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Should we be looking at and interpreting each model (with 1-4 state processes) or just the one the with most support?

Pretty much at the end of the page for "2.2. Matrix Form 1", when we want to solve for "D", I think, the "D" in the formula is misspelled as "d = ...", while it should be a "D" (big d instead of small d).

https://nwfsc-timeseries.github.io/atsa-labs/sec-mss-four-subpopulations-with-temporally-correlated-errors.html

Hi, thank you for sharing such a great lecture note, it really helps me understanding the JAGS model. But I've got two questions here.

1. Chapter 12.3 “tau.cor <- tau.obs / (1-phi*phi)”: After drawing the DAG and considering the context, I think it should be "tau.cor <- tau.obs * (1-phi*phi)".
2. Chapter 12.4 "E[y_t] = y_{t-1} + e_{t-1}": As the expectation of y_t is a constant, I think maybe it's better to change it to be "E[y_t] = y_{t-1}" and "y_t = y_{t-1} + e_{t-1}".

Thank you again for providing such a clear note and good examples!

The fitted process variance of the coefficients for PDO are 0.00. It seems really unlikely that this would be the "best fit" value, and of course the fits to the data don't look good. Any idea what I could be doing wrong? Happy to post code here or email it.

See issue posted to atsar

Problem 1.7.1 states "Build a 4×3 matrix with the numbers 1 through 4 in each row."

But it should be one of the following options:
"Build a 4×3 matrix with the numbers 1 through 4 in each column."
or
"Build a 3×4 matrix with the numbers 1 through 4 in each row."

I know you said not to fuss with markdown, but I'd like some help debugging what's going on here.

Code, copy-pasted from the lab Rmd file.
Using Form 1 $\yy=\ZZ\xx+\ee$, write out the model, showing the $\ZZ$ and $\xx$ matrices, being fit by this command.

The inline equations are not knitting properly, and it happens if I just knit the lab Rmd file, so I assume it must be a setting I have or a package that isn't loaded?

Thanks!

missing spaces and such

RPK caught this prior notation that needs to be changed:

https://nwfsc-timeseries.github.io/atsa-labs/sec-stan-uss.html

You have the weakly informative prior as x_1 ~ N(0, 0.01), but I think you mean N(0, 10).

(And also, in the HTML it is called x_1, but in the stan code itself, the parameter is called x0; not sure if that matters or not).

I might be the only one having these questions, and if that's the case, I apologize, but after mostly working through the homework questions, I'm realizing I have a few big-picture gaps in my understanding that I'm hoping we can spend a few minutes reviewing in lecture.

Mainly, I'm missing the link between fitting arima models, determining the model order, getting parameters, and then interpreting what the model orders and parameters mean for a plain-language statement about whatever trend we're observing. For example, when we see that our best model is (1,2,3) or (2,1,2) with a seasonal lag, what do we say about the overall trend in landings? And what is the interpretation of the ar/ma parameter estimates? Or is it less about making a statement about the observed trend and more about predicting forward? Or both?

Admittedly I'm only caught up on about half of last week's reading, so maybe that would help, but thanks!

1. I'm trying to use my own data in the linear filtering example, and was wondering if there was a clever way to implement the code in 3.6 in a multi-variate example. What if we wanted to look at the trends for air passengers and train passengers side-by-side?

2. What would be the best way to systematically test the best lag times for covariates? My project is on monthly marine mammal strandings and oceanographic conditions, and I have looked at glm models with some of these data, but I don't have a sense for how to test different lag times for ocean covariates. Maybe once I honed in on significant predictors using glm(), I could then put those into a marss() model and look at AIC values for different lag times? Would the ccf examples of the lynx and sun spots help me with this?

Happy to hold my questions for in-person if the answer is more involved.

Thanks!

I'm still at the beginning stages of working my way through the homework/lab, but one question - in section 7.3.2 Model Fitting for harbor seals as one big population, it says 'the model fits fine', but I'm not sure I'm understanding how we're gauging that based on MARSS() output. Is it the 'Success!' message? What would it look like if the model fit poorly or didn't converge?

@eeholmes @mdscheuerell Is the assignment that you wanted us take a look at for tomorrow the problems at the end of chapter 4 in the lab book?

Sort of a stupid question... Do the four-layer decomposition plots not clump together? In other words, this code doesn't work - the plots all pop up independently rather than in a 2x2 grid.

par(mfrow = c(2,2), oma=c(0,0,0,0), mar=c(1,1,1,1))
plot <- plot(decomp_hs, yax.flip = TRUE, xlab = 'Harbor seal')
plot <- plot(decomp_csl, yax.flip = TRUE, xlab = 'California sea lion')
plot <- plot(decomp_ssl, yax.flip = TRUE, xlab = 'Steller sea lion')
plot <- plot(decomp_sp_cet, yax.flip = TRUE, xlab = 'Dalls porpoise')

Thanks!