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A computer simulation is used to study collective judgements that an expert panel reaches on the basis of qualitative probability judgements contributed by individual members. The simulated panel displays a strong and robust crowd wisdom effect. The panel’s performance is better when members contribute precise probability estimates instead of qualitative judgements, but not by much. Surprisingly, it does not always hurt for panel members to interpret the probability expressions differently. Indeed, coordinating their understandings can be much worse.

Making good decisions depends on having accurate information - quickly, and in a form in which it can be readily communicated and acted upon. Two features of medical practice can help: deliberation in groups and the use of scores and grades in evaluation. We study the contributions of these features using a multi-agent computer simulation of groups of physicians. One might expect individual differences in members' grading standards to reduce the capacity of the group to discover the facts on which well-informed decisions depend. Observations of the simulated groups suggest on the contrary that this kind of diversity can in fact be conducive to epistemic performance. Sometimes, it is adopting common standards that may be expected to result in poor decisions.

We report the results of a meta-analysis study of the relative accuracies for a range of methods for aggregating confidence interval estimates of unknown quantities. We found that a simple “trim-and-average” method—that is, remove outliers and then average—produced the most accurate estimates. Our results show that more complicated methods of confidence interval aggregation, which factor in confidence levels and estimate imprecisions, do not produce estimates more accurate than those produced by the simple trim-and-average method.

It is natural to think of precise probabilities as being special cases of imprecise probabilities, the special case being when one’s lower and upper probabilities are equal. I argue, however, that it is better to think of the two models as representing two different aspects of our credences, which are often (if not always) vague to some degree. I show that by combining the two models into one model, and understanding that model as a model of vague credence, a natural interpretation arises that suggests a hypothesis concerning how we can improve the accuracy of aggregate credences. I present empirical results in support of this hypothesis. I also discuss how this modeling interpretation of imprecise probabilities bears upon a philosophical objection that has been raised against them, the so-called inductive learning problem.

Kolmogorov's axiomatization of probability is the standard probability axiom system that most people learn in high school or university. And it is widely considered to be undeniably true—in much the same way that arithmetic seems to be undeniably true. However, over the years, various philosophers, mathematicians, statisticians, and scientists have found potential faults with Kolmogorov's axiom system. In this chapter these potential faults are reviewed and discussed. Among them are the problematic countable additivity, as well as finite additivity. The chapter also includes critical examinations of conditional probability, positive real numbers and sets and algebras as deployed by Kolmogorov.

It is usually supposed that the central limit theorem explains why various quantities we find in nature are approximately normally distributed—people's heights, examination grades, snowflake sizes, and so on. This sort of explanation is found in many textbooks across the sciences, particularly in biology, economics, and sociology. Contrary to this received wisdom, I argue that in many cases we are not justified in claiming that the central limit theorem explains why a particular quantity is normally distributed, and that in some cases, we are actually wrong.

AquaticHealth.net is an open-source aquatic biosecurity intelligence gathering and analysis application. The system collects information in much the same way as other similar systems (e.g. HealthMap, BioCaster). However, the information collected undergoes minimal automated analysis, and analysis is largely left to AquaticHealth.net's users. The result is an automated system of intelligence gathering, combined with a manual system of intelligence analysis. This approach relies on a large number of users, and so AquaticHealth.net relies on an open-intelligence analysis method: any user can publish their own analyses for all to see and analyse further. By combining automated data collection and human analysis, AquaticHealth.net will provide fast and accurate forecasts, accompanied with nuanced explanations. These methods can be applied to other areas of biosecurity and disease surveillance.

In this chapter, the author reviews some of the philosophical issues that arise in connection with the concept of data. He first asks what data are, and he evaluates a number of different answers to this question that have been given. The author then examines the concept of so-called big data and the corresponding concept of big science. It has been claimed that the advent of big science calls for a fundamental change to science and scientific methodology. The author argues that such claims are too strong. Finally, the author reviews the distinction between data and phenomena, due to Bogen and Woodward 1988, and discusses some of its connections to big data and big science.

Three web-based biosecurity intelligence systems - BioCaster, EpiSPIDER and HealthMap--are compared with respect to their ability to gather and analyse information relevant to public health. Reports from each system for the period 2-30 August 2010 were studied. The systems were compared to the volume of information that they acquired, their overlaps in this information, their timeliness, their sources, their focus on different languages and their focus on different geographical regions. Main results were as follows: EpiSPIDER obtains the most information and does so mainly through Twitter; no significant difference in systems' timeliness was found; there is a relatively small overlap between the systems (10-20%); the systems have significant differences in their ability to acquire information relevant to different countries, which may be due to the sources they use and the languages they focus on.

David Malament argued that Hartry Field’s nominalisation program is unlikely to be able to deal with non-space-time theories such as phasespace theories. We give a specific example of such a phase-space theory and argue that this presentation of the theory delivers explanations that are not available in the classical presentation of the theory. This suggests that even if phase-space theories can be nominalised, the resulting theory will not have the explanatory power of the original. Phase-space theories thus raise problems for nominalists that go beyond Malament’s initial concerns.

AquaticHealth.net is an open-source aquatic biosecurity intelligence application. By combining automated data collection and human analysis, AquaticHealth.net provides fast and accurate disease outbreak detection and forecasts, accompanied with nuanced explanations. The system has been online and open to the public since 1 January 2010, it has over 200 registered expert users around the world, and it typically publishes about seven daily reports and two weekly disease alerts. We document the major trends in aquatic animal health that the system has detected over these two years, and conclude with some forecasts for the future.

In the philosophy of probability there are two central questions we are concerned with. The first is: what is the correct formal theory of probability? Orthodoxy has it that Kolmogorov’s axioms are the correct axioms of probability. However, we shall see that there are good reasons to consider alternative axiom systems. The second central question is: what do probability statements mean? Are probabilities “out there”, in the world as frequencies, propensities, or some other objective feature of reality, or are probabilities “in the head”, as subjective degrees of belief? We will survey some of the answers that philosophers, mathematicians and physicists have given to these questions.