Problems 2.3. Characterizing uncertainty

  1. To characterize uncertainty in our ecological forecast model, we need more flexibility than the assumptions of general linear models (or ‘traditional statistical models’).
    1. What are these assumptions? [4 marks]


  1. See equation 6.1 on p81 of Ecological Forecasting describes a logistic regression.
    1. What assumption of the general linear model is not met for a logistic regression? [1 mark]
    2. Describe in words what the link function is? [1 mark]


  1. See section 6.3 starting on p83.
    1. Define process error and observation error. [2 marks]
    2. How are ‘data model’ and ‘observation error’ different? [1 mark]
    3. What is residual error (consult the index of Ecological forecasting if needed), and what point is made about residual error in section 6.3? [2 marks]

 

  1. See section 6.5 starting on p90.
    1. In chapter 11, we will consider the population size, recorded over time, at different sites. Site may be considered a random effect. Explain why site could be considered a random effect? [2 marks]

 

  1. Complete Task 1 of Chapter_06_FittingUncertainites.Rmd
    1. Provide a write-up of your work to complete Task 1. [20 marks]
    • Some of the plots are large relative to a laptop figure window. While it is possible to print the figures to a folder, I found that slow because of how often you need to look at the results of the plots. I recommend completing this task as an .Rmd because it is much easier to read your plots.
    • In your write-up, comment on whether your MCMC is meeting the standards outlined for convergence, but continue with the task even if your MCMC doesn’t meet the standards. It is more important to move through the task at a good pace, than to spend a lot of time getting a more precise result.
    • When plotting the fitted model compared to data, note that estimated parameters are for the model which is then transformed by the link function.
    1. With a uniform prior, the code to complete this problem is summary(glm(y ~ TDR, family = "poisson")). How does the mean of the posterior distribution of the parameter estimates for the Bayesian analysis compare to the estimation using the frequentist method (i.e., a uniform prior)? [1 mark]