Dialogues Around Models and Uncertainty

The following sections are included:

• Preface
• About the Editor
• About the Contributors
• Contents

Can you describe your field briefly?

I am an applied microeconomist, and my research is on health economics and industrial organisation. My main interest is in the health market, and my favourite way to describe my work is by means of a “three-circle” diagram. Each circle represents a “party”: an insurer, a provider, and a consumer. The economics of the health market is about how these three parties interact.

Can you describe your field briefly? Present a paradigmatic example of a model in your field, describing it in terms that are accessible to non-experts.

The basic model example I want to propose is the theory of seismic wave propagation which represents the Earth’s internal structure in terms of spatially variable elastic properties such as rigidity or density. Actually, it is better if seismologists use seismic velocities (e.g. the speed of primary P and S waves in Earth rock materials) and density as the parameters to describe the elastic behaviour of geological media. Depending on the observed parameter to reproduce, a model can show the generally nonlinear, mathematical relationship between data and model parameters. The travel times of seismic waves propagating from a deep earthquake source to the receivers deployed at the Earth’s surface are typically the physical quantities which seismologists measure and use to reconstruct elastic images of the Earth’s interior in terms of spatially varying seismic velocities. In this case, the model is the theory allowing us to compute the travel time of the seismic waves. This requires the estimation of the wave trajectory and knowledge about the local variation of the seismic velocity along the travel path. In a simple uniform velocity medium, wave trajectories are straight lines, so the model is a simple linear equation ($T=\frac{r}{v}$, T is the travel time, r is the travelled distance and v is the seismic wave velocity). In a more complex geological medium, the seismic velocity can vary according to the different rock materials encompassed by seismic waves. In this case, the models become an integral equation ($T={\displaystyle {\int }_{\text{path}}\frac{ds}{v\left(x,y,z\right)}}$, where ds is a small portion of the ray trajectory , v(x, y, z) is the velocity field) where the integral extends to the wave trajectory and the total travel time is obtained from the integral of partial travel times along a small portion of the wave path.

Can you describe your field briefly?

I do qualitative research on strategic management processes and practices in complex pluralistic organisations, focusing on phenomena such as organisational change, the role of management tools, decision-making, leadership processes, and organisational identity, drawing on organisation and management theory…

Can you describe your field briefly?

I am a statistician with a particular interest in the design of experiments, that is, in the choice of informative conditions at which to make observations.

Can you describe your field briefly?

My field is to understand Nature as mathematics. What that means is, we try to understand the world through a logical (mathematical) description of physical phenomena, one that also has the power of prediction…

Can you describe your field briefly?

Within economics, I generally work on the theory of incentives, which can be broadly defined as the formal analysis and design of means to direct the efforts of autonomous agents towards the achievement of given objectives.

Can you describe your field briefly?

I’m a mathematician originally, and I came into using fluid mechanics essentially to understand how the atmosphere works. So, I’ve been involved in what’s often called dynamic meteorology, that’s how the atmosphere moves, but essentially in weather and in climate.

Can you describe your field briefly?

I do econometrics with primary applications to public policy.

Can you describe your field briefly?

My research field is observational cosmology, which is the study of the size and shape of the universe, and my speciality is how galaxies and the super-massive black holes they contain have grown and evolved over cosmic time.

Can you describe your field briefly?

My field is molecular modelling. The background is pharmaceutical sciences. So the aim would be to create, design, construct, whatever that means (we can come to that later) a new therapeutic. Since, in the classical world, therapeutics are, to 80%, molecular-defined entities, it would translate into creating a new molecule, by playing with existing ones.

Can you describe your field briefly?

I would say we work at the interface between models and reality, trying to get observations of the real world into the model-land, and then interpreting simulations in model-land so as to say something about the real world, usually something about the future. My work draws from many different traditional disciplines and often focuses on nonlinearity, on how the mathematics of nonlinear systems differs from that of linear systems. If there is a common thread, I guess it is in the attempt to see to what extent our best theories, in combination with carefully chosen observations, tell us about reality.

Can you describe your field briefly?

My field tries to understand biological processes quantitatively and predictively; in the narrower sense, what I’m trying to do is to understand how we can learn the structure and dynamics of biological systems from data.

Can you describe your field briefly?

I’m a doctor, and I’m one of a relatively small group of doctors whose job is split 50% doing clinical work within a hospital and 50% doing research within a university. A lot of people do predominantly one or the other, but I genuinely am 50% — I’m paid half by NHS and half by the University.

Could you describe your field briefly?

I study urban energy systems, which is basically the demand for and use of energy and its supply within urban areas.

Can you describe your field briefly?

My field is modelling of energy systems and process systems. So, process systems are for making products, whereas energy systems are for converting energy into different forms and eventually into a useful service.

Can you describe your field briefly?

First and foremost, I am a mathematician with strong research and teaching interests in actuarial mathematics. At the Department of Mathematics of the ETH Zürich, I am responsible for the education of actuaries, i.e. insurance mathematicians. Based within a very strong research department, my teaching and research in this more applied area also mirrors that environment. Our position on the educational/research scale within the worldwide actuarial community is hence to be located at the more mathematical, quantitative end. So essentially, my current research field is Quantitative Risk Management (QRM) within insurance and finance, with a particular interest in the modelling of extreme events and in gaining a better understanding of concepts related to risk aggregation and risk diversification.

Can you describe your field briefly?

My work involves the development and application of mathematical and statistical tools and methods to engineering problems for the robust design of industrial products and processes.

Can you describe your field briefly?

I’m an economist, and most of my research is on environmental issues, in particular, climate change.

Can you describe your field briefly?

I am a mathematical philosopher, which means that I use mathematical and computational methods to solve philosophical problems. Having a background in physics, I am especially interested in applying modelling and simulation methods, which happen to be enormously powerful tools every philosopher should know about.