AdMitIS {AdMit} | R Documentation |

Performs importance sampling using an adaptive mixture of Student-t distributions as the importance density

AdMitIS(N = 1e5, KERNEL, G = function(theta){theta}, mit = list(), ...)

`N` |
number of draws used in importance sampling (positive
integer number). Default: |

`KERNEL` |
kernel function of the target density on which the
adaptive mixture of Student-t distributions is fitted. This
function should be vectorized for speed purposes (i.e., its first
argument should be a matrix and its output a vector). Moreover, the function must contain
the logical argument |

`G` |
function of interest used in importance sampling (see *Details*). |

`mit` |
list containing information on the mixture approximation (see *Details*). |

`...` |
further arguments to be passed to |

The `AdMitIS`

function estimates
*E_p[g(theta)]*, where *p* is the target
density, *g* is an (integrable w.r.t. *p*) function and *E* denotes
the expectation operator, by importance sampling using an adaptive
mixture of Student-t distributions as the importance density.

By default, the function `G`

is given by:

G <- function(theta) { theta }

and therefore, `AdMitIS`

estimates the mean of
`theta`

by importance sampling. For other definitions of
`G`

, see *Examples*.

The argument `mit`

is a list containing information on the
mixture approximation. The following components must be provided:

`p`

vector (of length

*H*) of mixing probabilities.`mu`

matrix (of size

*Hxd*) containing the vectors of modes (in row) of the mixture components.`Sigma`

matrix (of size

*Hxd*d*) containing the scale matrices (in row) of the mixture components.`df`

degrees of freedom parameter of the Student-t components (real number not smaller than one).

where *H (>=1)* is the number of components of the
adaptive mixture of Student-t distributions and
*d (>=1)* is the dimension of the first argument in `KERNEL`

. Typically,
`mit`

is estimated by the function `AdMit`

.

A list with the following components:

`ghat`

: a vector containing the importance sampling estimates.
`NSE`

: a vector containing the numerical standard error of the components of `ghat`

.
`RNE`

: a vector containing the relative numerical efficiency of the
components of `ghat`

.

Further details and examples of the **R** package `AdMit`

can be found in Ardia, Hoogerheide, van Dijk (2009a,b). See also
the package vignette by typing `vignette("AdMit")`

.

Further information on importance sampling can be found in Geweke (1989) or Koop (2003).

Please cite the package in publications. Use `citation("AdMit")`

.

David Ardia

Ardia, D., Hoogerheide, L.F., van Dijk, H.K. (2009a).
AdMit: Adaptive Mixture of Student-t Distributions.
*R Journal* **1**(1), pp.25-30.
doi: 10.32614/RJ-2009-003

Ardia, D., Hoogerheide, L.F., van Dijk, H.K. (2009b).
Adaptive Mixture of Student-t Distributions as a Flexible Candidate
Distribution for Efficient Simulation: The R Package AdMit.
*Journal of Statistical Software* **29**(3), pp.1-32.
doi: 10.18637/jss.v029.i03

Geweke, J.F. (1989).
Bayesian Inference in Econometric Models Using Monte Carlo Integration.
*Econometrica* **57**(6), pp.1317-1339.

Koop, G. (2003).
*Bayesian Econometrics*.
Wiley-Interscience (London, UK). ISBN: 0470845678.

`AdMit`

for fitting an adaptive mixture of Student-t
distributions to a target density through its `KERNEL`

function,
`AdMitMH`

for the independence chain Metropolis-Hastings
algorithm using an adaptive mixture of Student-t distributions
as the candidate density.

## NB : Low number of draws for speedup. Consider using more draws! ## Gelman and Meng (1991) kernel function GelmanMeng <- function(x, A = 1, B = 0, C1 = 3, C2 = 3, log = TRUE) { if (is.vector(x)) x <- matrix(x, nrow = 1) r <- -.5 * (A * x[,1]^2 * x[,2]^2 + x[,1]^2 + x[,2]^2 - 2 * B * x[,1] * x[,2] - 2 * C1 * x[,1] - 2 * C2 * x[,2]) if (!log) r <- exp(r) as.vector(r) } ## Run the AdMit function to fit the mixture approximation set.seed(1234) outAdMit <- AdMit(KERNEL = GelmanMeng, mu0 = c(0.0, 0.1), control = list(Ns = 1e4)) ## Use importance sampling with the mixture approximation as the ## importance density outAdMitIS <- AdMitIS(N = 1e4, KERNEL = GelmanMeng, mit = outAdMit$mit) print(outAdMitIS)

[Package *AdMit* version 2.1.8 Index]