Wedge_Gaussian: Restricted Gaussian density The function 'Wedge_Gaussian'...

In maroulaslab/BayesTDA: Bayesian inference for persistence diagrams

Description

The function Wedge_Gaussian computes Gaussian density restricted to wedge W. Require mvtnorm package for computing multivariate normal pdf and cdf.

Usage

Wedge_Gaussian(z, mean, sigma)

Arguments

z:	two element vector. These are the points to evaluate density at.
mean:	two element vector, mean of the restricted Gaussian
sigma:	positive constant. Covariance matrix of the restricted Gaussian has the form sigma*I_2, where I_2 is the 2x2 identity matrix.

Details

The function Wedge_Gaussian computes Gaussian density restricted to wedge W. For a death vs. birth persistence diagram wedge is defined as the two dimensional coordinate (b,d) such that d>b>0. For a tilted representation, i.e., persistence vs. birth persistence diagram wedge is defined as T(b,d) = (b, d-b).

Value

The function Wedge_Gaussian returns numerical value of the Gaussian density restricted to wedge W.

Examples

# input the mean and constant sigma of covariance matrix
w <- Wedge_Gaussian(z = c(1,2), mean = c(1,1), sigma = 0.1)

maroulaslab/BayesTDA documentation built on June 6, 2019, 4:43 p.m.