabilistic ...
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R CODE Transition Matrix having zeroes for some transitions

I have been trying to create a Transition Matrix using the data from 2000 entities over 40 observations (Years). I have ranked the data into percentiles, for example the highest value entity in a ...
23 views

Estimating transition probabilities of a Markov chain with bayesian approach

I am trying to model heteroskedasticity in time series data,and the volatility $\left(\sigma_{t}\right)$ is taken as a Markov chain with two values $\sigma_{h}>\sigma_{l}>0$ with transition ...
1 vote
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Approximating a countable-state (infinite) Markov model with a finite-state one

TL;DR—in a nutshell I have a countable-state Markov model (with a countably infinite number of states) in which the probability of transitioning to states $S_{i>k}$ for large $k$s are practically ...
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R MSM: unexpected identical transition rate matrices for different values of covariate; why?

I am fitting a continuous-time Markov model to a panel dataset using the R package MSM. Because I am interested in sex-differences in transition rates, I fit the ...
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What is the relationship between 2 covariance matrices of 2 variables?

Assume variable $\textbf{x} = [x_1, x_2]^\top$ with mean $\mathbf{\mu} = [\mu_1, \mu_2]^\top$ and covariance matrix: \Sigma_{\textbf{x}} = \begin{bmatrix} \sigma_1^2 & \text{cov}(\...
1 vote
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Estimating transition probability from a state to itself with the MSM package

For a given panel dataset I have used the MSM package to estimate transition probabilities between states. Using the pnext.msm function I can obtain the ...
• 1,560
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Transition Matrix for a non-trivial example

So I've just been introduced to Transition Matrices; and I was wondering what one for look like the following example: "Symmetric random walk on the integers" $S$ $=$ $\mathbb{Z}$, $\forall$ ...
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1 vote
60 views

"Forcing" equal probabilities in the matrix exponential of a Markov intensity matrix

I have an upper-right triangular transition intensity matrix $Q$ for a 7-state Markov model (with states $X_1,X_2,...,X_7$), from which I numerically calculate the matrix exponential to derive a ...
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1 vote
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1 vote
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Calculating 7-step transition matrix for example

In my notes on Markov processes, I am presented with two related examples: Example 1: Classify daily weather for some region as Sunny (state $1$), Cloudy (state $2$), or rainy (state $3$). ...
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443 views

Proof that the $n$-step transition matrix is the $n$th power of $\mathcal{P}$

I am presented with the following theorem in the context of Markov chains and stochastic systems: The $n$-step transition matrix is the $n$th power of $\mathcal{P}$: $$\mathcal{P}^{(n)} = P^n.$$ And ...
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1 vote
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Transition probability matrix

A gambler tosses a coin and a tetrahedron at each stage. If $H$, he receives the amount appearing at the face of the tetrahedron. If $T$, he pays the amount. The tetrahedron is fair, but probability ...
17 views

Find transition probability matrix

A box contains 3 balls. Each is either white or red. The game is to draw a ball from each period. If red is drawn, a white is replaced. But if white is drawn, all the balls in the box is replaced by ...
109 views

Number of stationary distributions of a Markov chain

How do i determine the number of stationary distributions that a Markov chain has if it is not irreducible or regular. The transition matrix is ...
455 views

1 vote
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Biased coins and Markov processes

Good day, I am attempting an optional exercise and I am finding it hard to interpret the problem in terms of matrices and vectors. Coin 1 has probability 0.4 of coming up heads, and coin 2 has ...
106 views

Formulating a Transition matrix for Markov Process

I am dealing with a medical process which is as follows. There are 10000 Veterans who are enrolled in this study. All 10000 have medical condition called onychocryptosis which is a fancy term for ...
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What is the difference betwen a time non-homogenous Markov Chain and a non-linear Markov Chain? Example

A time non-homogenous Markov Chain is one in which the transition probabilities are not constant over time. A non-linear Markov Chain is a model that is not linear in parameters and satisfies the ...
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1 vote
552 views

Irreducible Markov chain and transition matrix

We know that a matrix is irreducible if it is not similar via a permutation to a block upper triangular matrix. Is the transition matrix of a irreducible Markov chain irreducible?
1 vote
210 views

Bayesian inference of parameter governing Markov transition matrix

A 3-state Markov chain $X = \{x_i : i \in \{1, \cdots, N\}\}$ is observed, and its transition matrix $P$ is assumed to be of the form  \begin{pmatrix} (1-a)^2 & 2a(1-a) & a^2 \\ b(1-a) &...
1 vote
137 views

Bayesian inference of non-homogeneous Markov transition matrix

The data consists of several discrete-time Markov chains, indexed by a global time. I assume all the chains are governed by the same transition matrix, but that this can change in time. I want to ...
426 views

A Hidden Markov model with covariates in the transition probabilities

I would like to construct a Hidden Markov model with data about online customer journeys. A well-known concept related to the customer journey literature is the sales funnel. Consumers walk through ...
83 views

How two transition probability matrices can be used to find one variable in analysis

I'm working on a research paper for cricket analysis but I'm stuck on the point of the estimation of $\tau_{owj}$, which is defined in the appendix. I have calculated up through $\alpha_{owj}$ and \$\...
940 views

Second order markov tranision probability matrix

I tried to find the second order Markov chain of the following sequence Dat= A A B A B A A A B B A A B I tried it on "Markov chain" package in R. ...
837 views

Markov-Chain transition probabilities for 3 variables

I am a bit confused as I need to calculate the Markov-Chain transition probabilites for 3 variables. Example data, let's assume a sequence of letters at specific and progressively-constant time steps:...
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