geoBayes (version 0.7.4)

select_proposals: Selection of multiple importance sampling distributions

Description

Selection of multiple importance sampling distributions

Usage

select_proposals_SEQ(
  pargrid,
  K,
  istart,
  relativeSE = FALSE,
  N1,
  N2,
  Nthin,
  Nbi,
  formula,
  family = "gaussian",
  data,
  weights,
  subset,
  offset,
  atsample,
  corrfcn = "matern",
  betm0,
  betQ0,
  ssqdf,
  ssqsc,
  dispersion = 1,
  longlat = FALSE,
  nbatch1 = 0.5,
  nbatch2 = 0.5,
  S1method = c("RL", "MW"),
  bvmethod = c("Standard", "TukeyHanning", "Bartlett"),
  transf = c("no", "mu", "wo")
)
select_proposals_MNX(
  pargrid,
  istart,
  nfix,
  relativeSE = FALSE,
  N1,
  N2,
  Nthin,
  Nbi,
  cooling,
  formula,
  family = "gaussian",
  data,
  weights,
  subset,
  offset,
  atsample,
  corrfcn = "matern",
  betm0,
  betQ0,
  ssqdf,
  ssqsc,
  dispersion = 1,
  longlat = FALSE,
  nbatch1 = 0.5,
  nbatch2 = 0.5,
  S1method = c("RL", "MW"),
  bvmethod = c("Standard", "TukeyHanning", "Bartlett"),
  transf = c("no", "mu", "wo"),
  verbose = FALSE
)
select_proposals_ENT(
  pargrid,
  istart,
  nfix,
  relativeSE = FALSE,
  N1,
  Nthin,
  Nbi,
  cooling,
  formula,
  family = "gaussian",
  data,
  weights,
  subset,
  offset,
  atsample,
  corrfcn = "matern",
  betm0,
  betQ0,
  ssqdf,
  ssqsc,
  dispersion = 1,
  longlat = FALSE,
  nbatch1 = 0.5,
  nbatch2 = 0.5,
  S1method = c("RL", "MW"),
  bvmethod = c("Standard", "TukeyHanning", "Bartlett"),
  transf = c("no", "mu", "wo"),
  verbose = FALSE
)

Value

A list with components

selected

The rows of pargrid selected.

isel

The indices of the rows of pargrid selected.

se

The standard error corresponding to the selected parameters.

samples

A list containing the samples from the selected parameters.

Arguments

pargrid

A data frame with components "linkp", "phi", "omg", "kappa". Each row gives a combination of the parameters to compute the new standard errors.

K

How many proposal densities in total to choose among the rows of pargrid. Needed for SEQ only. For MNX and ENT this is determined by the length of istart.

istart

Start with these rows of pargrid. A vector of indices.

relativeSE

Logical. Whether the choice is based on the standard error (FALSE), or relative standard error (TRUE).

N1

The sample size for stage 1.

N2

The sample sie for stage 2.

Nthin

Thinning

Nbi

Burn-in

formula

A representation of the model in the form response ~ terms. The response must be set to NA's at the prediction locations (see the examples on how to do this using the function stackdata). At the observed locations the response is assumed to be a total of replicated measurements. The number of replications is inputted using the argument weights.

family

The distribution of the data. The "GEVbinomial" family is the binomial family with link the GEV link (see Details).

data

An optional data frame containing the variables in the model.

weights

An optional vector of weights. Number of replicated samples for Gaussian and gamma, number of trials for binomial, time length for Poisson.

subset

An optional vector specifying a subset of observations to be used in the fitting process.

offset

See lm.

atsample

A formula in the form ~ x1 + x2 + ... + xd with the coordinates of the sampled locations.

corrfcn

Spatial correlation function. See geoBayes_correlation for details.

betm0

Prior mean for beta (a vector or scalar).

betQ0

Prior standardised precision (inverse variance) matrix. Can be a scalar, vector or matrix. The first two imply a diagonal with those elements. Set this to 0 to indicate a flat improper prior.

ssqdf

Degrees of freedom for the scaled inverse chi-square prior for the partial sill parameter.

ssqsc

Scale for the scaled inverse chi-square prior for the partial sill parameter.

dispersion

The fixed dispersion parameter.

longlat

How to compute the distance between locations. If FALSE, Euclidean distance, if TRUE Great Circle distance. See spDists.

nbatch1

A scalar or vector of the same length as runs. All values must be integers or less than 1. This is used for calculating how many batches to split each of the sample in runs for the calculation of the Bayes factors standard errors for the parameters corresponding to runs.

nbatch2

A scalar or vector of the same length as runs. All values must be integers or less than 1. This is used for calculating how many batches to split each of the sample in runs for the calculation of the Bayes factors standard errors for the parameters corresponding to pargrid.

