sq_disp: Squared Displacement for a Target Event

In eratosthenes: Archaeological Synchronism

Squared Displacement for a Target Event

Description

Computes the squared displacement for a target event within the joint conditional density, estimating how much the omission of another event will change the date of that event. See also msd.

Usage

sq_disp(
  marginalized,
  target,
  sequences,
  finds = NULL,
  max_samples = 10^5,
  size = 10^3,
  mcse_crit = 0.5,
  tpq = NULL,
  taq = NULL,
  alpha_ = -5000,
  omega_ = 1950,
  rule = "naive"
)

## S3 method for class 'marginals'
sq_disp(
  marginalized,
  target,
  sequences,
  finds = NULL,
  max_samples = 10^5,
  size = 10^3,
  mcse_crit = 0.5,
  tpq = NULL,
  taq = NULL,
  alpha_ = -5000,
  omega_ = 1950,
  rule = "naive"
)

Arguments

marginalized	The results of gibbs_ad.gibbs_ad.
target	The target event (any event in marginalized) for which to estimate squared displacement.
sequences	A list of relative sequences of elements (e.g., contexts) used to compute marginalized.
finds	Optional. A list of finds related to (contained in) the elements of sequences.
max_samples	Maximum number of samples to run. Default is 10^5.
size	The number of samples to take on each iteration of the main Gibbs sampler. Default is 10^3.
mcse_crit	Criterion for the Monte Carlo standard error to stop the Gibbs sampler. A higher MCSE is recommended for situations with a higher number of events in order to reduce computational time.
tpq	A list containing termini post quos used to compute marginalized. See gibbs_ad for details.
taq	A list containing termini ante quos used to compute marginalized. See gibbs_ad for details.
alpha_	An initial t.p.q. to limit any elements which may occur before the first provided t.p.q. Default is -5000.
omega_	A final t.a.q. to limit any elements which may occur after the after the last provided t.a.q. Default is 1950.
rule	The rule for computing an estimated date of production. See gibbs_ad for details.

Details

Displacement is computed via the following jackknife/leave-one-out-style routine:

• Each event, excluding the target event itself, is omitted from all relative and absolute sequences, and the function gibbs_ad is re-run to compute a "jackknifed" Monte Carlo mean for the target event.

  • The squared difference of this jackknifed Monte Carlo mean and the original is then computed as its squared "displacement" in time.

If an event has a low squared displacement, it has a low impact on the dating of the target event. If it is has a high squared displacement, the target event's date depends heavily upon its inclusion in the full joint density.

Trimming is not implemented in the estimation of squared displacement, and so attention should be paid to the selection of alpha_ and omega_, and reported. This is owing to the way in which, if an absolute constraint (tpq or taq) is omitted that happens to be an earliest or latest bounding event, there still needs to be earliest and latest thresholds in place.

This function is fairly computationally intensive, and so a lower value of max_samples or higher value of mcse_crit may be warranted.

Value

Output is a list containing a data frame sq_disp giving the diplacement with respect to all other events and a vector bounds of the values of alpha_ and omega_.

Examples

x <- c("A", "B", "C", "D", "E", "F", "G", "H", "I", "J")
y <- c("B", "D", "G", "H", "K")
z <- c("F", "K", "L", "M")
contexts <- list(x, y, z)

f1 <- list(id = "find01", assoc = "D", type = c("type1", "form1"))
f2 <- list(id = "find02", assoc = "E", type = c("type1", "form2"))
f3 <- list(id = "find03", assoc = "G", type = c("type1", "form1"))
f4 <- list(id = "find04", assoc = "H", type = c("type2", "form1"))
f5 <- list(id = "find05", assoc = "I", type = "type2")
f6 <- list(id = "find06", assoc = "H", type = NULL)

artifacts <- list(f1, f2, f3, f4, f5, f6)
 
# external constraints
coin1 <- list(id = "coin1", assoc = "B", type = NULL, samples = runif(100,-320,-300))
coin2 <- list(id = "coin2", assoc = "G", type = NULL, samples = seq(37, 41, length = 100))
destr <- list(id = "destr", assoc = "J", type = NULL, samples = 79)

tpq_info <- list(coin1, coin2)
taq_info <- list(destr)

result <- gibbs_ad(contexts, finds = artifacts, tpq = tpq_info, taq = taq_info)

# max_samples lowered and msce_crit raised for examples

# squared displacement for depositional context "E"
E_sqdisp <- sq_disp(result, target = "E", sequences = contexts, 
                    max_samples = 3000, mcse_crit = 2, tpq = tpq_info, taq = taq_info)

# squared displacement for production of artifact type "type1"
type1_sqdisp <- sq_disp(result, target = "type1", sequences = contexts, finds = artifacts,
                        max_samples = 3000, mcse_crit = 2, tpq = tpq_info, taq = taq_info)

eratosthenes documentation built on June 28, 2025, 1:08 a.m.