Of course you can make an inference about the evidenced skill of the scientists. Scientist 1 was capable of picking out of a large set of models that covered the first 10 variables, the considerably smaller set of models that also covered the second 10. He did that by reference to principles and knowledge he brought to the table about the nature of inference and the problem domain. The second scientist has not shown any of this capability. I think our prior expectation for the skill of the scientists would be irrelevant, assuming that the prior was at least equal for both of them.
Peter: “The first theorist had less data to work with, and so had less data available to insert into the theory as parameters. This is evidence that the first theory will be smaller than the second theory”
The data is not equivalent to the model parameters. A linear prediction model of [PREDICT_VALUE = CONSTANT * DATA_POINT_SEQUENCE_NUMBER] can model an infinite number of data points. Adding more data points does not increase the model parameters. If there is a model that predicts 10 variables, and subsequently predicts another 10 variables there is no reason to add complexity unless one prefers complexity.
Of course you can make an inference about the evidenced skill of the scientists. Scientist 1 was capable of picking out of a large set of models that covered the first 10 variables, the considerably smaller set of models that also covered the second 10. He did that by reference to principles and knowledge he brought to the table about the nature of inference and the problem domain. The second scientist has not shown any of this capability. I think our prior expectation for the skill of the scientists would be irrelevant, assuming that the prior was at least equal for both of them.
Peter: “The first theorist had less data to work with, and so had less data available to insert into the theory as parameters. This is evidence that the first theory will be smaller than the second theory”
The data is not equivalent to the model parameters. A linear prediction model of [PREDICT_VALUE = CONSTANT * DATA_POINT_SEQUENCE_NUMBER] can model an infinite number of data points. Adding more data points does not increase the model parameters. If there is a model that predicts 10 variables, and subsequently predicts another 10 variables there is no reason to add complexity unless one prefers complexity.