Gibbs Sampling for Archaeological Dates

Relative Sequences of Contexts

Relative sequences of contexts must be in the form of a list, with each object in the list being a vector whose ordering of elements is in agreement with all other elements. See the vignette Aligning Relative Sequences for more information.

The following object contexts provides an example of a valid set of relative sequences:

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)

seq_check(contexts) # check if the sequences are in agreement
#> [1] TRUE

Finds

Data on finds (i.e., any elements which pertain to a given context) are optional. Each find must be in the form of a list with the following structure:

• id: An id number or string of the find, such as an inventory number or bibliographic reference.
• assoc: The context to which the find belongs, which must be contained in the relative sequences of contexts.
• type: An optional vector or element denoting any types, subtypes, classes, etc., to which the find pertains. If not present, a NULL value must be given.

Each find must in turn be stored in a single list object:

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)

Missing information on types should be supplied with a NULL value.

Finds should have no absolute dating constrains on them. If they do, they should be specified as an absolute constraint.

Absolute Constraints

Absolute constraints are predicated on whether they provide a terminus post quem (t.p.q.) for a context or a terminus ante quem (t.a.q.) for a context. The information on these absolute dates is regarded as external or extrinsic information. For example, a radiocarbon date provides for information on when the sample died, not when its context was formed; a coin type may be known to have had a range of production dates, but the production date of that particular coin may be affected by the stratigraphic context in which it is found. Such constraints may take a variety of forms.

The formatting for a t.p.q. or a t.a.q is the same, as a list in which each constraint contains:

• id: An id number or string of the find, such as an inventory number or bibliographic reference.
• assoc: The context to which the find belongs, which must be contained in the relative sequences of contexts.
• type: An optional vector or element denoting any types, subtypes, classes, etc., to which the find pertains. If not present, a NULL value must be given.
• samples: A numeric vector or element containing potential dates of the t.p.q. or t.a.q., i.e., a sample of the probability density function which expresses when that constraint occurred. Common densities would include:
  • A single numeric if the constraint is known precisely and certainly.
  • Samples of \(n\) size from a continuous uniform distribution, runif(n, a, b), if known between two bounds \(a\) and \(b\), without any more or less certainty about any one date.
  • Samples of \(n\) size from a bespoke probability density, such as a calibrated radiocarbon date.

Constraints must be contained in two separate list objects, one for t.p.q. and the other for t.a.q.:

# external
coin1 <- list(id = "coin1", assoc = "B", type = NULL, samples = runif(100,-320,-300))
coin2 <- list(id = "coin2", assoc = "G", type = NULL, samples = runif(100,37,41))
destr <- list(id = "destr", assoc = "J", type = NULL, samples = 79)

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

Rules for Estimating Production Dates

Since archaeologists are typically interested in dates of production and use as much as deposition, the gibbs_ad() function will return the marginal densities for both production and deposition (from which the estimation of a use date can then be derived).

Estimating the date of the production of a find or find-type however necessitates some assumption, since in principle the absence of evidence is not viewed as evidence of absence. Without stipulating a rule, the earliest production date of any artifact could reach back endlessly into time, since an artifact does not need to have been produced after the initial occupation of a site where it has been found.

Here, two basic rules have been included for determining production dates of finds:

• "naive": The earliest potential threshold of a find-type occurs sometime before the first deposition of that type, and after the deposition of the next earliest context. A production date is then chosen uniformly at random between that threshold and the depositional date of that artifact.
• "earliest": The earliest potential date of a find-type occurs sometime before the first deposition of that type, and after the deposition of the next earliest context. A production date is then chosen uniformly at random between those two dates.

The "earliest" option will constrain the date of production to the earliest possible instances, while the "naive" option (the default) will select any date between an earliest threshold and the depositional date of the particular find.

If no finds are included in the gibbs_ad() arguments, then only depositional dates for contexts, not production dates, are estimated.