How many estimated parameters ?

[Dominique Soudant]

Hello, 

(This is the second publication of a question asked (too) quickly this morning, which I deleted and am now completing.)

Having more parameters than data increases the risk of overfitting. I'm not sure what to consider as parameters in my INLA model. The purpose of the question is to provide recommendations for using the model.

I'm analyzing time series. My model is an RW2 (aka integrated random walk, aka second-order dynamic linear model without evolution variance for the mean level) added to a Fourier-type seasonal model including the first two harmonics. As long as I was using the dlm package to perform an MLE, I considered the following as parameters:
Observation variance
Slope innovation variance
An innovation variance for each harmonic
This led to four parameters that must be supplemented by estimates of the distributions of the model components at t=0:
Mean => 2
Level => 2
First and second harmonics => 4
For a total of 12 estimated parameters.

I am using the same model with INLA and I am a little confused about what I should count as model parameters. Should I count the distribution parameters of the hyperparameters ? 

Observation variance => 2

RW2 variance => 2

First and second harmonics variances => 4

For a total of 8 estimated parameters

Thanks in advance for your help

Kind regards 

DS