When philosophers focused their attention on scientific explanation, they also turned to scientific prediction. In fact, Carl Hempel and Paul Oppenheim, the two main philosophers to systematize and set the agenda on philosophical studies on scientific explanation, believed that prediction was the other side of the same coin. These ideas flourished in and around 1948 with their seminal work Studies in the Logic of Explanation (Hempel and Oppenheim 1948), and continued until the demise of logical empiricism in 1969 at a symposium on the structure of theories in Urbana, Illinois (Suppe 1977).
Despite the joint birth, scientific explanation and prediction have pretty much gone in different directions ever since. While studies in scientific explanation grew significantly establishing different schools of thought, philosophers working on pre- diction are more difficult to find. It is interesting to note that when it comes to philosophical studies on computer simulations, much more effort has been put into studying prediction and much less into scientific explanation. This asymmetry can be explained by the practices of computer simulations in scientific and engineering contexts. Researchers are more interested in predicting future states of a system, rather than in explaining why such states are obtained. At the beginning of this chapter, we have discussed at some length scientific explanation. Now is the time to draw attention to some of the basic principles of scientific prediction in the context of computer simulations. But first, an example that illustrates predictions in science and helps to introduce the basic terminology.
A beautiful case in the history of science is Edmond Halley’s predictions of comets. The general beliefs about comets at the time of Halley was that they were mysterious astronomical interlopers moving unpredictably through the sky. Although Halley made some precise retrodictions – that is, predictions into the past – establishing that the comet that appeared in 1531, 1607, and 1682 were all man- ifestations of the same phenomena, his postdictions – that is, predictions into the future – of the next appearance of the comet were not as successful, confirming in this way the established scientific belief of the time. In fact, he postdicted that the comet would show up in the sky again by 1758, one year earlier than its actual appearance.
It was the job of Alexis Clairaut, a prominent Newtonian, to correctly postdict the next appearence of the comet, which was set to reach its perihelion by 1759. Clairaut based his postdictions on calculations that would include forces unknown at the time, but that made sense within the Newtonian theory. Such forces mainly refered to the actions and influence of distant planets – recall that Uranus was dis- covered in 1781 and Neptune remained unknown until 1846. It is interesting to note that, besides a successful postdiction, what was also at stake was the confirmation of Newtonian theory as the most adequate way to describe the natural world. The struggle among factions lead many physicists to at first reject Clairaut’s calculations, and many others to anticipate with some joy the failure of Newtonian theory. The story ends with Clairaut’s calculations correctly postdicting the next appearance of Halley’s Comet – despite some truncations in the higher terms of his equation – and with the Newtonian view of the world imposing overwhelmingly over less adequate theories.
The example of Halley’s Comet makes plain the importance of prediction for scientific research – and, in this particular case, also for confirming the Newtonian theory. Successful predictions are valuable because they go beyond what is know most directly and evidently by researchers, providing ‘hidden’ information about phenomena and empirical systems.7
Two important characteristics about prediction are the temporal dimension and the accuracy of the prediction. A common mistake is to presume that predictions are about saying something meaningful about the future (i.e., postdictions), but not about the past (i.e., retrodictions). This is typically the case when retrodictions are mistakenly confounded with scientific evidence of something happening. Thus, it is said that Halley found evidence that the comet that appeared in 1531, 1607, and 1682 were the same, but not that he made retrodictions. Although evidence and prediction can, in some cases, be related, they are still two separate notions. Retrodictions – as well as postdictions – are part of a theory’s implications, and this is so regardless of temporal constraints. Evidence, on the other hand, serves to either support or counter a scientific theory. In this sense, retrodictions and postdictions are the manifestation of the same phenomenon, namely, of predictions. Thus understood, it is correct to say that Halley predicted the three occurrences of the comet prior to his observation of 1682, just as Clairaut predicted its next appearance in 1759 because he made calculations using a theory – a form of theory implication.
The language of prediction is used to describe declarative assertions about the past as well as future events made in light of a theory, and thus we shall use it here. In fact, the temporal dimension entails an epistemic component: “to predict is to
7Incidentally, these same features render prediction inherently risky, since access to hidden infor-
mation typically depends on shared standards in a given community, and is therefore potentially intersubjective. Now, one way to avoid problems of intersubjectivity is by demanding convergent predictions. That is, by means of having disparate areas of research all predicting towards similar results, our confidence in the prediction must inevitably increase. This is what philosopher Heather Douglas calls convergent objectivity (Douglas 2009, 120). We must keep in mind, however, that there are other forms of objectivity as well. In here, we are not going to worry about questions on subjectivity and objectivity, as they deserve a study of their own. For further references, the reader is referred to ((Daston and Galison 2007) (Lloyd 1995), and of course (Douglas 2009)).
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make a claim about matters that are not already known, not necessarily about events that have not yet transpired” (Barrett and Stanford 2006, 586). In other words, pre- diction is about the ‘diction’ of an event, past, present, or future. Thus understood, prediction is asking ‘what does the theory tell us?’, ‘what knowledge is new?’ In our case, the answer is rather obvious: the next appearance of Halley’s Comet.
