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:
“This is my letter to the world,
That never wrote to me—
The simple news that Nature told,”
—Emily Dickinson (1830–1886)
“Every incident connected with the breaking up of the rivers and ponds and the settling of the weather is particularly interesting to us who live in a climate of so great extremes. When the warmer days come, they who dwell near the river hear the ice crack at night with a startling whoop as loud as artillery, as if its icy fetters were rent from end to end, and within a few days see it rapidly going out. So the alligator comes out of the mud with quakings of the earth.”
—Henry David Thoreau (1817–1862)
“AIDS occupies such a large part in our awareness because of what it has been taken to represent. It seems the very model of all the catastrophes privileged populations feel await them.”
—Susan Sontag (b. 1933)