BD.MCMC.SC: MCMC on Linear Birth Death Process
In DOBAD: Analysis of Discretely Observed Linear Birth-and-Death(-and-Immigration) Markov Chains

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.

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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 lambda
`Mguess`	Starting point for mu
`beta.immig`	Immigration rate = beta.immig * lambda.
`alpha.L`	Shape parameter for prior for lambda
`beta.L`	Rate parameter for prior for lambda
`alpha.M`	Shape parameter for prior for mu
`beta.M`	Rate parameter for prior for mu
`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-burnInx2 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

add.joint.mean.many

DOBAD documentation built on May 2, 2019, 3:04 a.m.