Closely related to this temporal dimension is the question of ‘how well does the theory predict the actual observed outcome?’ This is a chief question that gives us a purchase on the second characteristic about prediction relevant for our discussion, namely, the accuracy of predictions.
In the previous chapter we discussed accuracy as the set of measurements that provide an estimated value close to the true value of the quantity being measured. For instance, Halley’s Comet’s nucleus is about 15 kilometers long, 8 kilometers wide, and roughly 8 kilometers thick – a rather small nucleus for the vast size of its coma. The comet’s mass is also relatively low, an estimated 2.2x1014kg. As-
tronomers calculated the average density to 0.6g/cm3indicating that it is made of a
large number of small pieces held loosely together. With this information at hand, along with calculations of the trajectory, astronomers can accurately predict that Halley’s Comet is visible to the naked eye with a period of 76 years.
The accuracy of scientific predictions depend on a combination of the nature of the event, the adequacy of our theories, and the current state of our technology. Although it is true that by using computers we are able to predict with higher de- grees of accuracy than Clairaut’s the next time Halley’s Comet will show up in the sky,8predictions are possible because the trajectory of the comet can adequately be
described using Newtonian mechanics.
Now, for many occasions it is difficult to obtain exact predictions. This is so because of the nature of the phenomena to predict. Indeed, there are many events and phenomena for which we can only predict their behavior within a given range of probability of occurrence. A simple example is the following. Suppose I ask you to chose a card and place it face down on the table. Then I have to predict its suit (i.e., ‘hearts’, ‘diamonds’, ‘clubs’, or ‘spades’). Theory says that I have a 1 in 4 chance of being right. The theory does not entail which suit you just placed face down, but rather that the probability of me being correct is 1
4. Although this does not strictly
count as a prediction, it tell us something about the accuracy of the prediction. Another good example of inexact predictions are so-called chaotic systems. These are systems that are very sensitive to initial conditions, where small errors in computation can rapidly propagate into large predictive errors. This means that certain predictions are impossible after a given point in the calculation. The fact that chaotic systems past a certain point make predictions difficult and essentially im-
8Clairaut was involved in several computations of the orbital period of the Halley’s Comet. For
one of the first calculations, he divided the cometary orbit into three parts. First, from 0 to 90 of eccentric anomaly, the first quadrant of the ellipse from perihelion, which the comet took more than 7 years to traverse. Second, from 90 to 270 , the superior half of the orbit, which the comet needed more than 60 years to traverse. Third, from 270 to 360 , the final quadrant of the ellipse, which took about 7 years to traverse. Clairaut’s calculations were rectified in different moments throughout history (Wilson 1993).
possible in a practical sense has important consequences for scientific research. A standard example of a chaotic system is atmospheric conditions. In weather forecast- ing, it is very difficult to do long-range predictions due to the inherent complexity of the system which only allows predictions up to a certain point. This is the reason why the behavior of the weather is considered chaotic, the smallest changes in the initial conditions make long-term predictions unfeasible – if not utterly impossible. Let us now discuss how prediction works in computer simulations by discussing two simulations of an epidemic outbreak in Italy. The first simulation is a stochastic agent-based model, whereas the second simulation is a structured meta-population model – known as the GLobal Epidemic and Mobility – GLEaM. The agent-based model includes an explicit representation of the Italian population through highly detailed data of the socio-demographic structure. In addition, and for determining the probability of commuting from municipality to municipality, the model makes use of a general gravity model standard in transportation theory. The epidemic trans- mission dynamics is based on an influenza-like illnesses (ILI) compartmentalization based on stochastic models that integrate susceptible, latent, asymptomatic infec- tions, and symptomatic infections (Ajelli et al. 2010, 5). Marco Ajelli and his team, responsible for designing and programing these simulations, define the agent-based model as “a stochastic, spatially-explicit, discrete-time, simulation model where the agents represent human individuals [...] One of the key features of the model is the characterization of the network of contacts among individuals based on a realistic model of the socio-demographic structure of the Italian population” (4).
On the other hand, the GLEaM simulation integrates high-resolution population databases – estimating the population with a resolution given by cells of 15 x 15 minutes of arc – with the air transportation infrastructure and short-range mobility patterns. Many standard GLEaM simulations consist of three data layers. A first layer, where the population and mobility allows the partition of the world into geo- graphical regions. This partition defines a second layer, the subpopulation network, where the inter-connection represents the fluxes of individuals via transportation infrastructures and general mobility patterns. Finally, and superimposed onto this second layer, is the epidemic layer, that defines inside each subpopulation the dis- ease dynamic (Balcan et al. 2009). In the study, the GLEaM also represents a grid- like partition where each cell is assigned the closest airport. The subpopulation net- work uses geographic census data, and the mobility layers obtain data from different databases, including the International Air Transport Association database consisting in a list of airports worldwide connected by direct flights.