S1method

Which method to use to calculate the Bayes factors: Reverse logistic or Meng-Wong.

bvmethod

Which method to use for the calculation of the batch variance. The standard method splits to disjoint batches. The second and third method use the spectral variance method with different lag windows.

transf

Whether to use a transformed sample for the computations. If "no" or FALSE, it doesn't. If "mu" or TRUE, it uses the samples for the mean. If "wo" it uses an alternative transformation. The latter can be used only for the families indicated by .geoBayes_models$haswo.

nfix

In the case of MNX and ENT, the first nfix elements of istart will always be included.

cooling

A decreasing sequence of temperature values for the simulated annealing. All elements must be positive. A suggested value is Tinit / log(((0:N) %/% Tstp)*Tstp + exp(1)) for N+1 iterations, where Tinit is the initial temperature and Tstp is the number of iterations before the temperature is reduced.

verbose

Logical. Prints information about the simulated annealing.

Details

SEQ

is a sequential method starting with istart and additng to it until K proposals have been selected. At each iteration, the point with the highest (relative?) standard error is added

MNX

is the minimax method. The chosen proposal corresponds to the lowest maximum (relative?) standard error.

ENT

is the entropy method. The chosen proposal corresponds to the highest determinant of the (relative?) covariance matrix at the first stage.

References

Roy, V., & Evangelou, E. (2018). Selection of proposal distributions for generalized importance sampling estimators. arXiv preprint arXiv:1805.00829.

Examples

if (FALSE) {
data(rhizoctonia)
### Define the model
corrf <- "spherical"
kappa <- 0
ssqdf <- 1
ssqsc <- 1
betm0 <- 0
betQ0 <- .01
family <- "binomial.probit"
formula <- Infected ~ 1
atsample <- ~ Xcoord + Ycoord
### Skeleton points
philist <- seq(100, 200, 10)
omglist <- 0
parlist <- expand.grid(linkp=0, phi=philist, omg=omglist, kappa = kappa)
### MCMC sizes
Nout <- 100
Nthin <- 1
Nbi <- 10
## Select proposals
K <- 3                        # Choose 3 proposals
istart_SEQ <- 6               # Start with middle
istart_MNX <- istart_ENT <- c(6, 2, 10)
cooling_MNX <- .05/log((0:24 %/% 5)*5 + exp(1))
cooling_ENT <- .3/log((0:49 %/% 10)*10 + exp(1))
prop_SEQ <- select_proposals_SEQ(pargrid = parlist, K = K,
                                 istart = istart_SEQ,
                                 relativeSE = TRUE, 
                                 N1 = Nout, N2 = Nout,
                                 Nthin = Nthin, Nbi = Nbi,
                                 formula = formula, family = family,
                                 data = rhizoctonia, weights = Total, 
                                 atsample = atsample, corrfcn = corrf,
                                 betm0 = betm0, betQ0 = betQ0,
                                 ssqdf = ssqdf, ssqsc = ssqsc,
                                 dispersion = 1, longlat = FALSE,
                                 nbatch1 = 0.5, nbatch2 = 0.5,
                                 bvmethod = "TukeyHanning",
                                 transf = "mu")
prop_MNX <- select_proposals_MNX(pargrid = parlist,
                                 istart = istart_MNX, nfix = 1L,
                                 cooling = cooling_MNX, 
                                 relativeSE = TRUE, 
                                 N1 = Nout, N2 = Nout,
                                 Nthin = Nthin, Nbi = Nbi,
                                 formula = formula, family = family,
                                 data = rhizoctonia, weights = Total, 
                                 atsample = atsample, corrfcn = corrf,
                                 betm0 = betm0, betQ0 = betQ0,
                                 ssqdf = ssqdf, ssqsc = ssqsc,
                                 dispersion = 1, longlat = FALSE,
                                 nbatch1 = 0.5, nbatch2 = 0.5,
                                 bvmethod = "TukeyHanning",
                                 transf = "mu",
                                 verbose = TRUE)
prop_ENT <- select_proposals_ENT(pargrid = parlist,
                                 istart = istart_ENT, nfix = 1L,
                                 cooling = cooling_ENT, 
                                 relativeSE = TRUE, 
                                 N1 = Nout, 
                                 Nthin = Nthin, Nbi = Nbi,
                                 formula = formula, family = family,
                                 data = rhizoctonia, weights = Total, 
                                 atsample = atsample, corrfcn = corrf,
                                 betm0 = betm0, betQ0 = betQ0,
                                 ssqdf = ssqdf, ssqsc = ssqsc,
                                 dispersion = 1, longlat = FALSE,
                                 nbatch1 = 0.5, nbatch2 = 0.5,
                                 bvmethod = "TukeyHanning",
                                 transf = "mu",
                                 verbose = TRUE)
}