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Stochastic Methods
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What does stochastic mean?
Outputs are not predictable
What is the opposite of stochastic?
Deterministic
What happens if you sort sets of numbers before adding them?
They retain uniform distribution
What is central limit theorem?
When you combine numbers from several populations, the data becomes normally distributed regardless of the starting populations
What is regression to the mean?
When you combine samples, it is unlikely that very large or very small numbers are summed
How can you generate random numbers?
A seed from a computer clock, or atomic decay or thermal noise for 'true' random
What can you use random numbers for?
Simulations or bootstrapping
What is bootstrapping used for?
Avoids the assumption of normality by resampling data to get confidence intervals
How do you resample data?
Take some numbers from the data and find the mean, then repeat many times. The resampled means are now normally distributed around the original mean
What else can you resample apart from means?
Medians, although these may be sensibly asymmetrical around the mean
What happens if you bootstrap a normal distribution?
You should have confidence intervals similar to the original data
What is replacement?
You can sample with or without 'returning' numbers after choosing them
Should you replace?
Usually, especially with small datasets
What can you use random numbers for in simulations of human data?
Generating noise
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