As expected, there are advantages and disadvantages of using the agent-based and the GLEaM simulations. As far as the GLEaM model is concerned, the detailed space mobility networks provide an accurate description of the channels of trans- portation available for spreading the disease. However, accurate estimations of the impact of the disease at a more local level are difficult to obtain due to the low level detail contained in this model. As for the agent-based approach, although it is highly detailed in regards to the structures of households, schools, hospitals, etc., it suffers from gathering high confidence datasets from most regions of the world (Ajelli et
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al. 2010, 12). Despite each simulation offering different features, and thus affecting their respective predictive attack rate of the disease, Ajelli and his team notice that there is a steady convergence in the results that provides confidence in each one of the simulations’ prediction. The heterogeneity of the transportation network pro- vided by the GLEaM model, for instance, makes possible accurate predictions of the spatio-temporal spread of the ILI disease at a global scale. On the other hand, the explicit representation of individuals in the agent-based model facilitates accurate predictions of the spread of an epidemic on a more local scale.
Getting more specific about the predictions, the difference in the peak amplitudes varies depending on several factors, mainly based on the values for the reproductive number.9The average epidemic size predicted by GLEaM is 36 % for a reproductive
ratio of R0=1.5, whereas for the agent-based model with the same reproductive
ratio, the average epidemic size goes down to 25 %. On the other end of the epidemic outbreak, the epidemic size predicted by GLEaM is 56 % of the population for a reproductive ratio of R0=2.3, while it is 40 % for the agent-based. Researchers
observed an absolute difference of about 10 % for R0=1.5 and of about 7 % for
R0=2.3. Predictions were also made for a reproductive ratio of R0=1.9, showing
similar behavior in the average epidemic size predicted by both simulations. To Ajelli et al. these predictions look quite accurate as they see convergence in the average epidemic size. The team, however, is unable to evaluate which of the two predictions is better. The high level of realism of the agent-based model should, in principle, speak in favor of the accuracy of the prediction. But unfortunately such a realistic model is not free of modeling assumptions. Indeed, in order to determine the probability of commuting from municipality to municipality, Ajelli et al. imple- ment a general gravity model used in transportation theory as well as assuming a power law functional form for the distance – despite the fact that other functional forms such as exponential decay can also be considered (3). Another assumption stems from taking homogeneous mixing in households, schools, and workplaces, while random contacts in the general population are assumed to depend explicitly on distance (3). Despite the fact that both assumptions are perfectly reasonable, they inevitably affect the prediction and, therefore, the grounds for preferring the agent-based model prediction over the GLEaM’s. Similarly, the prediction of the structured metapopulation model is equally hard to asses precisely because of its lack of realism. “The correct value”, says Ajelli et al., “should be in between the prediction of the models, as supported by the fact that the difference between the models decreases as R0increases, with the models converging to the same value for
the attack rate” (8).
9In epidemiology, the reproductive ratio – or reproductive number – represents the number of
emerging cases that one infected individual generates on average over the course of an infectious period in an otherwise uninfected population. Thus, for R0<1, an infectious outbreak will die
out in the long run, whereas for a R0>1 an infection will be able to spread out and infect the
population. The larger the number, the harder it will be to control the epidemic. Thus, the metric helps to determine the speed that an infectious disease can spread through a healthy population. In the case of both simulations, the authors report that for large R0, the local epidemics become more
widespread across all the layers of the population, making the population structure less and less relevant.
At this point we must highlight a crucial difference between the predictions of- fered by Ajelli et al.’s simulations, and Clairaut’s: whereas the predictions of the later can be empirically confirmed, the predictions of the computer simulations could not. On what grounds, then, do Ajelli and his team claim that these are ac- curate predictions? Their answer is to insist that the good agreement reached by the results of both simulations constitute reasons that speak in favor of an accurate prediction.10Surely, the fact that both simulations are, in their own terms, good rep-
resentations of the target system also contributes to the researcher’s confidence. But it is convergence of results that firmly grounds the confidence in accurate predic- tions.
Such a standpoint is not lacking good reasons. Convergence of results does speak in favor of the simulations as well as of the accuracy of the prediction. In the pre- vious chapter, we saw how verification and validation methods can be used to grant reliability on the simulation and thus help researchers to trust in their results. The interesting twist introduced by Ajelli and team is that validation is not against em- pirical data, but rather against another computer simulation.11 This means that the
results of one simulation works as a confirmatory instance of the results of the other simulation – and vice versa. This is a fairly common practice among researchers making intensive use of computer simulations and from whose target systems there are no empirical data available for validation. In other words, the reliability of com- puter simulations are used for providing grounds for trust in their results which, under conditions of convergence, serve in turn as grounds for believing in the accu- racy of all sorts of predictions.
Having said this, predictive practices should be tempered with some healthy pre- cautionary principles. As any researcher knows, models are based on our representa- tion of how the real-world works. Although the corpus of scientific and engineering beliefs is extremely successful, it is by no means infallible. That is why validation against empirical data is a good and a necessary practice in scientific and engineer- ing research. It virtually forces researchers to ‘test’ their results against the world, and to find a workaround in cases of a mismatch. In this particular case, Ajelli and his team take convergence of results as a positive sign – although not a confirma- tory instance – of an accurate prediction. Thus much is, I believe, correct. However, as they also explain in their article, prediction by convergence of results presup- poses a common basis in the modeling frameworks within which the simulations are located. That is, information such as parametrization, data integration, initial