Wrap-up and outlook

Final remarks and things we did not discuss…

Sara Martino
sara.martino@ntnu.no

Dept. of Mathematical Science, NTNU

Janine Illian
Janine.Illian@glasgow.ac.uk

University of Glasgow

Jafet Belmont
Jafet.Belmont@glasgow.ac.uk

University of Glasgow

Modelling movement data

  • models can also be fitted to movement data in inlabru

  • sometimes locations treated as a point pattern, ignoring sequential nature of the data

  • model development is an area of active research

  • approaches include:

    • discrete time step-selection processes and

    • continuous time Langevin diffusion models

Metric Graph

  • Not all phenomena leave on \(\mathcal{R}^2\)

  • Example: Traffic on roads, fishes in a river, etc…

  • What is different from \(\mathcal{R}^2\)?

Metric Graph

  • What is different from \(\mathcal{R}^2\)?

    • Think about distances on the road network…they often do not correspond to the euclidian distance in \(\mathcal{R}^2\)

  • The random walk has to account for the shape of the graph

  • ..this is what the MetricGraph library does

Non linear predictor

  • Sometimes one is interested in models whose parameters interact in a non-linear way

Example Growth model

\[ \begin{aligned} y_t&\sim\mathcal{N}(\mu_t, \sigma^2)\\ \eta_t &= \mu_t = L(1-\exp(-k\ (t-t_0))) \end{aligned} \] where \(t\) is the age and \(y_t\) the length of the fish

with parameters \((L,k,t)\)

This model cannot be implemented in the original INLA framework. inlabru linearizes the problem and by an iterative procedure is (often) able to estimate the parameters. You can read more here

Space/time varying covariate effects

Space/time varying covariate effects

The model

\[ \eta(s) = \beta_0 + \beta_1(s)\ x(s) \]

Implementation

cmp = ~ Intercept(0) + space_beta(geometry, weights = covariate, model = spde)

# OR

cmp = ~ Intercept(0) + space_beta(idx_region, weights = covariate, model = "besag")

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