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You would add a variance (P), estimate of the value and the timestamp of the last measurement. Using the last timestamp you can calculate Q. Generally, the older the last measurement, the higher Q.

The calculation is straightforward once you let some things be the value of identity:

  P1 = P0 + Q
  K = P0 / (P0 + R)
  x1 = x0 + K * (z - x0)
  P1 = (1 - K) * P0
Now you have the new score for your data (x1) and a new variance to store (P1). Other values are:

x0, P0 - previous score, previous covariance Q - Roughly related to the age of the last measurement. Goes up with age. R - Measurement error. Set it close to 0 if you are sure your measurements are always error-free. z - the most recent measured value.

Let's say you measure number of clicks per 1000 impressions. Now you can estimate the expectation value (x1) for the next 1000. After the second 1000 re-estimate again.




Thanks for explaining that!




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