setalpha: Set diffusion parameter on observations.
In shazhe/mvst0: Multi-variate ST modelling on globe

Description Usage Arguments Details Value Examples

Accounts for averaging over observations, to account for signal leakage with nearby observations. See details.

setalpha(.Object, alpha, av_dist)

## S4 method for signature 'Obs'
setalpha(.Object, alpha, av_dist)

`.Object`	Object of class `Obs`.
`alpha`	The diffusion coefficient. See details.
`av_dist`	The distance within which observations are assumed to be coupled.

This function sets the diffusion parameter α in the model

z = P(α)y + e

where the matrix P(α) is defined as

P^{(i,j)} = ≤ft\{ \begin{array}{ll} α, & i \sim j, (n_i)θ > 0.9 \\ [2ex] 1 - (n_i)θ & i = j, (n_i)θ > 0.9 \\ [2ex] \displaystyle \frac{1}{(n_i)+1} & \textrm{otherwise} \end{array} \right.

where n_i denotes the number of neighbours of observation i and \sim denotes ‘neighbour of’. The matrix describes the proportion of signal n_iα which should be attributed to the spatial regions associated with the neighbouring observations. If n_iθ exceeds 0.9 (indicative of poor localisation), the observation is assumed to be an equal average of itself and its neighbours. Two (observations are assigned as neighbours if their geometric centres are distanced by less than av_dist.

Object of class Obj with updated diffusion parameter alpha0 and averaging matrix P.

# Create three polygon 'footprints'
pol_df <- rbind(data.frame(id=1,x1=0,x2=0,x3=1,x4=1,y1=0,y2=1,y3=1,y4=0,t=0),
                data.frame(id=2,x1=1,x2=1,x3=2,x4=2,y1=1,y2=2,y3=2,y4=1,t=0),
                data.frame(id=3,x1=2,x2=2,x3=3,x4=3,y1=2,y2=3,y3=3,y4=2,t=0))
df <- rbind(data.frame(id=1,x=0.5,y=0.5,z=1,std=1,t=0),
            data.frame(id=2,x=1.5,y=1.5,z=2,std=1,t=0),
            data.frame(id=3,x=2.5,y=2.5,z=1.5,std=1,t=0))
O <- Obs_poly(df=df,pol_df=pol_df)
plot(O,"z")
Odiff <- setalpha(O,0.1,av_dist=2)