Questions tagged [markov-process]

A stochastic process with the property that the future is conditionally independent of the past, given the present.

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Using Markov Chains to predict market share for prescription drugs

I wish to understand if the approach I am researching holds up to analytical rigor. I am planning to use historical data of 4 prescription drugs to forecast the market share of the same 4 drugs some ...
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Probability of simultaneous events given different conditions [closed]

We are dealing with a probability-theoretic back-of-the-envelope calculation for a thesis and have run into a problem - hope somebody can help! Our case is the following: We observe an agent, $i$, ...
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How to produce a transitional matrix when there is no example of some starting states in your data using R?

I am working toward building a Markov chain model, and need to produce a transition matrix for the model to be built. Using three categorical variables, Student Type, Full-time/Part-Time status, and ...
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LR test for overlapping return data using bootstrap

I wish to test a null hypothesis as in Christoffersen (1998) to see whether a sequence of Value-at-Risk forecasts $Q_t(p) \in \mathcal{F}_t$ possesses correct conditional coverage. Here $p \in [0,1]$ ...
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derivation for piecewise deterministic Markov process

I was reading a formulation of piecewise-deterministic Markov process $\Pi_t$, $ t \in \mathbb{R}_+$. In particular $\Pi_t$ is defined as $\Pi_t = P (X_t | \mathcal{F}_{\lfloor t/ \Delta \rfloor}) $ ...
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Deciding on sequence prediction approach

I have a space of 128 states expressed with binary bitstrings. The transition probabilities among these states are known to me, as follows: ...
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Event-based markov chain with observed covariates at non-constant time intervals

I am working on a project where I need to identify the traffic state at intersections. More specifically, I want to classify the situation in 5 states: undersaturation (where the traffic needs to stop ...
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When does a stationary distribution for a CTMC not exist?

Recalling that a Continuous-time Markov Chain (CTMC) is defined by its generator matrix $Q$, when does a stationary distribution for a CTMC not exist? Or when does there not exist a probability vector ...
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Markov Chain for Amino Acid Sequence

I was wondering if it is possible to apply Markov Chain to this amino acid sequence "ddvlsldeddddsdyncgednd" to find the probability of this sequence forming in this particular positional ...
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Proving positive recurrence for a finite state space DTMC

Let $$P = \begin{pmatrix} 0.3 & 0.5 & 0 & 0 & 0 & 0.2 \\ 0 & 0.5 & 0 & 0.5 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0.3 & 0 & 0 &...
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Markov Chains - Can we set the Initial distribution as $X_{1}$ instead of $X_{0}$ to calculate a non-conditional probability?

Had a small question when I was going through Ross – Probability Models. Given a discrete-time Markov chain $\{X_{n}: n=1,2,3 \ldots\}$ with a state space $\mathcal{S} = \{0,1\}$, and an initial ...
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Rankings transition matrix

I have heard of ratings transition matrices in finance, where it is possible to derive the probability of moving from one rating to another in a Markov chain process. If I have N individuals who are ...
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What does it mean for a Markov CHAIN to be recurrent (not just a state)?

There are many resources offering equivalent definitions of recurrence for a state in a Markov Chain - for example, state $x$ is recurrent if, starting in state $x$ you will eventually return to state ...
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Question regarding limiting probability

Does there exist an irreducible discrete time Markov chain such that all limiting probabilities exist, i.e. $\lim\limits_{k \to \infty} \mathbb{P}(X_k = i)$ exists for all states $i$, and $\sum_{i} \...
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How to calculate var(var) in time series

I try to calculate var(var) with Markov Process in time series by Bartlett(1946, P28) https://www.jstor.org/stable/2983611?seq=2#metadata_info_tab_contents , I use quadratic form calculate,but I didn'...
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When to use a markov switching model?

