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Overfit or not, you should pick the one with the highest test accuracy, conditional on the fact that you have truly kept your test data separate. I would be tempted to find more unseen test data to double check that it has truly generalised well to new data.


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Yes, it is. As you mentioned, the classical rule is $P(A,B) = P(A|B)P(B)$, but it can also be applied to conditional probabilities like $P(\cdot|C)$ instead of $P(\cdot)$. It then becomes $$ P(A,B|C) = P(A|B,C)P(B|C) $$ (you just add a condition on $C$, but otherwise that's the same formula). You can then apply this formula for $A = y$, $B = \theta$, and $C ...


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There are examples in the ABC literature of model selection through Bayes factors. An ecological individual based model example is here: https://doi.org/10.1016/j.ecolmodel.2017.07.017 The paper involves picking between models of different complexity so hopefully it will be useful even if it doesn't deal with SDEs directly. However, I should also mention ...


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So, first of all, this is an answer based on the one by @cbeleites above, this one here, and the question itself (all these contributions helped me understand). There is nothing original in it, and although it makes sense to me, I am still a student in this topic so I am not 100% sure of it. Therefore, any feedback is appreciated. However, it gives a ...


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I think a lot depends on what the purpose of the model is. Inference or prediction ? If it is inference then you really need to incorporate some domain knowledge into the process, otherwise you risk identifying completely spurious associations, where an interaction may appear to be meaningful but in reality is either an artifact of the sample, or is masking ...


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It can be difficult to find the order of an ARMA process by the ACF alone, since the AR and MA components will behave in ”opposite” ways. If you visualise the correlation with a PACF and EACF as well, and read up on what they do I think things will be clearer.


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For the Gaussian model (with variance $\sigma_{\epsilon}^2 = \hat{\sigma}_{\epsilon}^2$ assumed known), the AIC statistic is equivalent to $C_p$, and so we refer to them collectively as AIC. Suppose a Gaussian model with variance $\sigma_{\epsilon}^2 = \hat{\sigma}_{\epsilon}^2 = \sigma^2$ Mallow's $C_p$ [ C_p = \frac{1}{n} (RSS + 2 d \sigma^2) ] AIC is \...


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The AIC is normally a criterion that is used to compare models with different numbers of parameters to fit. It is not really clear exactly how many parameters you have fitted here (chances are 2-3 for most if not all of these, but for example it is not clear where you got the degrees of freedom of the t from; also it seems you have shifted or cut off ...


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This seems to be an example of where binning a continuous variable is leading to problems, as it often does. With half-hour bins, over 3/4 of your observations are restricted to the first 3 bins. It's going to be hard to gauge any model fit very well, whether visually or by a statistic related to a fit, with data values restricted this way. I'm also a bit ...


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