Читать книгу Statistical Approaches for Hidden Variables in Ecology - Nathalie Peyrard - Страница 28

Let us illustrate model [1.4] using a toy example. Consider an individual with a total of three possible behaviors. Thus, let J = 3 be the number of activities for this individual. Each of these activities is characterized by a different movement pattern: for example, a direct trajectory at high velocity, a more sinuous pattern at a lower speed, and a third, different pattern. As we have seen, these differences may be characterized using different metrics. In this example, we have chosen to model persistent velocity and turning velocity, using equations [1.7] and [1.8].

Thus, in model [1.4], ν₀ is a probability vector of size 3, Π is a 3 × 3 matrix such that the sum of the elements in each line is equal to 1, and, for 1 ≤ j ≤ 3, distribution (θj) is a distribution ℕ (μj, Σ_j), where:

 – μj is a vector of dimension 2 (the mean of V p and V r for activity j);

 – Σj is a variance–covariance matrix (of size 2 × 2).