By ‘Bayesian’ philosophy of science I mean the position that (1) the objective of science is, or should be, to increase our ‘credence’ for true theories [...]
Phew, I thought for a moment he was about to refute the actual Bayesian philosophy of science...
Snark aside, as others have noticed, point 1 is highly problematic. From a broader perspective, if Bayesian probability has to inform the practice of science, then a scientist should be wary of the concept of truth. Once a model has reached probability 1, it becomes an unwieldy object: it cannot be swayed by further, contrary evidence, and if we ever encounter an impossible piece of data (impossible for that model), the whole system breaks down. It is then considered good practice to always hedge models with a small probability for ‘unknown unknowns’, even with our most certain beliefs. After all, humans are finite and the universe is much, much bigger.
On the other hand, I don’t think it’s fair to say that the objective of science is either to “just explain” or “just predict”. Both views are unified and expanded by the Bayesian perspective: “explanation”, as far as the concept can be modelled mathematically, is fitness to data and low complexity. On the other hand, predictive power is fitness to future data, which can only be checked once the future data had been acquired. What is one man’s prediction can be another man’s explanation.
“explanation”, as far as the concept can be modelled mathematically, is fitness to data and low complexity
Nope. To explain, e.g. to describe “why” something happened, is to talk about causes and effects. At least that’s the way people use that word in practice.
Prediction and explanation are very very different.
To explain, e.g. to describe “why” something happened, is to talk about causes and effects.
I would still say that cause and effect is a subset of the kind of models that are used in statistics. A case in point is for example Bayesian networks, that can accomodate both probabilistc and causal relations. I’m aware that Judea Pearl and probably others reverse the picture, and think that C&E are the real relations, which are only approximated in our mind as probabilistic relations. On that, I would say that quantum mechanics seems to point out that there is something fundamentally undetermined about our relations with cause and effect. Also, causal relations are very useful in physics, but one may want to use other models where physics is not especially relevant. From what one may call “instrumentalist” point of view, time is a dimension so universal that any model can compress information by incorporating it, but it is not necessarily so, as relativity shows us: indeed, general relativity shows us you can compress a lot of information by not explicitly talking about time, and thus by sidestepping clean causal relations (what is cause in a reference frame is effect in another).
Prediction and explanation are very very different.
I’m not aware of a theory or a model that uses vastly different entities to explain and to predict. The typical case of a physical law posits an ontology governed by a stable relation, thus using the precise same pieces to explain the past and predict the future.
Besides, such a model would be very difficult to tune: any set of data can be partitioned in any way you like between training and test, and it seems odd that a model is so dependent from the experimenter’s intent.
I would still say that cause and effect is a subset of the kind of models that are used in statistics.
You would be wrong, then. The subset relation is the other way around. Bayesian networks are not causal models, they are statistical independence models.
Compressing information has nothing to do with causality. No experimental scientist talks about causality like that, in any field. There is a big literature on something called “compressed sensing,” for example, but that literature (correctly) does not generally make claims about causality.
I’m not aware of a theory or a model that uses vastly different entities to explain and to predict.
I am.
You can’t tune (e.g. trade off bias/variance properly) causal models in any kind of straightforward way, because the parameter of interest is never unobserved, unlike standard regression models. Causal inference is a type of unsupervised problem, unless you have experimental data.
Rather than arguing with me about this, I suggest a more productive use of your time would be to just read some stuff on causal inference. You are implicitly smuggling in some definition you like that nobody uses.
Phew, I thought for a moment he was about to refute the actual Bayesian philosophy of science...
Snark aside, as others have noticed, point 1 is highly problematic. From a broader perspective, if Bayesian probability has to inform the practice of science, then a scientist should be wary of the concept of truth. Once a model has reached probability 1, it becomes an unwieldy object: it cannot be swayed by further, contrary evidence, and if we ever encounter an impossible piece of data (impossible for that model), the whole system breaks down. It is then considered good practice to always hedge models with a small probability for ‘unknown unknowns’, even with our most certain beliefs. After all, humans are finite and the universe is much, much bigger.
On the other hand, I don’t think it’s fair to say that the objective of science is either to “just explain” or “just predict”. Both views are unified and expanded by the Bayesian perspective: “explanation”, as far as the concept can be modelled mathematically, is fitness to data and low complexity. On the other hand, predictive power is fitness to future data, which can only be checked once the future data had been acquired. What is one man’s prediction can be another man’s explanation.
Nope. To explain, e.g. to describe “why” something happened, is to talk about causes and effects. At least that’s the way people use that word in practice.
Prediction and explanation are very very different.
I would still say that cause and effect is a subset of the kind of models that are used in statistics. A case in point is for example Bayesian networks, that can accomodate both probabilistc and causal relations.
I’m aware that Judea Pearl and probably others reverse the picture, and think that C&E are the real relations, which are only approximated in our mind as probabilistic relations. On that, I would say that quantum mechanics seems to point out that there is something fundamentally undetermined about our relations with cause and effect. Also, causal relations are very useful in physics, but one may want to use other models where physics is not especially relevant.
From what one may call “instrumentalist” point of view, time is a dimension so universal that any model can compress information by incorporating it, but it is not necessarily so, as relativity shows us: indeed, general relativity shows us you can compress a lot of information by not explicitly talking about time, and thus by sidestepping clean causal relations (what is cause in a reference frame is effect in another).
I’m not aware of a theory or a model that uses vastly different entities to explain and to predict. The typical case of a physical law posits an ontology governed by a stable relation, thus using the precise same pieces to explain the past and predict the future. Besides, such a model would be very difficult to tune: any set of data can be partitioned in any way you like between training and test, and it seems odd that a model is so dependent from the experimenter’s intent.
You would be wrong, then. The subset relation is the other way around. Bayesian networks are not causal models, they are statistical independence models.
Compressing information has nothing to do with causality. No experimental scientist talks about causality like that, in any field. There is a big literature on something called “compressed sensing,” for example, but that literature (correctly) does not generally make claims about causality.
I am.
You can’t tune (e.g. trade off bias/variance properly) causal models in any kind of straightforward way, because the parameter of interest is never unobserved, unlike standard regression models. Causal inference is a type of unsupervised problem, unless you have experimental data.
Rather than arguing with me about this, I suggest a more productive use of your time would be to just read some stuff on causal inference. You are implicitly smuggling in some definition you like that nobody uses.