A Very Simple Weather Model
The probabilities of weather conditions (modeled as either rainy or sunny), given the weather on the preceding day, can be represented by a transition matrix:
The matrix P represents the weather model in which a sunny day is 90% likely to be followed by another sunny day, and a rainy day is 50% likely to be followed by another rainy day. The columns can be labelled "sunny" and "rainy", and the rows can be labelled in the same order.
(P)i j is the probability that, if a given day is of type i, it will be followed by a day of type j.
Notice that the rows of P sum to 1: this is because P is a stochastic matrix.
Read more about this topic: Examples Of Markov Chains
Famous quotes containing the words simple, weather and/or model:
“Your apple face, the simple crèche
Of your arms, the August smells
Of your skin. Then I sorted your clothes
And the loves you had left, Elizabeth,
Elizabeth, until you were gone.”
—Anne Sexton (1928–1974)
“States that rise quickly, just as all the other things of nature that are born and grow rapidly, cannot have roots and ramifications; the first bad weather kills them.”
—Niccolò Machiavelli (1469–1527)
“Your home is regarded as a model home, your life as a model life. But all this splendor, and you along with it ... it’s just as though it were built upon a shifting quagmire. A moment may come, a word can be spoken, and both you and all this splendor will collapse.”
—Henrik Ibsen (1828–1906)