Risky Objectivity

A Dictionary of Objectivity

To be objective, one must not be subjective – that much is clear.   What is objective is visible while what is subjective is hidden.  But, what is hidden? It’s often hard to say, really.  After all, it’s subjective.   However, with the aid of a little psychoanalysis, at least two major notions of “not subjective” may be distinguished:

Empirical Objectivity.  The essence of empirical objectivity is the recorded observation.   Ostensibly, a scientific datum conveys the state of the world, or at least a small part of it, to any and all interested parties:  It’s what is out there where anybody can see it, if they care to look.  There are more than a few caveats though.  Data can be falsified, misrepresented or misunderstood.  For example, in computer engineering data is anything that can be stored in in a computer’s memory - whether it is true, false, or meaningless.  Since scientific data are often kept in computers, it is easy to conflate one with the other.

Formal Objectivity.  Unlike empirical objectivity, the subject of formal objectivity is an action or a decision process.   It is therefore more of a legal concept than a scientific one; ‘transparency’ is the common synonym for formal objectivity.  However, because the ostensible goal of formal objectivity is to limit subjective judgment, formal objectivity shares with empirical objectivity the goal of attaining impersonality.   If an entirely mechanistic process is used to determine what actions are to be then personal judgment can be banished altogether.  The regimented application of safety factors to determine a level of exposure that will be considered safe is one example of formal objectivity.  That is not necessarily a good idea, but it is possible.  Still, allowing the opportunity for criticism can be counted as a benefit of formal objectivity.

Mathematical Models and the Problem of Causation

A mathematical or conceptual model that is used to describe what has been observed and to make estimates to guide future endeavors can never quite be empirical in quite the same sense that data is.  But, it can come close.  If a mathematical model closely mimics a large set of observations, then calling it an empirical model is an apt description.  Furthermore, a mathematical model is always objective in a formal sense: If an estimate is produced by a mathematical model, then you can see where it came from.  Therefore, a model can be objective in both an empirical and formal sense.  However, an objective model isn’t necessarily entirely correct.  A flat map can be very useful, but the world is round.

If one accepts Hume’s account of causation  (Hume, 1739), then models that represent causal (e.g. dose-response) relationships can never really be considered to be empirical.  Yes, there may be an empirical association, but making a model of an empirically objective association objective in a formal sense may be worthy of derision.  In fact, in epidemiology and evidence-based medicine, a causal model that is justified solely by “observational” data is considered to be weaker than one justified by experimental trials (Santos SIlva, 1999) or also includes some theoretical justification such as  the Hill criteria (Hill, 1966).   

A causal model can still be objective in a formal sense.   In fact, the quest for objectivity may lead to formalizing the processes for the creation of mathematical models for data.  For example, for the creation of a cancer risk assessment model, using a maximum-likelihood estimate and a linear model is often considered de rigueur.  But the desire for formal objectivity may run counter to a need for theoretical justification where a formal process is difficult to impossible to come by.

The Intersection of Objectivity and Probability

So, we have two different notions of objectivity and three to five different notions of probability.  Is probability objective or subjective?  It depends; that is the short answer.  As a longer answer, each notion of probability must be taken one by one:

1. Frequency.  Although variability might not be truly considered to be probability per se, stone cold statistical facts can be objective in an empirical sense.   For example, a tabular representation of historical population data may be considered to be empirical.  However, frequencies can also be theoretical and represented by a mathematical model of a statistical distribution, which can lead to an invocation of formal objectivity.   In particular, there must be generally be a conceptual model that posits that the conditions of the estimate belong to the same class of events as the historical frequencies that the model is based on.
2. Abstract Probability.  This one is easy.  Abstract probability is never objective in an empirical sense, but it is always objective in a formal sense.
3. The Probability of Chance.   Since this form of probability arises when an infinite theoretical frequency is used to estimate the chance of a single instance or finite series, it can be just about as objective as the frequency theory that is used to make it.
4. The Probability of Causes.  It takes theory to kill a theory, and yes, one can and should use empirical data to make that argument; different theories may have varying degrees of empirical support.  Yet, when competing theories exhibit just about the same degree of concordance with historical data, the notion of empirical objectivity is pretty much superfluous and formal objectivity becomes the only option.  For example, the Hill criteria can be used to structure a scientific argument for a causal model, and/or a quantitative measure goodness-of-fit technique may be used to gauge empirical support.  But that doesn’t really confer empirical objectivity; at best a formal method for assigning probabilities to theories is intersubjective instead of personally subjective.
5. Mixed Probability.  For many decision problems, the whole enchilada of probability must combine probabilistic notions of both chance and theory.  That brings a new layer of potential subjectivity to the front.  Will a Bayesian scheme be used to combine “prior” probabilities and empirical observation, or not (e.g. a probability tree)?  And who will decide – the quants with statistical training or the scientists with a background that is primarily not quantitative? 

References

Hill, Sir Arthur Bradford (1965).  The Environment and Disease: Association or Causation?  Proc Royal Soc Med 58:295-300.

Hume. D. (1739). ATreatise of Human Nature, EC Mossner (ed.), London: Penguin Books. 

dos Santos Silva, I (1999).  Cancer epidemiology: principles and methods.  IARC, Lyon.  Chapter 5: Overview of study designs.  International Agency for Research on Cancer, Lyon.

Official Post Soundtrack

Cure, The (1979).  Object.  In: Three Imaginary Boys, Track 5.

Post Notes

Thesis Post #48.  Ideally read after A Dictionary of Probability.  Three Imaginary Boys is the UK title of the first album by The Cure.  I going with that because I'm posting from Oxford, the title fits the essay better, plus the U.S. CD version titled Boys Don't Cry left "Object" off. Bummer.