gammaiid: gammaiid
In maroulaslab/BayesTDA: Bayesian inference for persistence diagrams

Description Usage Arguments Value

gammaiid

1 2	gammaiid(Dy, alpha, prob.prior, weight.prior, mean.prior, sigma.prior, sigma.y, weights.unexpected, mean.unexpected, sigma.unexpected, Nmax, b)

`x:`	a 2 by 1 vector where the posterior intensity is computed. Cosequently, x is a coordinate in the wedge where the tilted PD is defined.
`Dy:`	a list of n vectors(2 by 1) representing points observed in a tilted persistence diagram of a fixed homological feature.
`alpha:`	0<=alpha<1. The probability of a feature in the prior will be detected in the observation.
`prob.prior:`	The prior cardinality pmf is defined as a binomial and prob.prior is the probability term (p_x in Eqn.(2)).
`weight.prior:`	a N by 1 vector of mixture weights (c^X_{j} of Eqn (1)) for the prior density estimation.
`mean.prior:`	a list of N vectors(2 by 1) each represets mean of the prior density (μ^X_{j} of Eqn (1))
`sigma.prior:`	a N by 1 vector of positive constants, σ^X_{j} of Eqn (1).
`sigma.y:`	a positive constant. Variance coefficient (σ) of the likelihood density l(y\|x) defined in the description above. This represents the degree of faith on the observed PDs representing the prior.
`weights.unexpected:`	a M by 1 vector of mixture weights for the unexpected features. i.e., (c^Y_{i} of Eqn (2) above.
`mean.unexpected:`	a list of M vectors (2 by 1),each represets mean of the Gaussian mixture density (μ^Y_{i} of Eqn (2)) for the unexpected features.
`sigma.unexpected:`	a M by 1 vector of positive constants, σ^Y_{i} of Eqn (2).
`Nmax:`	The maximum number of points on which the posterior cardinality will be truncated, i.e., p_n is computed for n=0 to n=Nmax. Also, this Nmax will be used to define prior cardinality too. So, it should be large enough so that all Binomials involved in the computation make sense
`b:`	0 or 1