The Prediction Model
The most common representation is
where is the predicted signal value, the previous observed values, and the predictor coefficients. The error generated by this estimate is
where is the true signal value.
These equations are valid for all types of (one-dimensional) linear prediction. The differences are found in the way the parameters are chosen.
For multi-dimensional signals the error metric is often defined as
where is a suitable chosen vector norm. Predictions such as are routinely used within Kalman filters and smoothers to estimate current and past signal values, respectively.
Read more about this topic: Linear Prediction
Famous quotes containing the words prediction and/or model:
“Recent studies that have investigated maternal satisfaction have found this to be a better prediction of mother-child interaction than work status alone. More important for the overall quality of interaction with their children than simply whether the mother works or not, these studies suggest, is how satisfied the mother is with her role as worker or homemaker. Satisfied women are consistently more warm, involved, playful, stimulating and effective with their children than unsatisfied women.”
—Alison Clarke-Stewart (20th century)
“...that absolutely everything beloved and cherished of the bourgeoisie, the conservative, the cowardly, and the impotent—the State, family life, secular art and science—was consciously or unconsciously hostile to the religious idea, to the Church, whose innate tendency and permanent aim was the dissolution of all existing worldly orders, and the reconstitution of society after the model of the ideal, the communistic City of God.”
—Thomas Mann (1875–1955)