Local and global error models to improve uncertainty quantification

In groundwater applications, Monte Carlo methods are employed to model the uncertainty on geological parameters. However, their brute-force application becomes computationally prohibitive for highly detailed geological descriptions, complex physical processes, and a large number of realizations. The Distance Kernel Method (DKM) overcomes this issue by clustering the realizations in a multidimensional space based on the flow responses obtained by means of an approximate (computationally cheaper) model; then, the uncertainty is estimated from the exact responses that are computed only for one representative realization per cluster (the medoid). Usually, DKM is employed to decrease the size of the sample of realizations that are considered to estimate the uncertainty. We propose to use the information from the approximate responses for uncertainty quantification. The subset of exact solutions provided by DKM is then employed to construct an error model and correct the potential bias of the approximate model. Two error models are devised that both employ the difference between approximate and exact medoid solutions, but differ in the way medoid errors are interpolated to correct the whole set of realizations. The Local Error Model rests upon the clustering defined by DKM and can be seen as a natural way to account for intra-cluster variability; the Global Error Model employs a linear interpolation of all medoid errors regardless of the cluster to which the single realization belongs. These error models are evaluated for an idealized pollution problem in which the uncertainty of the breakthrough curve needs to be estimated. For this numerical test case, we demonstrate that the error models improve the uncertainty quantification provided by the DKM algorithm and are effective in correcting the bias of the estimate computed solely from the MsFV results. The framework presented here is not specific to the methods considered and can be applied to other combinations of approximate models and techniques to select a subset of realizations

SPATIAL UNCERTAINTY OF NUTRIENT LOSS BY EROSION IN SUGARCANE HARVESTING SCENARIOS

The assessment of spatial uncertainty in the prediction of nutrient losses by erosion associated with landscape models is an important tool for soil conservation planning. The purpose of this study was to evaluate the spatial and local uncertainty in predicting depletion rates of soil nutrients (P, K, Ca, and Mg) by soil erosion from green and burnt sugarcane harvesting scenarios, using sequential Gaussian simulation (SGS). A regular grid with equidistant intervals of 50 m (626 points) was established in the 200-ha study area, in Tabapuã, São Paulo, Brazil. The rate of soil depletion (SD) was calculated from the relation between the nutrient concentration in the sediments and the chemical properties in the original soil for all grid points. The data were subjected to descriptive statistical and geostatistical analysis. The mean SD rate for all nutrients was higher in the slash-and-burn than the green cane harvest scenario (Student’s t-test, p<0.05). In both scenarios, nutrient loss followed the order: Ca>Mg>K>P. The SD rate was highest in areas with greater slope. Lower uncertainties were associated to the areas with higher SD and steeper slopes. Spatial uncertainties were highest for areas of transition between concave and convex landforms.

Quantifying Uncertainty in Real Time Performance Measurement for Highway Winter Maintenance Operations – Phase 2, RB03-013, 2014

Winter weather in Iowa is often unpredictable and can have an adverse impact on traffic flow. The Iowa Department of Transportation (Iowa DOT) attempts to lessen the impact of winter weather events on traffic speeds with various proactive maintenance operations. In order to assess the performance of these maintenance operations, it would be beneficial to develop a model for expected speed reduction based on weather variables and normal maintenance schedules. Such a model would allow the Iowa DOT to identify situations in which speed reductions were much greater than or less than would be expected for a given set of storm conditions, and make modifications to improve efficiency and effectiveness. The objective of this work was to predict speed changes relative to baseline speed under normal conditions, based on nominal maintenance schedules and winter weather covariates (snow type, temperature, and wind speed), as measured by roadside weather stations. This allows for an assessment of the impact of winter weather covariates on traffic speed changes, and estimation of the effect of regular maintenance passes. The researchers chose events from Adair County, Iowa and fit a linear model incorporating the covariates mentioned previously. A Bayesian analysis was conducted to estimate the values of the parameters of this model. Specifically, the analysis produces a distribution for the parameter value that represents the impact of maintenance on traffic speeds. The effect of maintenance is not a constant, but rather a value that the researchers have some uncertainty about and this distribution represents what they know about the effects of maintenance. Similarly, examinations of the distributions for the effects of winter weather covariates are possible. Plots of observed and expected traffic speed changes allow a visual assessment of the model fit. Future work involves expanding this model to incorporate many events at multiple locations. This would allow for assessment of the impact of winter weather maintenance across various situations, and eventually identify locations and times in which maintenance could be improved.

