# Using Markov random field spatial weights to account for spatial autocorrelation

I am looking at the relationship between life expectancy and smoking rate within the London boroughs.

I thus created a bayesx spatial regression model including a term which assigns spatial covariates to deal with the spatial autocorrelation. From what I have read about the bs='spatial' argument, this specifies that the spatial covariates are created using a Markov random field prior.

boro<-poly2nb(london)
boro2<-nb2gra(boro)
i<-0:(length(london$$GSS_CODE)-1) star2<-bayesx(london$$LE~london\$smrate+ sx(i,bs='spatial', map=boro2))

So from this I can look at the spatial weights which are generated by using the function

predict(star2, type = "terms")

Which gives me information on the spatial weights that were created for my spatial covariates in the column of Mean:

So these are the 32 weights that are assigned to my 32 polygons. What I am not sure about is how these weights are thus applied in order to account for the existing spatial autocorrelation?

If a polygon x is a neighbour of two adjacent polygons (y and z), then do the observed values for my independent variable (smoking rate) from y and z get multiplied by their respective wieghts and then added to contribute to the estimated fitted value of my dependent variable (life expectancy) for the polygon x?