Publications

Summary

Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods that introduce auxiliary data. These methods typically approximate the transition densities of the process numerically, both for calculating the posterior densities and proposing auxiliary data. Here, the Euler–Maruyama scheme is the standard approximation technique. However, the MCMC method is computationally expensive. Using higher-order approximations may accelerate it, but the specific implementation and benefit remain unclear. Hence, we investigate the utilization and usefulness of higher-order approximations in the example of the Milstein scheme. Our study demonstrates that the MCMC methods based on the Milstein approximation yield good estimation results. However, they are computationally more expensive and can be applied to multidimensional processes only with impractical restrictions. Moreover, the combination of the Milstein approximation and the well-known modified bridge proposal introduces additional numerical challenges.

Summary

Ecological systems can often be characterised by changes among a set of underlying states pertaining to individuals, populations, communities, or entire ecosystems through time. Owing to the inherent difficulty of empirical field studies, ecological state dynamics operating at any level of this hierarchy can often be unobservable or" hidden". Ecologists must therefore often contend with incomplete or indirect observations that are somehow related to these underlying processes. By formally disentangling state and observation processes based on simple yet powerful mathematical properties that can be used to describe many ecological phenomena, hidden Markov models (HMMs) can facilitate inferences about complex system state dynamics that would otherwise be intractable. However, while HMMs are routinely applied in other disciplines, they have only recently begun to gain traction within the broader ecological community. We provide a gentle introduction to HMMs, establish some common terminology, and review the immense scope of HMMs for applied ecological research. By illustrating how practitioners can use a simple conceptual template to customise HMMs for their specific systems of interest, revealing methodological links between existing applications, and highlighting some practical considerations and limitations of these approaches, our goal is to help establish HMMs as a fundamental inferential tool for ecologists.

Summary

State-switching models such as hidden Markov models or Markov-switching regression models are routinely applied to analyse sequences of observations that are driven by underlying non-observable states. Coupled state-switching models extend these approaches to address the case of multiple observation sequences whose underlying state variables interact. In this paper, we provide an overview of the modelling techniques related to coupling in state-switching models, thereby forming a rich and flexible statistical framework particularly useful for modelling correlated time series. Simulation experiments demonstrate the relevance of being able to account for an asynchronous evolution as well as interactions between the underlying latent processes. The models are further illustrated using two case studies related to a) interactions between a dolphin mother and her calf as inferred from movement data; and b) electronic health record data collected on 696 patients within an intensive care unit.

Summary

We propose two novel methods to “bring Agent Based Models (ABMs) to the data”. First, we describe a Bayesian procedure to estimate the numerical values of ABM parameters that takes into account the time structure of simulated and observed time series. Second, we propose a method to forecast aggregate time series using data obtained from the simulation of an ABM. We apply our methodological contributions to a specific medium-scale macro ABM.

Summary

Neurobiological data such as electroencephalography measurements pose a statistical challenge due to low spatial resolution and poor signal‐to‐noise ratio, as well as large variability from subject to subject. We propose a new modelling framework for this type of data based on stochastic processes. Stochastic differential equations with mixed effects are a popular framework for modelling biomedical data, e.g. in pharmacological studies. Whereas the inherent stochasticity of diffusion models accounts for prevalent model uncertainty or misspecification, random‐effects model intersubject variability. The two‐layer stochasticity, however, renders parameter inference challenging. Estimates are based on the discretized continuous time likelihood and we investigate finite sample and discretization bias. In applications, the comparison of, for example, treatment effects is often of interest. We discuss hypothesis testing and evaluate by simulations. Finally, we apply the framework to a statistical investigation of electroencephalography recordings from epileptic patients. We close the paper by examining asymptotics (the number of subjects going to ∞) of maximum likelihood estimators in multi‐dimensional, non‐linear and non‐homogeneous stochastic differential equations with random effects and included covariates.

Summary

A price on emissions can be achieved through an emission tax or permit trading. The advantages and drawbacks of either instrument are debated. We present an agent-based model to compare their performance under bounded rationality and dynamic markets. It describes firms that face uncertainty about future demand and prices; use heuristic rules to decide production levels, trading prices, and technology adoption; and are heterogeneous in terms of production factors, abatement costs, and trading behavior. Using multiple evaluation criteria and a wide range of parameter values, we find that the main difference between the two policies lies in the fact that permit prices fall after successful abatement. This can lead to higher production levels under permit trading, but can also drive emission-efficient firms out of the market. Scarcity rents under permit trading can further create higher profit rates for firms, the extent of which is shown to depend on the mechanisms for market-clearing and initial allocation.

