# phat

##### Estimate Type-Specific Probabilities

Estimate the type-specific probabilities for a multivariate Poisson point process with independent component processes of each type.

- Keywords
- multivariate, regression, smooth, spatial, nonparametric

##### Usage

`phat(gpts, pts, marks, h)`

##### Arguments

- gpts
matrix containing the

`x,y`

-coordinates of the point locations at which type-specific probabilities are estimated.- pts
matrix containing the

`x,y`

-coordinates of the data points.- marks
numeric/character vector of the types of the point in the data.

- h
numeric value of the bandwidth used in the kernel regression.

##### Details

The type-specific probabilities for data \((x_i, m_i)\), where \(x_i\) are the spatial point locations and \(m_i\) are the categorical mark sequence numbers, \(m_i=1,2,\ldots\), are estimated using the kernel smoothing methodology \(\hat p_k(x)=\sum_{i=1}^nw_{ik}(x)I(m_i=k)\), where \(w_{ik}(x)=w_k(x-x_i)/\sum_{j=1}^n w_k(x-x_j)\), \(w_k(.)\) is the kernel function with bandwidth \(h_k>0\), \(w_k(x)=w_0(x/h_k)/h_k^2\), and \(w_0(\cdot)\) is the standardised form of the kernel function.

The default kernel is the *Gaussian*. Different kernels can be
selected by calling `setkernel`

.

##### Value

A list with components

- p
matrix of the type-specific probabilities for all types, with the type marks as the matrix row names.

- ...
copy of the arguments

`pts, dpts, marks, h`

.

##### References

Diggle, P. J. and Zheng, P. and Durr, P. A. (2005) Nonparametric estimation of spatial segregation in a multivariate point process: bovine tuberculosis in Cornwall, UK.

*J. R. Stat. Soc. C*,**54**, 3, 645--658.

##### See Also

`cvloglk`

, `mcseg.test`

, and
`setkernel`

*Documentation reproduced from package spatialkernel, version 0.4-23, License: CC BY-NC-SA 4.0*