# Questions tagged [transition-matrix]

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

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### Estimating markov transition matrix using total elevator "ups" and "downs" by floor

I have data on elevator presses and I am hoping to use them to estimate a Markov transition matrix, so I can ultimately estimate how frequently people go to different floors. For each floor from 1-4, ...
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### Is it possible to use Particle Marginal Metropolis Hastings to estimate the transition matrix and input?

A state space model is defined as: $$x_{t+1} = A_tx_t + B_tu_t$$ $$y_{t+1} = H_tx_{t+1}$$ So my question is: is it possible to use Particle Marginal Metropolis Hastings to estimate the transition ...
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### Sum of powers (geometric series) of state transition matrix

I am working discrete time Markov chain analysis for some large state transition graph. I want to find the rewards/cost to reach from the init state to the terminal/accepting states. I have the state ...
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### Which variable is best suited for edge weights when computing graph algorithms instead of relative risks?

I am currently trying to develop graph data. Which variable is best suited for edge weights when computing graph algorithms? Relative risk Relative Risk: Many networks in my field use relative risks ...
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### msm package: Mutlti state model initial value in 'vmmin' is not finite

I am new to msm package and markov models. I have a randomized trial dataset with readings from three time points: baseline, at 1 year, and at 2 year. I am trying to calculate annual transition ...
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### How to understand the definition of Markov Chain $P(X_{n+1}\in B\mid \mathcal{F}_n)=p(X_n,B)$?

The definition of Markov Chain in Durrett (Probability: Theory and Examples, 2019, Section 5.2) is: $$P(X_{n+1}\in B\mid \mathcal{F}_n)=p(X_n,B),$$ where $p$ is the Markov transition kernel ...
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### Smoothing a transition matrix

I have a dataset containing observations at time t and t+1 of ratings A (best) to E (worst) and Default. I want to use transition matrices to predict future ratings t+2, t+3, etc The transition matrix ...
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### Transition Probabilities and Weibull Regression

I am currently reading a book on health technology assessment: Decision Modelling for Health Economic Evaluation (Briggs et al). Given all information below, I'd appreciate if someone could show how ...
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### How to calculate the probability Matrix (Alpha) for Regular Markov chains

Pardon me for being a novice here. In the image attached, eq 3.1 represents the transition matrix (it's pretty clear). I am not able to comprehend the eq 3.2, alpha*P = alpha, as well as the further ...
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### $\pi_i P^n_{i, j} =$ long-run proportion of time the chain is in $i$ and will be in $j$ after $n$ transitions?

I am currently studying the textbook Introduction to Probability Models by Sheldon M. Ross. Chapter 4.4 Long-Run Proportions and Limiting Probabilities says the following: Because $\pi_i$ is the long-...
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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 ...
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### 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 ...
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### 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 ...
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