Maths of Planet Earth Conference
Melbourne, July 2013 Bayesian statistics for
planet earth
Professor Kerrie Mengersen QUT, Brisbane Bayesian staAsAcs in mining UAVs? Design? Change DetecAon in MulAvariate Time Series and Space Time Data Chris Strickland et al. (2013) Data: x = (x1; x2;…; xn), xs:t = (xs; xs+1; … ; xt) •  A Gaussian state space model (CGSSM) is generated by yt = gt + Htxt + Gtet •  The state vector is modelled as xt+1 = ht + Ftxt + Γtut iniAalised by x1 ~ N (m1,V1). •  The system matrices are considered known, condiAonal on a set of unknown parameters, ω and a set of discrete random variables Kt used to model non-­‐
linear effects. Challenges •  Practical: apply to (very large dimensional) analysis of environmental change in remotely sensed data •  Computationally feasible: algorithm advantage of the condiAonally Gaussian structure of the model and sampling the latent discrete r.v.s that denote the mixture marginally of the state •  Fast: algorithm is millions of Ames faster for realisAc sized datasets •  Extensible: e.g., add mulAvariate change points •  Generalisable: apply to any dynamic mixture model with a condiAonally Gaussian state space representaAon Case study •  Predict vegetaAon change using NDVI from MODIS data: –  pixel size 250m, area 35km x 32 km, every 16 days, Feb 2000 to Sept 2011 –  total 17792 observaAons over space at 268 Ame points, i.e. ~5 million observaAons. •  Daily climaAc data for the region aggregated for each 16 day interval: –  maximum temperature, minimum temperature, rainfall, evaporaAon, short wave solar radiaAon for a horizontal surface, atmospheric water vapour pressure, relaAve humidity at maximum temperature, relaAve humidity at minimum temperature and reference potenAal evapotranspiraAon. •  Two lags of each regressor are included as explanatory variables (capture relaAvely short term seasonal informaAon); longer term seasonal impact feeds into the trend. Plot of NDVI data over Ame Trend, seasonal padern, spaAal padern for the four derived factors Component 1: trend explained by rainfall Component 2: reflects prolonged inundaAon, leading to long term damage Components 3 and 4: within-­‐region and within-­‐season variaAon Bayesian staAsAcs in conservaAon Sandra Johnson et al. (2013) Bayesian Networks (BN) OOBN interface nodes Human factors Similar OOBNs for Ecological and Biological subnetworks QuanAfying the BN QuanAfying the BN Top 10 factors Free roaming cheetah popula1on viability Pr = 0.524 Based on entropy •  LegislaAon implementaAon •  Land use •  Environmental educaAon •  Local community awareness •  Farmer educaAon •  Social impacts •  Plant biomass producAon •  Cheetah removal •  Human habitat impact •  Health Based on mutual informaFon •  Mortality •  Recruitment •  Health •  Prey availability •  Plant biomass producAon •  ImmigraAon-­‐emigraAon •  Cheetah removal •  Rain •  GeneAc •  Female mate choice Scenario assessment Free roaming cheetah popula1on viability Pr = 0.524 •  Farmer a:tudes: Farmers stop shooAng them? Pr(viable populaAon) increases to 58.1%. + higher economic benefits to farmers (inc. 64.4%) •  Ecological effects: Disease outbreak? Pr(viable populaAon) drops to 38.0% •  Climate change: increased temperature, reduced rainfall, insufficient plant biomass? •  Pr(viable populaAon) drops to 40.9% + insufficient prey + decline in cheetah populaAon health Bayesian staAsAcs in industry Paul Wu, Jegar Pitchforth, Jim Lewis et al. (2013) hdp://www.youtube.com/watch?feature=player_detailpage&v=EUDyDzaVfik Bayesian staAsAcs in industry Electricity consumpFon by household profile For Queensland (with different percentages for the other centres being modelled.) So what? •  The BN allows Ergon to use an evidence base to plan strategies aimed at reducing peak demand: –  idenAfy trigger points to maximise behavioural change –  recommend adaptaAon strategies through ‘what if’ scenarios –  provide evidence-­‐base for policy decisions –  act as a repository for data and other relevant informaAon to assist in knowledge retenAon and decision making over Ame Bayesian staAsAcs in rural health Susanna Cramb, Nicole White et al. (2013) What is the impact of living in the country on the risk of cancer? SpaAal mapping and modelling Model: 478 SLAs, i=1,..,478 di ~ Poisson(µi) log(µi) = b0 + b1 Socioeconomic statusi + b2 Ruralityi + vi + ei vi ~ Normal(µj~i, σ2) SpaAal mapping and modelling Learning about breast cancer Socioeconomic status Rurality Standardised incidence rate (SIR) Bayesian staAsAcs in epidemiology and biosecurity Wenbiao Hu, Mark Stanaway et al. Hierarchical Bayesian model for plant pest spread •  Data Model: Pr(data | incursion process and data parameters)
–  How data is observed given underlying pest extent
•  Process Model: Pr(incursion process | process parameters)
–  Potential extent given epidemiology / ecology
•  Parameter Model: Pr(data and process parameters)
–  Prior distribution to describe uncertainty in detectability, exposure, growth …
•  Posterior distribution of the incursion process (and parameters) :
Pr(process, parameters | data) ∝
Pr(data | process, parameters ) Pr( process | parameters ) Pr(parameters)
Early Warning Surveillance n
Priors based on emergency
plant pest characteristics
n
exposure rate for
colonisation probability
n  spread rates to link sites
together for spatial analysis
Add surveillance data
n
Posterior evaluation
n
n
n
n
modest reduction in area
freedom
large reduction in estimated
extent
residual “risk” maps to target
surveillance
ObservaAon Parameter EsAmates •  Hosts – Host suitability •  Inspector efficiency – IdenAfy contribuAons When it comes to Maths of
Planet Earth:
Bayesian statisticians Rock!
k.mengersen@qut.edu.au Acknowledgements for images Credit: Rio Tinto Clair Alston John Mumford STDF team CoopsetalIntJRemSen.04.pdf hJp://cimar.mae.ufl.edu/CIMAR/ www.bing.com/images www.womp-­‐int.com wikipedia cheeseimages.com www.terragalleria.com/vietnam traveltovietnam.cc/