Event, Process, and Occurrence: A Bayesian View

Thomas S. Dye (tdye@hawaii.edu)

11 April 2019

Public Availability

The slides and text for this talk are publicly available at http://tsdye.online/athens/saa-2019.html

Steve Athens and Chronology

Let's start with chronology.

Steve's contributions to Hawaiian chronology effectively led archaeologists away from the confusion created by the combination of lax dating technique and an ad hoc approach to estimation that dominated Hawaiian archaeology for half a century.

This figure illustrates the history of Hawai`i colonization date estimates. The grey band at the top shows Steve Athens' Bayesian settlement estimate, while the colored bars show various settlement date estimates based on analyses of tradition and radiocarbon dating.

The initial decades of radiocarbon dating in Hawai`i empowered archaeologists to move confidently in the wrong direction. Matt Spriggs' and Atholl Anderson's chronometric hygiene worked to right the listing ship, but this effort was unfortunately followed by another two decades when "early" and "late" schools competed with one another for territory that we now know was too early.

Steve's seminal contribution, shown in light blue, was based on the coring project at Ordy Pond that established solid new evidence that tried to pull the settlement estimate in the right direction and which was key to solving the decades long project to estimate when Hawai`i was settled by Polynesians.

Bayesian Chronology

Bayes and Ramsey

On the left is an image of the Reverend Thomas Bayes, whose ideas on inverse probability were published posthumously in 1764. The theorem that today bears his name was a curiosity for a century and a half, until Frank Ramsey, whose image is on the right, "figured out how to measure partial belief and hence lay the groundwork for decision theory and Bayesian statistics".

Bayesian age estimation, as it is typically practiced in archaeology today, uses what Frank Ramsey called an event view of time.

Ramsey and other philosophers contrast an event view of time with a substance view of time. Bayesian age estimation also provides the information needed to carry out an inquiry framed by a substance view of time.

Let's see how these two views of time differ from one another, and how they are operationalized in Bayesian age estimation.

Event View of Time

Time: relative, an inseparable part of space time
Event: a region or volume of space time
Universe: events are the ultimate constituents

Substance View of Time

Time: absolute, to avoid circular reasoning
Occurrence (Event): change in the qualities and relations of objects at a time
Universe: objects with changing qualities and relations

Stratification: Event View

This slide illustrates a typical use of an event view of time in archaeology.

On the left is a hypothetical stratigraphic section taken from Edward Harris' book, Principles of Archaeological Stratigraphy, where all the interfacial and depositional contexts have been labeled.

To the right of the stratigraphic section is a directed graph. The directed graph represents the interfaces and deposits of the stratigraphic section as events. It illustrates their ages relative to one another with the convention that lines connect a younger context above to an older context below.

The stratigraphic section and the directed graph together illustrate an event view of time, where archaeological contexts represent regions of space time and time is expressed in a relative way.

In a recent paper, Caitlin Buck and I proposed a graph theoretic algorithm that takes this stratigraphic information as input and yields a chronological model for Bayesian age estimation. Thus, my claim that chronology based on stratification represents a typical event view of time in archaeology.

Marginal Posteriors of Events

Leeward Kohala System of Temples

This is all well and good. I think it is certainly an advance over ad hoc approaches to age estimation. I'm hopeful that Bayesian chronology building will become a standard practice of archaeological inquiry in Hawai`i, as it has in parts of Europe.

Nevertheless, archaeological inquiry is typically framed by a substance view of time, which as we have seen differs from an event view of time.

Whenever an archaeologist poses a question about change in an institution, a tradition, or a practice, then the particular institution, tradition, or practice becomes an object of inquiry whose changes mark the passage of time.

When we archaeologists look out over the leeward Kohala field system, it is natural to think about what Valerio Valeri called the system of temples. As archaeologists, we are curious about how the temple system here in the field system developed.

When we express our curiosity this way, we are thinking about the temple system in a substance view of time, where development of the system of temples marks the passage of time.

Joint Posteriors of Occurrences

Once we have identified the individual temples as parts of a temple system, we are led to an investigation in which the posteriors of the Bayesian age estimation are considered jointly, as parts of a whole, rather than marginally as individual events. Here, we are interested in facts about those individual events, or what Ramsey called occurrences, rather than the individual events by themselves.

This occurrence plot of the joint posteriors of the temple construction date estimates shows the first, second, third etc. changes to the temple system. Information about individual construction events provides a basis for this analysis, but the individual events do not appear in the results.

Note how this occurrence plot gives a sense of progress and change that is absent in the plot of individual events.

Joint Posteriors as Process

The sense of progress and change fostered by a substance view of time can be augmented by viewing these same data as a process.

In a processual view, the description is of the changing at a point in time, which we typically refer to in English as "now". From the viewpoint of "now", one looks to the past and finds actuality. From "now" one looks to the future with an expectation of continuity and contingency. This is a substance view of time with tenses.

Ramsey thought a process was best viewed as "a time series of images which come one by one in succession", something like a movie. The tempo plot shown here doesn't achieve this ideal, but Ramsey thought that graphic displays similar to this tempo plot were convenient "since we can attend to either aspect at will, and enjoy now the sense of succession, now the repose which enables us to look backwards and forwards till we find what we want".