How do we attach probabilities to the real world?

19 Jul, 2016 at 11:11 | Posted in Statistics & Econometrics | 1 Comment

Econometricians usually think that the data generating process (DGP) always can be modelled properly using a probability measure. The argument is standardly based on the assumption that the right sampling procedure ensures there will always be an appropriate probability measure. But – as always – one really has to argue the case, and present warranted evidence that real-world features are correctly described by some probability measure.

There are no such things as free-standing probabilities – simply because probabilities are strictly seen only defined relative to chance set-ups – probabilistic nomological machines like flipping coins or roulette-wheels. And even these machines can be tricky to handle. Although prob(fair coin lands heads|I toss it) = prob(fair coin lands head & I toss it)|prob(fair coin lands heads) may be well-defined, it’s not certain we can use it, since we cannot define the probability that I will toss the coin given the fact that I am not a nomological machine producing coin tosses.

No nomological machine – no probability.

A chance set-up is a nomological machine for probabilistic laws, and our description of it is a model that works in the same way as a model for deterministic laws … A situation must be like the model both positively and negatively – it must have all the characteristics featured in the model and it must have no significant interventions to prevent it operating as envisaged – before we can expect repeated trials to give rise to events appropriately described by the corresponding probability …

Probabilities attach to the world via models, models that serve as blueprints for a chance set-up – i.e., for a probability-generating machine … Once we review how probabilities are associated with very special kinds of models before they are linked to the world, both in probability theory itself and in empirical theories like physics and economics, we will no longer be tempted to suppose that just any situation can be described by some probability distribution or other. It takes a very special kind of situation withe the arrangements set just right – and not interfered with – before a probabilistic law can arise …

Probabilities are generated by chance set-ups, and their characterisation necessarily refers back to the chance set-up that gives rise to them. We can make sense of probability of drawing two red balls in a row from an urn of a certain composition with replacement; but we cannot make sense of the probability of six per cent inflation in the United Kingdom next year without an implicit reference to a specific social and institutional structure that will serve as the chance set-up that generates this probability.

1 Comment

1. I believe the notion of probability is one of the most over wrought concepts known to man.

Firstly, probability is not a real phenomenon. I cannot go to my cupboard and find a packet of probability. I cannot look through an electron microscope and observe a body of probability wizzing around. I cannot look through a telescope and view a body of probability floating in space. Probability is an abstract theoretical construct designed to explain what human beings cannot otherwise explain. It exists only in people’s minds.

Randomness, a related concept, suggests that certain phenomena have no cause – they are beyond deterministic consideration.. How can this be? Everything observable has a cause, a cause which can be rationalized and discovered outside of the notion probability.

There are also absurd considerations around measures of central tendency. The mean and average are given special significance, being considered to be the most likely of events to occur. How can this be? The mean might have the highest level of probability of all events, however, the cumulative probability of all events outside of the mean is considerably higher than the probability of the mean. That is, the probability of the mean occurring is actually much less than anything else occurring.

Personally, I think we should get interested in variability and discover the causes of variability in any phenomenon, not seek to ignore it and treat it as evidence of “randomness”.

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