Talk Florian Hartig at ISEC 2014 Montepellier / France

Florian Hartig Department of Biometry and Environmental System Analysis


Consistency of Bayesian and maximum likelihood inference in state-space models of ecological systems with strongly nonlinear dynamics

Florian Hartig, Carsten F. Dormann

University of Freiburg, Department of Biometry and Environmental System Analysis

http://florianhartig.wordpress.com/ ISEC 2014, Montpellier,

Figures by Ernst Haeckel, scans by Kurt Stüber, MPI Köln


Introduction: a strange result …

Claim: population models, fit in a Bayesian state-space framework to data produced by themselves (no model error), lead to worse forecasts than a non-parametric forecasting method; for chaotic dynamics, # data >> # parameters


Worrying, given that state-space models widely advertised as state-of-the-art


1: Population model – logistic map


2: Process error on population dynamics


3: Observation error on those dynamics


4: The final observations (red triangles)


State-space model to recover parameter estimates from those observations

Population model

Observation model

Observed data

SSM: calculate P(Observations|Parameter) by summing over all possible „latent“ trajectories (state space), find parameters that have the highest likelihood to „produce“ the observations


Growth rate estimates for increasing true growth rates

Model estimated with JAGS, median posterior values shown

No bias line


Hypothesis I

Why? Imagine you are the „statistical model“

Observations

Hypothesis II Stable dynamics ------, All variability from observation error

Hypothesis I Chaotic pop dynamics, Medium observation error

Hypothesis II


Solution: chopping up the data

Fit small chunks of the data independently, Optimize joint likelihood / posterior Pisarenko & Sornette (2004), Phys. Rev. E


Suddenly, all is fine

Hartig, F. & Dormann, C. F. (2013) Does model-free forecasting really outperform the true model? PNAS, 110, E3975.


Conclusions / implications

►  MLE / Bayesian inference can be asymptotically inconsistent for nonlinear dynamical systems ►  This conditions may readily occur in more complex predator-prey / food

web / host-parasitoid systems

►  When / why? ►  Asymptotic inconsistency formally proven by Judd (2007), Phys.

Rev. E for SSM + chaotic + observation error only ►  Our conclusion (without formal proof): remains the same for

process << observation error, we think this is what happens here.

►  Additional consideration: if observation error sufficiently rigid, likelihoods might get extremely ragged, problems for the samplers, see Wood (2010) Nature, Wood & Fasiolo (plenary).


Recommendations

►  Be aware that parameter estimates in a state-space framework can be massively biased if the dynamics are strongly nonlinear.

►  Remedies: ►  Chopping up the data Pisarenko & Sornette (2004), Phys.

Rev. E ►  Diagnose by comparing model / data with summary

statistics Judd (2007), Phys. Rev. E ►  Use of ABC / synthetic likelihoods? Wood (2010) Nature,

Hartig et al. (2011), Ecol. Lett. ►  Get strong data on observation models!


Thank you!

Hartig, F. & Dormann, C. F. (2013) Does model-free forecasting really outperform the true model? PNAS, 110, E3975.

Available at http://arxiv.org/abs/1305.3544 , code

https://github.com/florianhartig/NonlinearOrChaoticBayesianStateSpaceModels

Talk Florian Hartig at ISEC 2014 Montepellier / France

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Transcript of Talk Florian Hartig at ISEC 2014 Montepellier / France