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From disease mapping to archaeology and presence-only modelling

From disease mapping to archaeology and presence-only modelling. Elena Moltchanova, PhD Canterbury Statistics Day. Disease Mapping. A Bit of History:. Besag J (1974 ) ‘Spatial Interaction and the Statistical Analysis of Lattice Systems’ JRSS B 36(2) 192-236

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From disease mapping to archaeology and presence-only modelling

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  1. From disease mapping to archaeology and presence-only modelling Elena Moltchanova, PhD Canterbury Statistics Day

  2. Disease Mapping. A Bit of History: • Besag J (1974) ‘Spatial Interaction and the Statistical Analysis of Lattice Systems’ JRSS B 36(2) 192-236 • Besag J (1975) ‘Statistical Analysis of Non-Lattice Data’ JRSS D 24(3) 179-195 • Besag J (1986) ‘On the Statistical Analysis of Dirty Pictures’ JRSS B 48, 259-302 • Besag J, York J, and Mollie A (1991) ‘Bayesian image restoration, with two applications in spatial statistics’. Annals of the Institute of Statistical Mathematics 43(1) 1-20

  3. Fig 1. Observed incidence of childhood diabetes (T1DM) in Finland in 1987-1996. Incidence = number of cases/ population at risk* 100 000

  4. BYM: risk Observed cases Area-specific spatial residual Background level Systematic part Population at risk or expected counts Non-spatial residual

  5. Back to BYM: Conditional AutoRegressive (CAR) Areas close together have similar values Neighborhood Matrix W

  6. BYM model DAG

  7. Applying BYM model to diabetes incidence data: Observed Estimated by BYM model

  8. Argeopop project • http://www.helsinki.fi/bioscience/argeopop • aims to shed new light on the prehistory of the Finns by integrating evidence from genetic and archeological data within a Bayesian statistical framework.

  9. 9000-6400 BP From Onkamo, P, Kammonen, J, Pesonen P, Sundell, T, Moltchanova E, Oinonen M, Haimila M, Arjas E. “Bayesian Spatiotemporal Analysis of Radiocarbon Dates in Eastern Fennoscandia” Radiocarbon (in press)

  10. 6400-5100 BP From Onkamo, P, Kammonen, J, Pesonen P, Sundell, T, Moltchanova E, Oinonen M, Haimila M, Arjas E. “Bayesian Spatiotemporal Analysis of Radiocarbon Dates in Eastern Fennoscandia” Radiocarbon (in press) www.helsinki.fi/bioscience/argeopop

  11. 5100-4000 BP From Onkamo, P, Kammonen, J, Pesonen P, Sundell, T, Moltchanova E, Oinonen M, Haimila M, Arjas E. “Bayesian Spatiotemporal Analysis of Radiocarbon Dates in Eastern Fennoscandia” Radiocarbon (in press) www.helsinki.fi/bioscience/argeopop

  12. 4000-3500 BP From Onkamo, P, Kammonen, J, Pesonen P, Sundell, T, Moltchanova E, Oinonen M, Haimila M, Arjas E. “Bayesian Spatiotemporal Analysis of Radiocarbon Dates in Eastern Fennoscandia” Radiocarbon (in press) www.helsinki.fi/bioscience/argeopop

  13. 3500-2500 BP From Onkamo, P, Kammonen, J, Pesonen P, Sundell, T, Moltchanova E, Oinonen M, Haimila M, Arjas E. “Bayesian Spatiotemporal Analysis of Radiocarbon Dates in Eastern Fennoscandia” Radiocarbon (in press) www.helsinki.fi/bioscience/argeopop

  14. 2500-1500 BP From Onkamo, P, Kammonen, J, Pesonen P, Sundell, T, Moltchanova E, Oinonen M, Haimila M, Arjas E. “Bayesian Spatiotemporal Analysis of Radiocarbon Dates in Eastern Fennoscandia” Radiocarbon (in press) www.helsinki.fi/bioscience/argeopop

  15. Presence only data…? • We only find where we dig • We only dig where we’ve found something • Similar to ecological niche modelling?

  16. MaxEnt modeling Maximize Subject to Where • x[i] is a ‘feature’ i.e. value of the covariate • y[i]=1 for presence and 0 for absence • p[i] is (multinomial) probability of presence • i=1,…,N areas

  17. BYM model recast: probability Observed distribution of occurrences Y[i]=1 if there is an observation in area I … and is missing otherwise X is therefore also missing, with lower limit known Placing a suitable prior either on X produces an identifiable Bayesian spatial CAR model!

  18. Will it work? A very simple example.

  19. Further Work: • Implement multinomial BYM model (MCMC algorithm) with various spatial autocorrelation structures: • None • CAR prior only • CAR prior + non-spatial residual • Perform sensitivity analysis • Compare to MaxEnt performance

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