En este post veremos como ajustar *Conditional Autoregressive Models* (Una variante de Gaussian Markov Random Fields) a un conjunto de datos generados por Biospytial.
Para cargar los datos vaya a https://ecomorphisms.holobio.me/2019/01/28/tutorial-para-analisis-de-datos-espaciales-en-r/
Requisitos
Instalar paquete CarBayes
install.packages(‘CARBayes’)
The conditional autologistic model (Besag, et. al 1991) has the following specification (Lee, 2013).
$$k \in {1…K}$$ Neighbours
$$ Y_k \sim Binomial(n_k,\theta_k) $$
$$ ln\left(\frac{\theta_k}{1-\theta_k}\right)= x_k^t \beta + O_k + \psi_k$$
$$\beta \sim N(\mu_\beta,\Sigma_\beta)$$
$$ \psi_k = \phi_k + \theta_k $$
$$ \phi_k | \phi_{-k}, \mathbb{W},\tau^2 \sim N \left( \frac{\sum_{i=1}^{K} w_{ki} \phi_i}{\sum_{i=1}^{K}w_{ki}}, \frac{\tau^2}{\sum_{i=1}^{K}w_{ki}}\right) $$
$$\theta_k \sim N\left(0, \sigma^2\right)$$
$$\tau^2, \sigma^2 \sim^{iid} Inv.Gamma(a,b) $$
Referencias
- Artículo del método: https://www.jstatsoft.org/article/view/v055i13
- Viñetas: https://cran.r-project.org/web/packages/CARBayes/vignettes/CARBayes.pdf
- Info en general: https://cran.r-project.org/web/packages/CARBayes/index.html
