Chapter 8: DataDriven Models

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Chapter 8 Data-Driven Models

• 8.2 Function Tutorial

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Background Data-Driven Models

• So far weve been given a model (dP/dt kP)
  and used it to generate data.
• Research often requires us to build a model based
  on (limited) data.
• To do this, it helps to be familiar with the
  standard mathematical functions used for building
  models.

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Linear Functions

• Straight line is the simplest model
• Human beings are biased toward viewing patterns
  as straight lines with positive slope (Busemeyer
  et al. 1997)

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Linear Functions
m slope b intercept
y
?y
b
?x
x
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Quadratic Functions
y
a special case of
x
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Polynomial Functions
f(x)
N degree
x
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Square Root Function
Useful when quantities are already squared e.g.
distance between two points (x1,y1 ) and (x2,y2 )

f(x)
x
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Exponential Function
P(t)
t
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Logarithmic Function
Useful when dealing with inherently exponential
measures, e.g. Richter scale for earthquakes.
y
x
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Log/Log Plot for Power Laws
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Logistic Function
P(t)
t
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Trigonometric Functions

• Useful for for modeling cyclic processes (ocean
  temperature, blood sugar level)
• Because sin(?) cos(?-?/2), we generally only
  need cos.

cos(x)
x