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3. Decaying Averages


The topic for this notebook is Decaying Averages. 1. We will see that Traditional Averages are the best for Static Data Sets, but inadequate for Living Data Streams. Live Data Streams demand Relevance and Sensitivity. 2. We will see that the Decaying Average is both Relevant and Sensitive. It is also easy to calculate. Because of these factors the computation of Decaying Averages yielded an early evolutionary advantage. The Decaying Average led to prediction, which enabled anticipation, which facilitated survival. 3. We will also discover that knowing the Realm of Probability is another helpful predictive measure. To calculate this Realm, we explore the Average Decaying Deviation, or just Deviation. We explore its computation and evolutionary advantages. 4. The final tool we explore is the Average Decaying Directional or just Directional. This allows the organism to compute local tendencies, which also aids the survival of organisms and businesses. (Below are the contents of this Notebook. Click on Headings to access them.)

1. Traditional Averages & Live Data Sets

A. Traditional Averages good for Static Data Sets
B. Live Data Streams
C. Live Data Streams need more than a Mean Average

2. The Decaying Average, Relevant & Sensitive

A. Alternative Approaches to Decay & Sensitivity... 9
B. Derivation of the Decaying Average
C. Behavior of Averages
D. Analysis of a Graph
E. Evolutionary Advantages
F. Rating complexity of computations
G. An Application of Computational Complexity
H. Neural Networks can easily handle this Computation... 19
I. Experience, Prediction & Anticipation... 20
J. Philosophical Approaches to the Decay Factor... 21

3. The Average Deviation, Realm of Probability

A. Possibility vs. Probability
B. Generation & Calculation
C. Evolutionary Possibilities

4. The Average Directional, Local Tendencies

A. Generation & Calculation
B. Evolutionary advantages



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