Uncertainty, electoral incentives and political myopia

We study the determinants of political myopia in a rational model of electoral accountability where the key elements are informational frictions and uncertainty. We build aframework where political ability is ex-ante unknown and policy choices are not perfectlyobservable. On the one hand, elections improve accountability and allow to keep well-performing incumbents. On the other, politicians invest too little in costly policies withfuture returns in an attempt to signal high ability and increase their reelection probability.Contrary to the conventional wisdom, uncertainty reduces political myopia and may, undersome conditions, increase social welfare. We use the model to study how political rewardscan be set so as to maximise social welfare and the desirability of imposing a one-term limitto governments. The predictions of our theory are consistent with a number of stylised factsand with a new empirical observation documented in this paper: aggregate uncertainty, measured by economic volatility, is associated to better fiscal discipline in a panel of 20 OECDcountries.

Behavioural queueing : cellular automata and a laboratory experiment

Dans cette thèse, nous étudions les aspects comportementaux d'agents qui interagissent dans des systèmes de files d'attente à l'aide de modèles de simulation et de méthodologies expérimentales. Chaque période les clients doivent choisir un prestataire de servivce. L'objectif est d'analyser l'impact des décisions des clients et des prestataires sur la formation des files d'attente. Dans un premier cas nous considérons des clients ayant un certain degré d'aversion au risque. Sur la base de leur perception de l'attente moyenne et de la variabilité de cette attente, ils forment une estimation de la limite supérieure de l'attente chez chacun des prestataires. Chaque période, ils choisissent le prestataire pour lequel cette estimation est la plus basse. Nos résultats indiquent qu'il n'y a pas de relation monotone entre le degré d'aversion au risque et la performance globale. En effet, une population de clients ayant un degré d'aversion au risque intermédiaire encoure généralement une attente moyenne plus élevée qu'une population d'agents indifférents au risque ou très averses au risque. Ensuite, nous incorporons les décisions des prestataires en leur permettant d'ajuster leur capacité de service sur la base de leur perception de la fréquence moyenne d'arrivées. Les résultats montrent que le comportement des clients et les décisions des prestataires présentent une forte "dépendance au sentier". En outre, nous montrons que les décisions des prestataires font converger l'attente moyenne pondérée vers l'attente de référence du marché. Finalement, une expérience de laboratoire dans laquelle des sujets jouent le rôle de prestataire de service nous a permis de conclure que les délais d'installation et de démantèlement de capacité affectent de manière significative la performance et les décisions des sujets. En particulier, les décisions du prestataire, sont influencées par ses commandes en carnet, sa capacité de service actuellement disponible et les décisions d'ajustement de capacité qu'il a prises, mais pas encore implémentées. - Queuing is a fact of life that we witness daily. We all have had the experience of waiting in line for some reason and we also know that it is an annoying situation. As the adage says "time is money"; this is perhaps the best way of stating what queuing problems mean for customers. Human beings are not very tolerant, but they are even less so when having to wait in line for service. Banks, roads, post offices and restaurants are just some examples where people must wait for service. Studies of queuing phenomena have typically addressed the optimisation of performance measures (e.g. average waiting time, queue length and server utilisation rates) and the analysis of equilibrium solutions. The individual behaviour of the agents involved in queueing systems and their decision making process have received little attention. Although this work has been useful to improve the efficiency of many queueing systems, or to design new processes in social and physical systems, it has only provided us with a limited ability to explain the behaviour observed in many real queues. In this dissertation we differ from this traditional research by analysing how the agents involved in the system make decisions instead of focusing on optimising performance measures or analysing an equilibrium solution. This dissertation builds on and extends the framework proposed by van Ackere and Larsen (2004) and van Ackere et al. (2010). We focus on studying behavioural aspects in queueing systems and incorporate this still underdeveloped framework into the operations management field. In the first chapter of this thesis we provide