from disease mapping to archaeology and presence-only modelling
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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 - PowerPoint PPT PresentationTRANSCRIPT
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From disease mapping to archaeology and presence-only modelling
Elena Moltchanova, PhDCanterbury Statistics Day
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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
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Fig 1. Observed incidence of childhood diabetes (T1DM) in Finland in 1987-1996.
Incidence = number of cases/population at risk*100 000
Click icon to add picture
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BYM:
Population at risk or expected counts
)Poisson( ~ iiY
Observed cases
risk
iiiii NX log)log( 0
Background level Area-specific spatial residual
Systematic part
Non-spatial residual
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Back to BYM: Conditional AutoRegressive (CAR)
),(~ ,00 iii mN
Areas close together have similar values
Neighborhood Matrix W
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BYM model DAG W j h i Ni Yi Xi
Nik Yik Xi
Nik Yik Xi
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Applying BYM model to diabetes incidence data:
ObservedEstimated by BYM model
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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.
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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)
9000-6400 BP
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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
6400-5100 BP
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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
5100-4000 BP
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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
4000-3500 BP
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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
3500-2500 BP
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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
2500-1500 BP
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Presence only data…? We only find where we dig We only dig where we’ve found
something Similar to ecological niche modelling?
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MaxEnt modelingMaximize
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
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BYM model recast:
),multinom(p ~ N:1:1 XY N
Observed distribution of occurrences
probability
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!
𝑋=∑𝑖=1
𝑁
𝑌 𝑖
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Will it work? A very simple example.
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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