Description Usage Arguments Details Value Author(s) See Also

Bayesian parameter estimation via Gibbs sampler MCMC on Linear Birth Death process, (_S_pecial _C_ase of constrained immigration) in which the data is the state at discrete time points.

1 2 3 | ```
BD.MCMC.SC(Lguess, Mguess, beta.immig, alpha.L, beta.L, alpha.M, beta.M,
data, burnIn = 100, N = 1000, n.fft = 1024,
verbose=1, verbFile=NULL, simMethod=-1,...)
``` |

`Lguess` |
Starting point for |

`Mguess` |
Starting point for |

`beta.immig` |
Immigration rate = beta.immig |

`alpha.L` |
Shape parameter for prior for |

`beta.L` |
Rate parameter for prior for |

`alpha.M` |
Shape parameter for prior for |

`beta.M` |
Rate parameter for prior for |

`data` |
Partially observed chain. Has components $times and $states where dat$states[i] is the state observed at time dat$times[i]. |

`N` |
Number of iterations to run the MCMC for. |

`burnIn` |
Number of initial parameter estimates to throw out. (So need burnIn << N.) Choose burnIn==0 throws nothing away. |

`n.fft` |
Number of terms to use in the fast fourier transform or the riemann integration when using the generating functions to compute probabilities or joint expectations for the birth-death process. See the add.joint.mean.many, etc, functions. |

`verbose` |
Chooses level of printing. Increasing from 0, which is no printing. |

`verbFile` |
Character signifying the file to print to. If NULL just to standard output. |

`simMethod` |
Switch between using Accept-reject simulation and using the exact simulation method. If -1, the function attempts to determine the best one of the two for the given parameters. Value of 0 fixes it at AR, and 1 fixes it at the exact method. |

`...` |
Unused at this point. |

Assume we have a linear-birth-death
process *X_t* with birth parameter *lambda*, death
parameter *mu*, and immigration parameter
*beta*lambda* (for some known, real
*beta*). We observe the process
at a finite set of times over a time
interval [0,T].
This runs MCMC to do parameter estimation. The method is Gibbs
sampling, by augmenting the state space to include the the
fully observed chain. Then Gibbs sampling is performed
using the the conditional simulation of sim.condBD and the fact that,
given the fully observed chain as data, independent gamma priors
are conjugate priors, with independent posteriors.

Returns a *N-burnIn*x2 matrix, the nth row being the
estimators/samples at the nth iteration. The first
column is for lambda (birth), the second for mu (death).

Charles Doss

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