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 |

`S` |
number of iterations for the chain. |

`y` |
integer matrix of size |

`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 |

`init` |
an optional initialization for the chain. If |

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.

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