Description Usage Arguments Details Value Author(s) References Examples

This function produces a stepping-stone sampling estimate of the marginal likelihood given a set of log-likelihood values at different temperatures. It can also be used to produce a generalised stepping-stone sampling estimate (see details below).

1 |

`x` |
A data frame with the folloging columns: |

`temp` |
It indicates the temperatures to be used in the analysis, for instance, c(1,3,K) considers the temperatures at those positions, where |

Power posterior methods, among them stepping-stone sampling, rely on a set of samples from different transitional distributions, connecting the prior and the posterior distributions, which is defined by the power posterior density

*p(θ) \propto L(x|θ)^{β} π(θ), *

where *θ* is the parameter vector, *0 ≤ β ≤ 1* is the inverse temperature, *x* is the data, *p(θ)* is the power posterior density, *L(x|θ)* is the likelihood function, and *π(θ)* is the prior density. See more details about the stepping-stone sampling algorithm in Xie et al. (2011).

`ss`

can be also used to produce a generalised stepping-stone sampling estimate. In this case, the power posterior density defines a path between a reference distribution *g* and the posterior and is given by

*p(θ) \propto (L(x|θ)π(θ))^{β} g(θ)^{1-β},*

where *0 ≤ β ≤ 1* is the inverse temperature. The reference distribution needs to be a reasonable approximation of the posterior. See more details about the generalised stepping-stone sampling algorithm in Fan et al. (2011).

It produces a stepping-stone sampling estimate.

Patricio Maturana Russel [email protected]

Fan, Y., Wu, R., Chen, M.-H., Kuo, L., Lewis, P. O., 2011. Choosing among
partition models in Bayesian phylogenetics. *Molecular Biology and Evolution* 28(1), 523–532.

Xie, W., Lewis, P. O., Fan, Y., Kuo, L., Chen, M.-H., 2011. Improving marginal
likelihood estimation for Bayesian phylogenetic model selection. *Systematic Biology* **60**(2), 150–160.

1 2 | ```
data(ligoVirgoSim)
ss(ligoVirgoSim, temp = NULL)
``` |

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