In other words, the argument should be reversed: how can you tell some function works better than, say, a coin toss? This is the same as how can you tell something is not a white noise.
Hence the motivation for statistical hypothesis testing. You start with an assumption that something is just white noise, then reject it after testing the hypothesis: p-value is sort of like the probability of making a mistake by rejecting the hypothesis that it's just white noise, and you want this probability to be as low as you can get. Since hypothesis testing is just a bunch of arithmetics, you can test any data, whether it is random or not. Just non-random data is meant to have a very low p-value - the test must be able to sniff out the data is not random.
Ok. Then maybe in this particular modelling they have developed a better hypothesis testing approach, or maybe they have a motivation why residuals are not meant to be normally distributed (say, maybe they are log-normally distributed, eh?). But this is what I am trying to find out :) what makes this specific model fitting process different from other models?
I've seen GLM fitting process for rainfall modelling (so I am sure GLM model fitting is applicable at least in some circumstances; what motivated me to study some of that book), which followed pretty much what I am saying as far as I can tell - i.e. optimising the parameters of the model to minimise the residuals (and to result in high confidence that the residuals are white noise). For many functions this is a matter of finding derivatives, etc, just as described in that book.
I do realise the actual oceanic or atmospheric thermal exchange modelling is not necessarily subject to some GLM. And yet we will ascribe some of the stuff to randomness - either because it is really stemming from some probabilistic quantum laws (for the lack of a better term), or just too complex to model, no matter. What we want to know is how much remains unexplained (confidence intervals), and whether we should be worried about being unable to explain the remainder (p-value for accepting the hypothesis that the residuals are white noise).
The general model testing principles seem to be applicable outside GLM specifically, because the goal is the ability to discern a better model from a less accurate model of a process for which we can't produce exactly the numbers we see in the weather station log.
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Date: 2020-02-05 09:30 am (UTC)In other words, the argument should be reversed: how can you tell some function works better than, say, a coin toss? This is the same as how can you tell something is not a white noise.
Hence the motivation for statistical hypothesis testing. You start with an assumption that something is just white noise, then reject it after testing the hypothesis: p-value is sort of like the probability of making a mistake by rejecting the hypothesis that it's just white noise, and you want this probability to be as low as you can get. Since hypothesis testing is just a bunch of arithmetics, you can test any data, whether it is random or not. Just non-random data is meant to have a very low p-value - the test must be able to sniff out the data is not random.
Ok. Then maybe in this particular modelling they have developed a better hypothesis testing approach, or maybe they have a motivation why residuals are not meant to be normally distributed (say, maybe they are log-normally distributed, eh?). But this is what I am trying to find out :) what makes this specific model fitting process different from other models?
I've seen GLM fitting process for rainfall modelling (so I am sure GLM model fitting is applicable at least in some circumstances; what motivated me to study some of that book), which followed pretty much what I am saying as far as I can tell - i.e. optimising the parameters of the model to minimise the residuals (and to result in high confidence that the residuals are white noise). For many functions this is a matter of finding derivatives, etc, just as described in that book.
I do realise the actual oceanic or atmospheric thermal exchange modelling is not necessarily subject to some GLM. And yet we will ascribe some of the stuff to randomness - either because it is really stemming from some probabilistic quantum laws (for the lack of a better term), or just too complex to model, no matter. What we want to know is how much remains unexplained (confidence intervals), and whether we should be worried about being unable to explain the remainder (p-value for accepting the hypothesis that the residuals are white noise).
The general model testing principles seem to be applicable outside GLM specifically, because the goal is the ability to discern a better model from a less accurate model of a process for which we can't produce exactly the numbers we see in the weather station log.