# 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`