1. You need a criterion of a goodness of fit, no matter how complex the explanation. 2. You need a criterion that is not dependent on the function or distributions involved. 3. You need a criterion that works for inexact matching. (The function that we think governs the behaviour of a system will never match exactly the data that we observe, unless we perform exact interpolation - but interpolation does not have predictive power)
We can then choose between two models, and decide which one is better.
We start with the assertion that you can always explain away anything as white noise. This is a model with zero systemic behaviour. The p at which we can accept the observation as white noise, is the measure of goodness of such an explanation.
You change the model by introducing some systemic behaviour, some function. The residuals (the remaining unexplained behaviour) will follow normal distribution for some p. If this p is smaller than the previous step, we accept the model.
You improve the model by modifying the function - adding new terms, removing others, etc. The residuals will follow normal distribution for some other p. If this p is lower than the previous step, we accept the model. If the same, use the model with fewer variables.
That's right. They are not modelling ENSO, solar, etc. They are just establishing a difference in temperature. This is like comparing two sets of observations and determining whether they are different, and if they are, what's the difference, and what's the confidence interval of the difference.
no subject
A handwavy explanation, perhaps:
1. You need a criterion of a goodness of fit, no matter how complex the explanation.
2. You need a criterion that is not dependent on the function or distributions involved.
3. You need a criterion that works for inexact matching. (The function that we think governs the behaviour of a system will never match exactly the data that we observe, unless we perform exact interpolation - but interpolation does not have predictive power)
We can then choose between two models, and decide which one is better.
We start with the assertion that you can always explain away anything as white noise. This is a model with zero systemic behaviour. The p at which we can accept the observation as white noise, is the measure of goodness of such an explanation.
You change the model by introducing some systemic behaviour, some function. The residuals (the remaining unexplained behaviour) will follow normal distribution for some p. If this p is smaller than the previous step, we accept the model.
You improve the model by modifying the function - adding new terms, removing others, etc. The residuals will follow normal distribution for some other p. If this p is lower than the previous step, we accept the model. If the same, use the model with fewer variables.
I went through probably only 50% of this book: https://reneues.files.wordpress.com/2010/01/an-introduction-to-generalized-linear-models-second-edition-dobson.pdf , which is to say that I am not pretending to be a guru of statistics. Section 2.3 is the principles of fitting and checking the model.
"ENSO, oscillation, solar"
That's right. They are not modelling ENSO, solar, etc. They are just establishing a difference in temperature. This is like comparing two sets of observations and determining whether they are different, and if they are, what's the difference, and what's the confidence interval of the difference.