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A game of snakes and ladders or any other game whose moves are determined entirely by dice is a Markov chain, indeed, an absorbing Markov chain. This is in contrast to card games such as blackjack, where the cards represent a 'memory' of the past moves. To see the difference, consider the probability for a certain event in the game.
Instead of defining to represent the total value of the coins on the table, we could define to represent the count of the various coin types on the table. For instance, X 6 = 1 , 0 , 5 {\displaystyle X_{6}=1,0,5} could be defined to represent the state where there is one quarter, zero dimes, and five nickels on the table after 6 one-by-one draws.
The possible values of X i form a countable set S called the state space of the chain. [ 1 ] Markov chains are often described by a sequence of directed graphs , where the edges of graph n are labeled by the probabilities of going from one state at time n to the other states at time n + 1, Pr ( X n + 1 = x ∣ X n = x n ) . {\displaystyle \Pr(X ...
In probability theory, a transition-rate matrix (also known as a Q-matrix, [1] intensity matrix, [2] or infinitesimal generator matrix [3]) is an array of numbers describing the instantaneous rate at which a continuous-time Markov chain transitions between states.
Shadowstats.com is a website that analyzes and offers alternatives to government economic statistics for the United States.Shadowstats primarily focuses on inflation, but also keeps track of the money supply, unemployment and GDP by utilizing methodologies abandoned by previous administrations from the Clinton era to the Great Depression.
An additive Markov chain of order m is a sequence of random variables X 1, X 2, X 3, ..., possessing the following property: the probability that a random variable X n has a certain value x n under the condition that the values of all previous variables are fixed depends on the values of m previous variables only (Markov chain of order m), and the influence of previous variables on a generated ...
In computational statistics, reversible-jump Markov chain Monte Carlo is an extension to standard Markov chain Monte Carlo (MCMC) methodology, introduced by Peter Green, which allows simulation (the creation of samples) of the posterior distribution on spaces of varying dimensions. [1]
The immediate value to this method is that the output represents what is acceptable, even when that is from imperfect geometry and, because it uses recorded data to perform its analysis, it is possible to include actual factory inspection data into the analysis to see the effect of proposed changes on real data.