scores3D {BMAmevt} R Documentation

## Logarithmic score and L^2 distance between two densities on the simplex (trivariate case).

### Description

Computes the Kullback-Leibler divergence and the L^2 distance between the "true" density (`true.dens`) and an estimated density (`est.dens`).

### Usage

```scores3D(true.dens, est.dens, npoints, eps)
```

### Arguments

 `true.dens` A `npoints*npoints` matrix: The reference density, typically the distribution from which data was simulated. Must be a valid `density` argument to be passed to `dgridplot`, with `equi=FALSE`. `est.dens` The estimated density: of the same type as `true.dens`. `npoints` Number of grid points used to construct the density matrices (see `discretize`). `eps` Minimum distance from a grid point to the simplex boundary (see `discretize`).

### Details

The integration is made via `rect.integrate`: The discretization grid corresponding to the two matrices must be constructed with `discretize(npoints, eps, equi=FALSE)`.

### Value

A list made of

• `check.true`: The result of the rectangular integration of `true.dens`. It should be equal to one. If not, re size the grid.

• `check.true`: Idem, replacing `true.dens` with `est.dens`.

• `L2score`: The estimated L^2 distance.

• `KLscore`: The estimated Kullback-Leibler divergence between the two re-normalized densities, using `check.true` and `check.est` as normalizing constants (this ensures that the divergence is always positive).

### Examples

```dens1=dpairbeta.grid(par=c(0.8,2,5,8),npoints=150,eps=1e-3,
equi=FALSE)
dens2=dnestlog.grid(par=c(0.5,0.8,0.4,0.6),npoints=150,eps=1e-3, equi=FALSE)

scores3D(true.dens=dens1,
est.dens=dens2,
npoints=150, eps=1e-4)

```

[Package BMAmevt version 1.0.4 Index]