When can you use a markov switching model? For example if I was looking at the effect of inflation on bank liquidity, could it be used here?
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Question on the transition analysis and if they happen by chance (R)

I am wondering if somebody could suggest there I can find a tutorial or a book how to write the code in for following problem. As the title sad I have a transition matrix , and I need to know id the ...
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Local independence vs global independence in markov network

I am having a hard time understanding the basic differences between the local independence and global independence of a markov network. Please help me illustrate with a graph or any example
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Markov Chains examples

So I've been given four examples of stochastic processes, and asked which are Markov chains: The four examples are henceforth: "Keep rolling a die and let $X_n$ be the value of the n-th roll.&...
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calculating factors of markov chain [closed]

How do i calculate these numbers(image below) in a markov chain. What is the intuition behind this. I understand, since these are undirected graphs we are trying to calculate the strength of edges as ...
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From two-state Markov Chains to Mean Time Between Failures / To Repair

Let $\mathcal T = \{1,2,\ldots,T\}$ denote the set of points in time, $S = \{0,1\}$ the state space, $X = (X_t)_{t \in \mathcal T} \in S^\mathcal T$ a time series, $\alpha = \mathbb P(X_{t+1} = 0 \mid ...
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“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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Is the data-processing inequality still true for higher-order Markov chains?

The data processing inequality states that if $X_1,X_2,...,X_n$ form the first-order Markov chain: $$ X_1 \rightarrow X_2 \rightarrow \cdots \rightarrow X_n $$ Then for all $i \leq j \leq k \leq l$: $$...
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Repeated Poisson draws - stationarity

Many individuals (say, $N=500$ or more) independantly draw from a Poisson distribution with mean $\lambda$. This gives the "Time until next update", $t_u$, for each respective individual. At ...
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Forward equations and global balance equations for SIRS model?

I have a system with 3 states: 0, 1, 2 (disease-free, infectious and isolated - is this a SIRS model? It's looking at an individual person rather than a population). Transition from 0 to 1 takes place ...
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Explain formally how expected time to hit 0 from two is the sum of the expected time to hit 1 from 2 and 0 from 1

I have a symmetric random walk on the integers with probability $p$ and $q$ of going up and down respectively started at $X_0 = 2$. Let $$ T^0 = \min\{ n > 0: X_n = 0\}, T^1 = \min\{ n > 0: X_n =...
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Creating transition states for a second order Markov Chain for Attribution

I'm pretty new to Markov Chains, and I'm exploring them for attribution. I'd like to play around with higher orders but I'm a little confused on how to do this. Most resources I can find show a second ...
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Prove the given transformation of a Markov Chain is a Markov Chain

Let $\{X_n:n=0,1,\dots\}$ be a discrete time Markov chain on state space $S$. We define $Y_n$ as the following: $$Y_n=(X_n, X_{n+1})$$ Prove that $\{Y_n:n=0,1,\dots\}$ is a discrete time Markov chain ...
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Is it possible to eye a reversible Markov Chain by it's transition matrix?

I was wondering if it's possible. Many of the other Markov-Chain properties can be (somewhat) easily eyed from the transition matrix. (e.g. irreducible - if there's an absorbing state (1 in the ...
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Calculating the expected number of visits to a state by a DTMC

Suppose we have a DTMC $X$ : $\{X_n : n = 0, 1,2,\dots\}$, a transition probability matrix $P$, and state space $S = \{1,2,3\}$. Suppose I want to calculate the expected amount of times we visit state ...
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Using Forward Backward algorithm to find posterior probability of all possible states

I understand that Viterbi finds the most probable sequence of states. However, I want the probability of all possible sequences of states. I understand that FB algorithm can be used to find the ...
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Why is Markov Property useful for modeling systems?

I came across this question in my data science interview practice, and am not sure how to answer. Markov models are based on the assumption of Markov property, so it is useful for modeling Markov ...
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Conditional probabilities with Discrete Time Markov Chain non-perishable inventory

Suppose $\{X_n : n =0,1,2,\dots \}$ is a DTMC that represents the inventory level at the end of day $n$. We have inventory policy $(2,4)$, i.e., if $X_n < 2$, we order enough units to have ...
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Is gamma actually an efficient way to weigh future rewards in reinforcement learning?

