bidc_pd: Bayesian Inference of Default Correlations Using...
In miguelbiron/BIDC: BIDC: Bayesian Inference for Default Correlations

Description Usage Arguments Details Value

This functions runs an MCMC chain to perform Bayesian inference on the default correlation parameter, by using probabilites of default estimated for each client. See Details for more information.

1	bidc_pd(S = 2000L, y, p_d, b = 50, verbose = 0L, init = NULL)

`S`	number of iterations for the chain.
`y`	integer matrix of size `N x tau` containing a 1 in (n,t) if the n-th client at time t defaulted, and 0 otherwise.
`p_d`	matrix with probability of default of the n-th client at time t.
`b`	shape2 parameter of the beta proposal for rho. Default value is 50 tends to work well.
`verbose`	integer. Function prints every `verbose` iterations. The default value of 0L prints no output.
`init`	an optional initialization for the chain. If `NULL` (default), the M_t's are initialized from the prior and rho from a beta close to 0.5.

The MCMC chain is a Metropolis-Hastings-withing-Gibbs (MHwG) sampler. The MH updates are needed because the full conditionals of the parameters are not analytically tractable. The prior on rho is uniform in (0,1), and for the latent factors are standard normals.

The approach used here requires knowing the actual outcomes of the defaults for a fixed number of clients (N) over a time period (tau), which are encoded in the matrix y. It also requires an estimate of the probability of default (PD) for each entry in y in a matrix we call p_d. The inferences are better when the estimates of the PDs are better.

It is crucial to understand that client n in time t1 does not need to correspond to the same person in the n-th row at time t2. In other words, we assume exchangeability within the rows of y. The user only needs to make sure that every entry in p_d is an estimate for the corresponding entry in y.

a matrix of size S x (tau+1), where the first tau columns correspond to the latent factors, and the last one contains samples for rho.

miguelbiron/BIDC documentation built on May 17, 2019, 3:12 a.m.