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What is sought in data analysis with regards to models?
They must account for the variability in data
What name is given to imperfect data?
How might one model be better than another?
If it is more accurate (accounts for more of the variability)
How are models improved?
- By discovering relevant factors
- When taken into account, these help to explain more of the variation in data
Why are models favoured by Scientists over anecdotal evidence?
- Science attempts to create general laws
- 'The purpose of formulating a model is not merely to account for the data at hand, but to use the data as a means of formulating a model that is 'true' more generally
What is the difference between the particular and the general?
Sample (particle) data are used to discover what is 'true' in the population (general)
What is a signal?
The model data
What is noise?
- Random fluctuations in the measurements of signal data
- It is the task of that statistical analyst to distinguish the signal from the background noise
What happens as the strength of background noise increases?
- Our ability to detect the signal decreases
- It is harder to discover the appropriate underlying model
- The accuracy of the model predictions also decrease
What is the general assumption when it comes to generalisation?
If a model works well for existing data, it can be used to predict the outcomes of data not yet observed
What is the principle of replicability?
Identical conditions yield identical results
What do models (signals) represent in terms of replicability?
The regular, reliable components of data
What does noise correspond to?
Aspects of the data that are unstable and unpredictable
What is assumed about noise with regards to replicability?
- It is considered to be random
- It is the result of a multitude of small and random influences
What does strict replicability demand?
Precisely the same measurement must be obtained under every repetition of an observation under a given set of circumstances
What does general replicability demand?
- The repetition of an experiment should lead to the same general conclusion
- Numerical values need not be identical