[Planned] Emission Reduction Strategies in Probabilistic Models: Another Look at Bovaer

Table of Contents:

• Introduction
• Conclusion

Introduction

Conclusion

Until next time,

- James Bergstra

Appendix: Removing "Simulation-based" Models

PlanZero's mission calls for both short-, medium-, and long-term prediction capabilities suitable for the evaluation of strategies. The credibility and usefulness of model predictions depends on three things:

1. The structure and elements of the model are reasonable.
2. The predictions refine people's prior beliefs, rather than contradicting them.
3. The predictions agree with data, where data is available, while also being precise.

Non-probabilistic modelling is not generally great across all three areas. The kind of modelling employed in the previous post on Bovaer, was an example of non-probabilistic modelling. from a computational perspective, the modelling proceeds from data and initial numerical assumptions, through arithmetic and statistical summaries, forward in time, and with one pass through the modelled time period of the model, it arrives at a result. Simulation-based modelling is good with regards to criterion (1) in that predictions can be reasonably explained directly in terms of the computation of the model. Simulation-based modelling is only so-so with regards to criterion (2) because simulation-based modelling does not naturally express how [un]likely a person's current beliefs are, the simulation just emits its own prediction. Critically, simulation-based modelling offers very little support for matching data. Data matching is entirely at the discretion of the modeller, and the result of simulation does not inherently characterize whether data was either used appropriately or fit well.

Probabilistic modelling is a generalization of simulation-based modelling that can produce models that are more credible. Probabilistic modelling (particularly so-called directed graphical modelling) starts with random variables instead of numbers. So for example, instead of starting with e.g. the NIR data, a probabilistic model starts with the idea that there are emission amounts in such-and-such sectors of such-and-such gases (random variables), and that there are emissions for all years we care to include in our model. While we're at it, we make up broad a-priori guesses at how much emissions there were in all these areas and for each year. These initial beliefs have a name in probabilistic modelling, they are our priors. For example, we might express a prior that ${\mathrm{C}\mathrm{O}}_2$ emissions from national electricity generation are relatively big, but still smaller than e.g. global emissions. As a contrasting example, we might express that the ${\mathrm{N}\mathrm{F}}_3$ emissions from a sector that isn't known for producing that gas, in a province that isn't known for activity in that sector, is probably zero, at least for most years. Priors should be broad, inclusive probability distributions that include most (if not all) people's beliefs about what the random variables represent.

The relationship between this probabilistic modelling and simulation-based modelling is that if we combine the random variables with arithmetic and statistical expressions (like we would do in a simulation-based model), then drawing a sample from all the random variables in our prior looks a lot like running a simulation-based model. This computation has a name in probabilistic modelling: sampling from the prior. It's kind of fun, to see your prior beliefs transformed into sets of numbers that look like hypothetical NIRs because they are our own predictions of the future! Looking back at our list of criteria for making credible predictions, a probabilistic model is similar to a simulation-based one in terms of model structure (criterion 1), and it's better than a single scenario from a simulation-based model at refining rather than contradicting beliefs (criterion 2) because it's natural to draw lots of scenarios from a probabilistic model, and the spread of scenarios will include people's beliefs and can reflect the degree of [dis]agreement among people. Where probabilistic models really excel though, is in their ability to make precise and accurate predictions (criterion 3), which I'll explain in the next section.

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