Given I am starting to make some posts to this blog (again) I was pleased to run across a youtube of Xiao-Li Meng being interviewed on the same topic by Suzanne Smith the Director of the Center for Writing and Communicating Ideas.
One thing I picked up was to make the problem being addressed in a any communication very clear as there should be a motivating problem – the challenges of problem recognising and problem defining should not be over looked. The other thing was that the motivating problem should be located in the sub-field(s) of statistics that addresses such problems.
The second is easier as my motivating problems mostly involve ways to better grasp insight(s) from theoretical statistics in order to better apply statistics in applications – so the sub-fields are theory and application, going primarily from theory to application. This largely involves trying to find metaphors or even better – various ways to re-represent theory in terms that are more suggestive of how/why it works or hopes to work. Vaguely (and overly hopeful), to try and get diagrammatic representations that facilitate a moving picture of how/why it works or hopes to. To see representing (modelling) at work.
At a very general level, my current sense is that statistics is best viewed as being primarily about conjecturing, assessing, and adopting idealised representations of reality, predominantly using probability generating models for both parameters and data. Now we want less wrong representations of reality and hopefully we can get them. This can only be a hope as we never have direct access to reality to ever in fact know. In light of this, my motivating problem is how to get less wrong representations of reality that remain hopeful.
This representation of reality venture can be broken into three stages:
1. Speculate a prior distribution for how unknowns (e.g. parameters) were determined or set in nature and then observations subsequently generated given those unknowns.
2. Deduce the most relevant representation given the actual observations that occurred (aka getting the posterior).
3. Evaluate the fit and credibility of the representation in light of 1 and 2 with prejudice for finding faults (ways to improve) returning to 1 until no further improvement seems currently plausible.
Steps of 1,2,3; 1,2,3; 1,2,3 – hold for now and hope.
Now the full theory I am trying to draw from is mostly statistical but some theory of (profitable) empirical inquiry (aka philosophy) is required as the aim is to enable others to avoid being misled when trying to learn from observations while being aware of the risks they are unable to avoid.
In summary my future posts will have these motivations, most likely will focus on speculation of _good_ priors and the evaluation of fitting, understanding, criticising and deciding to (tentatively) keep with representations. This should not be taken as suggesting that getting posteriors is less important – but that is not my strength (and I am hoping Stan will increasingly make that simple in more and more cases).