Eastern Fennoscandia has a rich archaeological record. A good portion of the finds has been radiocarbon dated; an ongoing work that currently allows for spatial and spatio-temporal analysis of the data. Radiocarbon dating gives a relatively good estimate of the point in time when an archaeological artefact was deposited. Analyzing the distribution of finds on a geographical area for different time periods is likely to provide clues of differential human activity in the area. To assess whether the current data is sufficient for wide-ranging spatio-temporal analysis, we predisposed a section of this data for tests with a piece of statistical software suitable for the analysis.In this paper, we present a Bayesian computing approach for spatio-temporal analysis of radiocarbon data from eastern Fennoscandia using the recently developed R-INLA software (http://www.r-inla.org). INLA stands for Integrated Nested Laplace Approximation, a statistical method that has found great use in approximating posterior marginals of non-Gaussian response variables frequently encountered in approximate Bayesian computing (Rue et al 2009). We employ a Poisson point process model to study the spread of archaeological depositions across the area of Finland and ceded Karelia. Point processes are a type of a random process and are well studied objects in probability theory (Daley & Vere-Jones 1988). In a Poisson point process the number of events in disjoint intervals are independent and have a Poisson distribution.In our previous approach to Bayesian analysis with radiocarbon data from period 4000-3500 cal BCE (Kammonen et al. in press), we employed a spatial model using MCMC (Markov chain Monte Carlo) methods of the WinBUGS software (Lunn et al. 2000). To extend this approach into the spatio-temporal domain, we included radiocarbon dates from a longer period of time and phased in a spatio-temporal Poisson point process model in R-INLA. We used the "toolbox" recommended by the R-INLA developers to implement this modification (Illian et al. submitted). In the first phase we adapted our previous spatial model to R-INLA. A test run showed that results from the INLA-approach are congruent with our previous MCMC approach. In the second phase, we effectively replaced the spatial model with a Poisson point process model. The INLA-approach proved computationally more efficient. Moreover, introducing the new model is the first step in actual spatio-temporal analysis of archaeological data from eastern Fennoscandia.Daley DJ & Vere-Jones D 1988 SpringerIllian et al submitted Annals of Applied StatisticsKammonen et al in press CAA2011 proceedingsLunn et al 2000 Statistics and ComputingRue et al 2009 Journal of The Royal Statistical Society
