Download Modelling: real-world situations

Modelling: real-world situations
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Review the types of models
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Main reason:
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Answer questions
Solve problems
Make predictions
Statistical models are used to model situations
involving uncertainty:
Probability models
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Reliability of appliances
(Chapter 3)
Spread of diseases
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It is uncertain whether the
uninfected person will catch
the disease.
The probability of getting
infected is affected by:
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contact
We will need parameters to
make a definite prediction
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Infected
The nature of the disease
General health of the person
Ect.
Uninfected
OUTCOME = not automatic infection
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Length of time before someone
who has caught the disease
becomes infectious themselves
Length of time before a person is
no longer infectious.
Regression models (Chapter 4)
y  a  bx
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Relationship between 2 variables
Use the equation to make predictions
Uncertainty: variables do not follow
relationships exactly
The reliability of predictions depends on how
closely the line fits the data
Parameters:
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values of a – intercept, b - gradient
Random variables: distribution models
Chapter 6 & 7
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Number of births before
a particular sex is born
1
p ( x)  x
2
x  1,2,3...
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The parameters:
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Most important
continuous distribution:
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Normal distribution
Mean
Standard deviation
If known, other facts
about the distribution can
be obtained.
Checking the validity of a model
Misuse of models = errors in
statistics
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Check:
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The assumptions it
makes correspond with
the situation being
modelled.
Example: no point in
applying a probability
model that assumes
outcomes to be
independent to situations
where this is not the
case.