# GetMAPEst: Retrieve the surface of MAP estimators In sppmix: Modeling Spatial Poisson and Related Point Processes

## Description

The function calculates the Maximum A Posteriori (MAP) estimate of the IPPP mixture intensity surface parameters. Use function `GetPMEst` if you want the surface of posterior means.

For examples see

## Usage

 ```1 2``` ```GetMAPEst(fit, burnin = floor(fit\$L/10), vals, truncate = FALSE, priortype = 1, d, mu0, Sigma0, df0, sig0) ```

## Arguments

 `fit` Object of class `damcmc_res` or `bdmcmc_res`. `burnin` Number of initial realizations to discard. By default, it is 1/10 of the total number of iterations. `vals` Contains the density values over the point pattern and realizations in the `fit` object. This can be obtained via a call to `GetDensityValues`. If this argument is missing then the density values are computed herein before computing the MAP estimates. `truncate` Logical variable indicating whether or not we normalize the densities of the mixture components to have all their mass within the window defined in the point pattern `pp`. `priortype` For different types of priors, ignored right now. `d, mu0, Sigma0, df0, sig0` Optional parameters for the prior distributions used: d are the weights of the Dirichlet prior on the component probabilities. mu0 and Sigma0 are the mean and covariance matrix of a bivariate normal that yields the component means. df0 and sig0 are the degrees of freedom and sig0^2*Identity the parameter matrix for the Inverse Wishart prior that yields the component matrices. If omitted they are set to the following values, which are the default values used in est_mix_damcmc: Sigma0=cov(cbind(pp\$x,pp\$y)), mu0=c(mean(pp\$x),mean(pp\$y)), sig0=1, df0=10, and d=rep(1,m).

## Value

An object of type `intensity_surface`.

## Author(s)

Sakis Micheas

`est_mix_damcmc`, `rmixsurf`, `rsppmix`, `GetPMEst`
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```truemix_surf <- rmixsurf(m = 3, lambda=100, xlim = c(-3,3), ylim = c(-3,3)) plot(truemix_surf,main="True IPPP intensity surface") genPPP=rsppmix(intsurf = truemix_surf, truncate = FALSE) #the larger the number of realizations the better fit <- est_mix_damcmc(genPPP, m = 3,L=100000) MAPest=GetMAPEst(fit) plot(GetPMEst(fit),main="IPPP intensity surface of posterior means") plot(MAPest,main="IPPP intensity surface of MAP estimates") fitBD <- est_mix_bdmcmc(pp = genPPP, m = 5) MAPest=GetMAPEst(fitBD) plot(MAPest,main="IPPP intensity surface of MAP estimates for MAP m") ```