# Extract a Path of (log) Bayes Factors

### Description

Extract a path (log) Bayes factors (BFs) from the log marginal posterior
probabilities of two `"dynaTree"`

-class objects

### Usage

1 | ```
getBF(obj1, obj2)
``` |

### Arguments

`obj1` |
a |

`obj2` |
another |

### Details

Simply calculates a difference in log marginal posterior
probabilities, setting BFs to zero for initial elements of the
path where one of the objects has more zero marginal probabilities
than the other. The BF is for the model in `obj1`

over
`obj2`

. If the objects are the output of repeated
fits as obtained from `dynaTrees`

, then multiple
traces are returned

### Value

Returns a vector or `matrix`

of a trace(s) of Bayes factors that
can be plotted; see examples below

### Author(s)

Robert B. Gramacy rbgramacy@chicagobooth.edu,

Matt Taddy taddy@chicagobooth.edu, and

Christoforos Anagnostopoulos christoforos.anagnostopoulos06@imperial.ac.uk

### References

Taddy, M.A., Gramacy, R.B., and Polson, N. (2011). “Dynamic trees for learning and design” Journal of the American Statistical Association, 106(493), pp. 109-123; arXiv:0912.1586

Gramacy, R.B., Taddy, M.A., and S. Wild (2011). “Variable Selection and Sensitivity Analysis via Dynamic Trees with an Application to Computer Code Performance Tuning” arXiv:1108.4739

http://bobby.gramacy.com/r_packages/dynaTree/

### See Also

`dynaTree`

, `update.dynaTree`

,
`link{logpost}`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
## parabola data
n <- 100
Xp <- sort(runif(n,-3,3))
Yp <- Xp + Xp^2 + rnorm(n, 0, .2)
XXp <- seq(-3,3,length=100)
## comparison by log Bayes Factor
R <- 2 ## use R >= 10 for better results
## small R is for faster CRAN checks
o <- apply(matrix(runif(n*(R-1)), ncol=R-1), 2, order)
lpc.p <- dynaTrees(Xp, Yp, R=R, rorder=o, verb=0)
lpl.p <- dynaTrees(Xp, Yp, model="linear", R=R, rorder=o, verb=0)
bf.p <- getBF(lpl.p, lpc.p)
## plot the log Bayes factors
matplot(bf.p, type="l", lty=1, col="gray", main="parabola",
xlab="time", ylab="log Bayes factor")
## see demo("reg1d") for further examples
``` |