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Quick Model References

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Model term	Definition	Equation notation
n.PA	number of blobs for both time periods (time1 and time2)	$n_{PA}$
i	index identifying blobs	$i \text{ where } i \in 1:n_{PA}$
y.PA[i]	presence (1) or absence (0) value in each i-th blob (overlapping surveys' area), can be for time1 or time2	$y_{PA_i}$
X.PA	design matrix including vector of 1s (for intercept) and all the covariates and spline bases for each blob, for both time periods	$\mathbf{X_{PA}}$
area.PA[i]	area of i-th blob in meters for both time periods	$area_{PA_i}$
effort[i]	sampling effort for i-th blob in the given period for both time periods	$effort_{PA_i}$
n.PO	number of grid-cells for both time periods concatenated (time1 and time2)	$n_{PO}$
j	index identifying grid cells	$j \text{ where } j \in j:n_{PO}$
n.PO.half	number of grid-cells for one time period	$n_{PO/2}$
y.PO[j]	count of observed points in j-th grid-cell, can be for time1 or time2	$y_{PO_j}$
X.PO	design matrix including vector of 1s (for intercept) and all the covariates and spline bases for each grid-cell for both time periods	$\mathbf{X_{PO}}$
area.PO[j]	area of each grid-cell in meters for both time periods	$area_{PO_j}$
acce[j]	accessibility from urban areas based on travel time for j-th grid-cell for both time periods	$acce_j$
country[j]	country name for j-th grid-cell for both time periods	$country_j$
n.X	total number of columns in X (`X.PA` or `X.PO`)	$n_X$
n.cntr	total number of countries	$n_{cntr}$
c	index identifying countries	$c \text{ where } c \in 1:n_{cntr}$
n.par	number of parameters considered (intercept and covariates)	$n_{par}$
r	index identifying parameters	$r \text{ where } r \in 1:n_{par}$
n.fac	number of factors of time in X (`X.PA` or `X.PO`)	$n_{fac}$
f	index identifying factors	$f \text{ where } f \in 1:n_{fac}$
n.spl	number of spline bases functions in in X (`X.PA` or `X.PO`)	$n_{spl}$
S.time1	spline values for the first time period (time1)	$S_{time1}$
S.time2	spline values for the second time period (time2)	$S_{time2}$
Z	a vector of zeros (0) of the length of the splines	$Z$
sigma.time1	variance of splines for the first time period (time1)	$\sigma_{time1}$
sigma.time2	variance of splines for the second time period (time2)	$\sigma_{time2}$
b	vector of parametric effects of covariates driving the point process intensity (it also includes an intercept)	$b_r \in \mathbf{b}$
alpha0	intercept of the thinning process in the presence-only data	$\alpha_0$
alhpa1	slope -steepness- of the thinning process in the presence-only data (decaying distance~P.ret relationship)	$\alpha_1$
beta	coefficient of the effect of sampling effort in the presence-absence data	$\beta$
gamma	prior for splines smoothing parameter	$\gamma$
eta.PA	linear predictor for presence-absence data	$\mathbf{\eta_{PA}}$
eta.PA[i]	expected presence-absence for the i-th blob	$\eta_{PA_i}$
eta.PO	linear predictor for presence-only data	$\mathbf{\eta_{PO}}$
eta.PO[j]	expected count points for the j-th grid-cell	$\eta_{PO_j}$
psi[i]	blob-specific probability of presence	$\psi_i$
P.ret[j]	cell-specific probability of retaining (observing) a point as a function of accessibility and country of origin	$P_{ret_j}$
nu[j]	true mean number of points per grid-cell (the true intensity)	$\nu_j$
lambda[j]	thinning of the true intensity	$\lambda_j$
eta.pred	linear predictor for the predicted probability of occurrence	$\mathbf{\eta_{pred}}$
eta.pred[j]	predicted count points for the j-th grid-cell	$\eta_{pred_j}$
P.pred[j]	predicted probability of occurrence for the j-th grid-cell	$P_{pred_j}$
A.time1	range area in the first time period (time1)	$A_{time1}$
A.time2	range area in the second time period (time2)	$A_{time2}$
delta.A	temporal change of range area (time2-time1)	$\Delta A$