Model Selection and Uncertainty in
Climate Change Mitigation Research
Martin Sewell
mvs25@cam.ac.uk
All models are wrong...
Model uncertainty & selection in complex models
14–16 March 2011
Groningen
The Cambridge Centre for Climate Change Mitigation Research (4CMR)
Uncertainty
Uncertainty is best described using a probability distribution, and the wider
the distribution, the greater the uncertainty.
Aspects of climate change about which we are:
• almost certain: the physical chemistry
• very uncertain: the effect of clouds, the ocean, the response of biological
processes, climate change mitigation
Reductionism
• Reductionism is a theory that asserts that the nature of complex things
is reduced to the nature of sums of simpler or more fundamental things.
• Anthropology is reducible to sociology, sociology is reducible to
psychology, psychology is reducible to biology, biology is reducible to
chemistry, chemistry is reducible to physics.
• I posit that there exists what an economist would call a structural break
between the natural sciences and the social sciences.
• Uncertainty decreases as we move through the disciplines from
anthropology to physics (excepting at the atomic and subatomic scales,
where, ironically, the only true uncertainty lies).
What is science?
• Hume (1739–40) pointed out that ‘even after the observation of the
frequent or constant conjunction of objects, we have no reason to draw
any inference concerning any object beyond those of which we have
had experience’.
• One can never generalize beyond one’s data without making subjective
assumptions, so science always involves a degree of uncertainty.
• If we insist upon intimating one’s degree of uncertainty and selfconsistent reasoning, science becomes applied subjective Bayesian
inference (observing some common sense criteria, science should also
be constrained by exchangeability (de Finetti 1937), the Reflection
Principle (van Fraassen 1984, 1995) and the Principal Principle (Lewis
1980)).
• Science involves putting probabilities on hypotheses.
Science in practice
• Using a scientist’s abstraction, a hypothesis is not simple, complex,
popular, fashionable, left wing, right wing, racist, sexist, equitable,
politically correct, dangerous, or abhorrent, it is merely surprising to a
certain degree.
• A scientist should be free of any ideology.
• A principled approach to science involves Bayesian model selection
(originally due to Jeffreys (1939)), which in practice may involve the
easy to calculate approximation the Bayesian information criterion (BIC)
(Schwarz 1978), followed by Bayesian model averaging.
• Science, in practice, progresses by peer review, and the
Intergovernmental Panel on Climate Change (IPCC) assessment
reports are arguably the most peer reviewed documents in the history of
science. This makes the IPCC reports excellent science, and more so if
and when any mistakes (e.g. melting Himalayan glaciers) come to light,
they are promptly corrected.
Science of climate change
• Starting with the physics and chemistry, there is no significant doubt
that CO2 is a greenhouse gas, and that levels of anthropogenic CO2 in
the atmosphere are increasing.
• The theory of anthropogenic global warming is built on peer reviewed
science that has accumulated since Fourier in the 1820s.
• In 2004, Naomi Oreskes analysed 928 abstracts, selected using the
keywords ‘global climate change’, published in refereed scientific
journals and found that none of the papers disagreed with the theory of
anthropogenic climate change.
• How can we trust climate models when we can’t even forecast next
week’s weather? Think of climate as the signal and weather as the
noise.
Uncertainty and climate change
According to the IPCC it is
• extremely likely (> 95% probability) that human activities have exerted a
substantial net warming influence on climate since 1750,
• very likely (> 90% probability) that anthropogenic greenhouse gas
increases caused most of the observed increase in global average
temperatures since the mid-20th century, and
• virtually certain (> 99% probability) that global warming shall continue in
the future.
The apparently counter-intuitive result that the past is less certain than the
future implies that we’re pretty sure of the physics, less sure of historical
measurements, and the forecast into the future of the global
temperature must be steeper than the rise in the past.
A more surprising hypothesis requires more evidence
• Laplace asserted that ‘the weight of evidence for an extraordinary claim
must be proportioned to its strangeness’.
• A more surprising hypothesis requires more evidence.
• Bayes’ theorem makes this explicit.
• The present-day form of Bayes’ theorem is actually due to Laplace,
Thomas Bayes only proved a special case.
• It is known with certainty that CO2 is a greenhouse gas and that levels
of anthropogenic CO2 in the atmosphere are increasing.
• So, a priori, it would be surprising if anthropogenic CO2 was not
contributing to global warming.