Typically the discounted sum of rewards is defined as follows: G_t = Sum(gamma ** n * reward_t...) But this means that rewards are worth exponentially less with ...
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MCMC beginner question at an example chain plot: Do I need more steps? How much burn-in do I need, if I can tell already?

I am using the emcee python library to fit a model to data via MCMC. Below an example plot for the chain of one of my parameters. Here I ran 1000 steps with 100 walkers. Now I have two beginner ...
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Fitting the transition matrix of a Markov chain given the series of state

Almost all examples I can found on Markov chain and python are giving the transition matrix as known. Is there any library that can fit the transition matrix from the series of state observations?
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Prove the joint distribution of an AR(1) process is Multivariate Gaussian

I'm struggling a bit with the proof of this if anyone can help! I keep ending up going in circles with the conditional probabilities and I don't know what are the right steps to take. For an $AR(1)$ ...
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To compute the class of states for the given transition probability matrix

I have been given the following transition probability matrix of a markov chain: $P = \begin{pmatrix} \frac{3}{4}{} & 0 & \frac{1}{4} &0 \\ \frac{1}{2} & 0 & 0 & \frac{1}{2}\\ ...
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A Markov chain {Xn, n ≥ 0} with states 1, 2,3 has the transition probability matrix with an initial distribution (1/2,0,1/2), what is P(X1=3|X2=1)

A Markov chain {Xn, n ≥ 0} with states 1, 2,3 has the transition probability matrix P \begin{bmatrix}0&0.4&0.6\\1&0&0\\0.3&0.3&0.4\end{bmatrix} with an initial distribution A (...
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Whats exactly deterministic and non deterministic in deterministic and nondeterministic MDP policies?

Consider below Markov Decision Process: Blue hexagons are states and orange circles are actions. I have rather simple confusion. What will be nature of deterministic and non deterministic MDPs? This ...
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Equivalence of two state Markov chain and sampling via geometric distribution

Let $\mathcal T = \{1,2,\ldots,T\}$ denote the set of points in time, $S = \{0,1\}$ the state space, $X = (X_t)_{t \in \mathcal T} \in S^\mathcal T$ a time series, $\alpha = \mathbb P(X_{t+1} = 0 \mid ...
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Is it possible to occupy two states at the same time in Markov process/chain?

As in the topic - is it possible for an agent in a system of Markov's fashion to move into two states at once?
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How to find the n-step matrix more efficiently?

Is there any clever way to find the n-step matrix of a chain? I have the following transition matrix However, $p^{(n)}_{1,2}$ I spent a lot of time trying to find a way of recurrence along the paths ...
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Are invariant and stationary distribution the same thing?

I am reading a material about Markov chains and in it the author works on the Markov chains part discrete the invariant distribution of the process. However, when addressing the part of continuous ...
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Birth and death process and Counting processes - What is the relationship?

Well, I started to study the birth and death process and can I say that a counting process is an example of a pure birth process or that the birth and death process is an example of a counting process?...
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Markov process of order one a Martingale?

I have two questions, and I am very confused about the concepts Can a Markov process of order one also be a Martingale? Is any Markov process of order one also a Martingale? can anyone help me solve ...
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Likelihood ratio test for Markov orders - What succession of tests?

I want to estimate the Markov order of a binary sequence. For that I calculated transition matrices and the log likelihoods for the orders of interest 0,1,2 and 3. Essentially the one with the highest ...
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Calculating marginal distribution of Markov process

i am studying markov processes and we have an example of a VAR process. i am trying to understand how to look at the marginal distribution so i can find a gaussian distribution for $Y_t$ which equates ...
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Queuing theory. Modification in the M/M/1 model

In a queue of type M/M/1 when making the following modification: when there are 3 customers in the system (2 in the queue and 1 being served) if another one arrives he will leave and never come back. ...
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Periodic Markov chain in 3D state space

Does someone have an example for a discrete time (time-homogeneous) Markov chain in a three-dimensional state space that is characterized by a transition matrix resulting in periodic behaviour? I am ...

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