transformations: Transformations In pomp: Statistical Inference for Partially Observed Markov Processes

Description

Some useful parameter transformations.

Usage

 ```1 2 3 4 5 6 7``` ```logit(p) expit(x) log_barycentric(X) inv_log_barycentric(Y) ```

Arguments

 `p` numeric; a quantity in [0,1]. `x` numeric; the log odds ratio. `X` numeric; a vector containing the quantities to be transformed according to the log-barycentric transformation. `Y` numeric; a vector containing the log fractions.

Details

Parameter transformations can be used in many cases to recast constrained optimization problems as unconstrained problems. Although there are no limits to the transformations one can implement using the `parameter_trans` facilty, pomp provides a few ready-built functions to implement some very commonly useful ones.

The logit transformation takes a probability p to its log odds, log(p/(1-p)). It maps the unit interval [0,1] into the extended real line [-∞,∞].

The inverse of the logit transformation is the expit transformation.

The log-barycentric transformation takes a vector Xi, i=1,…,n, to a vector Yi, where

Yi = log(Xi/sum(Xj)).

If X is an n-vector, it takes every simplex defined by sum(Xi)=c, c constant, to n-dimensional Euclidean space R^n.

The inverse of the log-barycentric transformation is implemented as `inv_log_barycentric`. Note that it is not a true inverse, in the sense that it takes R^n to the unit simplex, sum(Xi)=1. Thus,

 `1` ``` log_barycentric(inv_log_barycentric(Y)) == Y, ```

but

 `1` ``` inv_log_barycentric(log_barycentric(X)) == X ```

only if `sum(X) == 1`.

More on implementing POMP models: `Csnippet`, `accumulator variables`, `basic components`, `covariates`, `distributions`, `dmeasure specification`, `dprocess specification`, `parameter transformations`, `pomp-package`, `pomp`, `prior specification`, `rinit specification`, `rmeasure specification`, `rprocess specification`, `skeleton specification`, `userdata`