• This puts the onus on the climate sceptics.
Utility
• When hypotheses affect our utility, the expected utility hypothesis
informs us that we should seek to maximize the sum of the products of
the utility and the probability.
• Therefore the probabilities should be multiplied by the utility associated
with each cost/benefit to determine the best course of action.
• If mitigating anthropogenic global warming has an associated cost,
economically, the onus may move towards the proponents of
anthropogenic global warming.
Scepticism
• Note the reversal of the onus of weight of evidence as we move from
the science to policy, this is a source of some of the antagonism and
confusion between the consensus view and the sceptics.
• It makes no sense to be a climate sceptic, but a lot of sense being a
climate change mitigation sceptic.
• As with science in general, healthy scepticism is great, but climate
change denial is malicious mischief.
Altruism
• Some policy decisions should depend on our degree of altruism.
• National governments have a duty to act in the interests of their citizens,
but need a policy regarding giving aid to other nations, for example for
climate change adaptation.
• Using a gene-based biological approach, Salter (2006) estimates that
the relative investment that individuals allocate to their self is 70%, their
offspring 20%, their ethny 7% and humanity 3% (the numbers are
merely indicative).
• This account is descriptive, but as we cannot transcend our genes
(Moxon 2010), policy decisions should accommodate our innate
altruism (or lack thereof).
Social discount rate
• How much do we care about the future?
• If we wish to perform a cost-benefit analysis on a future public sector
project, such as climate change mitigation, we must choose a discount
rate that reflects society’s preference for present benefits over future
benefits.
• The discount rate used in the Stern Review on the Economics of
Climate Change was approximately 1.4%, and was criticized for being
too low.
• A colleague, Tim Joslin, wrote ‘I can see no justification whatsoever for
using a discount rate of greater than zero. Arguably it should be
negative.’
The social discount rate—my prescription
• An individual’s discount function is hyperbolic and reaches 100% at the
end of their lifetime. An equitable social discount function should
average the population’s individual discount functions.
• The social discount rate is a crucial variable in models of the economics
of climate change mitigation, and there is no consensus.
Climate sensitivity
• Climate sensitivity is a measure of how
responsive the temperature of the climate
system is to a change in the radiative
forcing.
• It is usually expressed as the temperature
change associated with a doubling of the
concentration of CO2 in the Earth’s
atmosphere.
• Climate sensitivity has a positive skew.
• The compounding effect of essentially
linear feedbacks dominates system
sensitivity, and the uncertainty here does
not diminishing with time, the estimates
are not expected to improve.
• We’re pretty certain of the uncertainty.
Economics of climate change mitigation
• Economics is a social science and an approximation of psychology.
• Economic models contain greater uncertainty than climate models.
• Economic forecasting is notoriously difficult, largely because we can’t
predict human creativity in innovation—if we knew what the next
innovation would be, we’d have already invented it.
• The efficient market hypothesis dictates that stock market returns
approximate a martingale, rendering financial markets inherently
uncertain.
• Energy-environment-economy (E3) models contain greater uncertainty
still.
Carbon tax and emissions trading
Two popular solutions to the problem of how to mitigate climate change
are 1) a carbon tax and 2) emissions trading (cap and trade).
They are theoretically equivalent except that they’re logically opposed
regarding where the uncertainty lies.
• A carbon tax fixes the rate of taxation and allows emissions to vary.
• Emissions trading fixes emissions and allows the cost of compliance to
vary.
• The physical science solution would be to fix emissions (implying a
preference for emissions trading).
• The economist’s solution would be to internalize an externality with a
carbon tax.
It would be a mistake to discount human behaviour, so my preference lies
with taxation.
Prisoner’s dilemma
• Finally turning to anthropology, we introduce greater uncertainty still
when considering climate change mitigation in terms of the behaviour of
different cultures, with their varying degrees of intelligence and ability to
demonstrate a capacity for altruism.
• Human-induced climate change is a classic case of Garrett Hardin’s
tragedy of the commons—the benefits of burning fossil fuels accrue to
individuals, companies and nations, whilst the costs accrue to the planet
as a whole.
• The tragedy of the commons is a multi-player generalization of the
prisoner’s dilemma.
• The best overall outcome in a prisoner’s dilemma is one of cooperation,
but economic theory informs us that the rational choice is for players to
always defect.
Martin Sewell
mvs25@cam.ac.uk