logDensityTipsCauchy {cauphy} | R Documentation |

## Log Density of a Cauchy Process

### Description

Compute the log density of the vector of trait at the tips of the phylogenetic tree, assuming a Cauchy process.

### Usage

```
logDensityTipsCauchy(
tree,
tipTrait,
root.value = NULL,
disp,
method = c("reml", "random.root", "fixed.root"),
rootTip = NULL,
do_checks = TRUE
)
```

### Arguments

`tree` |
a phylogenetic tree of class |

`tipTrait` |
a names vector of tip trait values, with names matching the tree labels. |

`root.value` |
the root starting value of the process. |

`disp` |
the dispersion value. |

`method` |
the method used to compute the likelihood.
One of |

`rootTip` |
the tip used to re-root the tree, when the REML method is used.
If |

`do_checks` |
if |

### Details

The parameters of the Cauchy Process (CP)
are `disp`

, the dispersion of the process,
and `root.value`

, the starting value of the process at the root (for `method="fixed.root"`

).

The model assumes that each increment of the trait `X`

on a branch going from node `k`

to `l`

follows a Cauchy distribution, with a dispersion proportional to the length `t_l`

of the branch:

`X_l - X_k \sim \mathcal{C}(0, \mbox{disp} \times t_l).`

The `method`

argument specifies the type of likelihood that is computed:

`method="reml"`

:-
the dispersion parameter is fitted using the REML criterion, obtained by re-rooting the tree to one of the tips. The default tip used to reroot the tree is:

`rootTip = which.min(colSums(cophenetic.phylo(tree)))`

. Any tip can be used, but this default empirically proved to be the most robust numerically; `method="random.root"`

:-
the root value is assumed to be a random Cauchy variable, centered at

`root.value=0`

, and with a dispersion`disp_root = disp * root.edge`

; `method="fixed.root"`

:-
the model is fitted conditionally on the root value

`root.value`

, i.e. with a model where the root value is fixed and inferred from the data.

### Value

the log density value.

### See Also

### Examples

```
phy <- ape::rphylo(5, 0.1, 0)
dat <- rTraitCauchy(n = 1, phy = phy, model = "cauchy", parameters = list(root.value = 0, disp = 1))
logDensityTipsCauchy(phy, dat, 0, 1, method = "fixed.root")
```

*cauphy*version 1.0.2 Index]