BD.EMInference.prodExpecs: Functions That Calculate Product Expectations Needed for...
In DOBAD: Analysis of Discretely Observed Linear Birth-and-Death(-and-Immigration) Markov Chains

Description Usage Arguments Details Value Author(s) See Also

In order to calculate the information matrix for partial data, several conditional expectations of products of sufficient statistics are needed.

1 2	getBDsummaryExpecs(sims, fnc=function(x){x}) getBDsummaryProdExpecs(sims, getsd=FALSE)

`sims`	A list of Birth-Death CTMCs.
`fnc`	A one argument function. It should be a function from Reals to Reals, capable of accepting a vector as its argument
`getsd`	Also return estimate of standard deviations of the prods

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].

In order to calculate the information matrix for partial data, several conditional expectations of products of sufficient statistics are needed. We have a method for simulation conditional on the data, sim.condBD, which we use to estimate these.

Generally for getting the information matrix after running the EM algorithm, sim.condBD is called to simulate with the given parameters (estimates, usually), and the output sims are passed. It is often important that the same set of sims are used to get all the results if the goal is to create an information matrix.

getBDsummaryExpecs simply returns (an estimate of) E(fnc(Nt+)), E(fnc(Nt-)), and E(fnc(Rt)), where Nt+, Nt-, and Rt are the numbre of jumps up, the number of jumps down, and the total holding time, respectively. They are returned in that order, also with labels "Nplus", "Nminus", and "Holdtime".

getBDsummaryProdExpecs returns E(Nt+ * Nt-), E(Nt+ * Rt), and E(Nt- * Rt), in that order, also with the labels "NplusNminus", "NplusHoldtime", "NminusHoldtime".

Returns another row of with corresponding standard deviations if getsd=TRUE.

Charles Doss

add.joint.mean.many, sim.condBD

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