22Bayesian Statistics
Instead of asking ‘what do my data show?’, the Bayesian analyst asks ‘how do my data alter our view of the world?’. It may not sound like much, but it is a fundamental change of outlook. The idea is that the results of the new study are assessed in the light of the existing knowledge to establish an updated assessment of parameter values and their uncertainties.
Imagine we have a model in mind for a data set. Whether we are Bayesian or not, there will be parameters, 
, in this model that we want to estimate (or learn about). The way that a Bayesian and frequentist view these parameters differs:
- A frequentist would view the parameters
as fixed quantities whose true values are unknown to us.
- – The key here is that the parameters are thought of as fixed (i.e. a single number which is unknown to us).
- – The aim is to estimate these parameters.
- A Bayesian would view the parameters
as random variables, represented by a probability distribution.
- – These are not thought of as fixed.
- – For a specified model with parameters
, we combine our existing (pre‐data) information ...
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