Summary

The narwhal (Monodon monoceros) is a high‐Arctic species inhabiting areas that are experiencing increases in sea temperatures, which together with reduction in sea ice are expected to modify the niches of several Arctic marine apex predators. The Scoresby Sound fjord complex in East Greenland is the summer residence for an isolated population of narwhals. The movements of 12 whales instrumented with Fastloc‐GPS transmitters were studied during summer in Scoresby Sound and at their offshore winter ground in 2017–2019. An additional four narwhals provided detailed hydrographic profiles on both summer and winter grounds. Data on diving of the whales were obtained from 20 satellite‐linked time‐depth recorders and 16 Acousonde™ recorders that also provided information on the temperature and depth of buzzes. In summer, the foraging whales targeted depths between 300 and 850 m where the preferred areas visited by the whales had temperatures ranging between 0.6 and 1.5°C (mean = 1.1°C, SD = 0.22). The highest probability of buzzing activity during summer was at a temperature of 0.7°C and at depths > 300 m. The whales targeted similar depths at their offshore winter ground where the temperature was slightly higher (range: 0.7–1.7°C, mean = 1.3°C, SD = 0.29). Both the probability of buzzing events and the spatial distribution of the whales in both seasons demonstrated a preferential selection of cold water. This was particularly pronounced in winter where cold coastal water was selected and warm Atlantic water farther offshore was avoided. It is unknown if the small temperature niche of whales while feeding is because prey is concentrated at these temperature gradients and is easier to capture at low temperatures, or because there are limitations in the thermoregulation of the whales. In any case, the small niche requirements together with their strong site fidelity emphasize the sensitivity of narwhals to changes in the thermal characteristics of their habitats.

Summary

We study the issue of assigning weights to players that identify winning coalitions in plurality voting democracies. For this, we consider plurality games which are simple games in partition function form such that in every partition there is at least one winning coalition. Such a game is said to be precisely supportive if it is possible to assign weights to players in such a way that a coalition being winning in a partition implies that the combined weight of its members is maximal over all coalitions in the partition. A plurality game is decisive if in every partition there is exactly one winning coalition. We show that decisive plurality games with at most four players, majority games with an arbitrary number of players, and almost symmetric decisive plurality games with an arbitrary number of players are precisely supportive. Complete characterizations of a partition's winning coalitions are provided as well.

Summary

Should policy-makers combine price incentives with behavioural nudges to encourage sustainable energy behaviour? Available evidence from various behavioural sciences is scarce and inconclusive about synergy of the two instruments. This is partly due to methodological limitations. We offer a framework to overcome such limitations in future research and to guide policy-making. It includes four cases: no synergy, positive synergy, weak negative synergy, and strong negative synergy or backfire. The adoption of a policy mix is recommended in the first two cases, and may be pursued in the third case. To clarify the underlying mechanisms of the synergy, a distinction is made between crowding (in/out) of intrinsic motivations by incentives and crowding (in/out) of extrinsic motivations by nudges. This distinction turns out to be especially relevant in the case of weakly negative synergy, as here behavioural and temporal spillover effects require consideration from the policy-maker as well. We end with broader reflections regarding other policy criteria for the design of an adequate energy policy mix.

Summary

We provide a detailed study of the threshold model, where both conformist and anti-conformist agents coexist. Our study bears essentially on the convergence of the opinion dynamics in the society of agents, i.e., finding absorbing classes, cycles, etc. Also, we are interested in the existence of cascade effects, as this may constitute an undesirable phenomenon in collective behavior. We divide our study into two parts. In the first one, we basically study the threshold model supposing a fixed complete network, where every one is connected to every one, like in the seminal work of Granovetter. We study the case of a uniform distribution of the threshold, of a Gaussian distribution, and finally give a result for arbitrary distributions, supposing there is one type of anti-conformist. In a second part, we suppose that the neighborhood of an agent is random, drawn at each time step from a distribution. We distinguish the case where the degree (number of links) of an agent is fixed, and where there is an arbitrary degree distribution. We show the existence of cascades and that for most societies, the opinion converges to a chaotic situation.