select_proposals: Selection of multiple importance sampling distributions

In geoBayes: Analysis of Geostatistical Data using Bayes and Empirical Bayes Methods

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
)

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.

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.

References

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

Examples

## Not run: 
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)

## End(Not run)

geoBayes documentation built on Aug. 21, 2023, 9:08 a.m.