On the move: Transition estimation

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# On the move: Transition estimation
### The team
### last updated: 2021-05-18

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## <span style="color: white;">Thank you Canada!</span>

![](img/deadpool.gif)

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## <span style="color: white;">Wintering site fidelity in Canada Geese</span>

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### 3 sites Carolinas, Chesapeake, Mid-Atlantic, with 21277 banded geese, data kindly provided by Jay Hestbeck ([Hestbeck et al. 1991](https://esajournals.onlinelibrary.wiley.com/doi/10.2307/2937193))

???

(large areas along East coast of US)

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### Biological inference

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???

+ Observations and states are closely related, but not entirely.

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### Biological inference

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### Biological inference

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### Biological inference

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### The model construction: How we should think.

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??? Generative model. States generate observations.

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### The model construction: How we should think.

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### The model construction: How we should think.

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### The model construction: How we should think.

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### HMM model for dispersal with 2 sites (drop Carolinas)

<br>

Transition matrix

$$
`\begin{matrix}
& \\
\mathbf{\Gamma} = 
    \left ( \vphantom{ \begin{matrix} 12 \\ 12 \\ 12 \end{matrix} } \right .
\end{matrix}`
\hspace{-1.2em}
`\begin{matrix}
    z_{t}=A & z_{t}=B & z_{t}=D \\ \hdashline
\phi_A (1-\psi_{AB}) & \phi_A \psi_{AB} & 1 - \phi_A\\ 
\phi_B \psi_{BA} & \phi_B (1-\psi_{BA}) & 1 - \phi_B\\ 
0 & 0 & 1
\end{matrix}`
\hspace{-0.2em}
`\begin{matrix}
& \\
\left . \vphantom{ \begin{matrix} 12 \\ 12 \\ 12 \end{matrix} } \right )
    \begin{matrix}
    z_{t-1}=A \\ z_{t-1}=B \\ z_{t-1}=D
    \end{matrix}
\end{matrix}`
$$

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### HMM model for dispersal with 2 sites (drop Carolinas)

<br>

Observation matrix

$$
`\begin{matrix}
& \\
\mathbf{\Omega} = 
    \left ( \vphantom{ \begin{matrix} 12 \\ 12 \\ 12 \end{matrix} } \right .
\end{matrix}`
\hspace{-1.2em}
`\begin{matrix}
    y_t=0 & y_t=1 & y_t=2 \\ \hdashline
1 - p_A & p_A & 0\\ 
1 - p_B & 0 & p_B\\ 
1 & 0 & 0
\end{matrix}`
\hspace{-0.2em}
`\begin{matrix}
& \\
\left . \vphantom{ \begin{matrix} 12 \\ 12 \\ 12 \end{matrix} } \right )
    \begin{matrix}
    z_{t}=A \\ z_{t}=B \\ z_{t}=D
    \end{matrix}
\end{matrix}`
$$

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### HMM model for dispersal with 2 sites (drop Carolinas)

<br>

Observation matrix

Note: You may code non-detections as `$y_t = 2$`, and the first column in the observation matrix should go last.

???

Quick answer about the -1 and the important issue of coding states and obs. I did this on purpose, to have folks think about the difference between observations and states (non-detection obs should not be confused with state for dead). This becomes even more crucial when we get to multievent models where several observations may be generated by a single state. I get the intuition argument perfectly, but I’d like them to fight against it at first, then once they’re comfortable with the difference, they may code obs/states as they see fit. Let’s see how it goes. I agree that we should mention that during the multistate lecture, in the spirit of « you’re free to code states and jobs the way you like ». I’ll add something.