a general introduction to the area, as well as an overview of the results. In Chapters 2 and 3, we use Cellular Automata (CA) to model service systems where captive interacting customers must decide each period which facility to join for service. They base this decision on their expectations of sojourn times. Each period, customers use new information (their most recent experience and that of their best performing neighbour) to form expectations of sojourn time at the different facilities. Customers update their expectations using an adaptive expectations process to combine their memory and their new information. We label "conservative" those customers who give more weight to their memory than to the xiv Summary new information. In contrast, when they give more weight to new information, we call them "reactive". In Chapter 2, we consider customers with different degree of risk-aversion who take into account uncertainty. They choose which facility to join based on an estimated upper-bound of the sojourn time which they compute using their perceptions of the average sojourn time and the level of uncertainty. We assume the same exogenous service capacity for all facilities, which remains constant throughout. We first analyse the collective behaviour generated by the customers' decisions. We show that the system achieves low weighted average sojourn times when the collective behaviour results in neighbourhoods of customers loyal to a facility and the customers are approximately equally split among all facilities. The lowest weighted average sojourn time is achieved when exactly the same number of customers patronises each facility, implying that they do not wish to switch facility. In this case, the system has achieved the Nash equilibrium. We show that there is a non-monotonic relationship between the degree of risk-aversion and system performance. Customers with an intermediate degree of riskaversion typically achieve higher sojourn times; in particular they rarely achieve the Nash equilibrium. Risk-neutral customers have the highest probability of achieving the Nash Equilibrium. Chapter 3 considers a service system similar to the previous one but with risk-neutral customers, and relaxes the assumption of exogenous service rates. In this sense, we model a queueing system with endogenous service rates by enabling managers to adjust the service capacity of the facilities. We assume that managers do so based on their perceptions of the arrival rates and use the same principle of adaptive expectations to model these perceptions. We consider service systems in which the managers' decisions take time to be implemented. Managers are characterised by a profile which is determined by the speed at which they update their perceptions, the speed at which they take decisions, and how coherent they are when accounting for their previous decisions still to be implemented when taking their next decision. We find that the managers' decisions exhibit a strong path-dependence: owing to the initial conditions of the model, the facilities of managers with identical profiles can evolve completely differently. In some cases the system becomes "locked-in" into a monopoly or duopoly situation. The competition between managers causes the weighted average sojourn time of the system to converge to the exogenous benchmark value which they use to estimate their desired capacity. Concerning the managers' profile, we found that the more conservative Summary xv a manager is regarding new information, the larger the market share his facility achieves. Additionally, the faster he takes decisions, the higher the probability that he achieves a monopoly position. In Chapter 4 we consider a one-server queueing system with non-captive customers. We carry out an experiment aimed at analysing the way human subjects, taking on the role of the manager, take decisions in a laboratory regarding the capacity of a service facility. We adapt the model proposed by van Ackere et al (2010). This model relaxes the assumption of a captive market and allows current customers to decide whether or not to use the facility. Additionally the facility also has potential customers who currently do not patronise it, but might consider doing so in the future. We identify three groups of subjects whose decisions cause similar behavioural patterns. These groups are labelled: gradual investors, lumpy investors, and random investor. Using an autocorrelation analysis of the subjects' decisions, we illustrate that these decisions are positively correlated to the decisions taken one period early. Subsequently we formulate a heuristic to model the decision rule considered by subjects in the laboratory. We found that this decision rule fits very well for those subjects who gradually adjust capacity, but it does not capture the behaviour of the subjects of the other two groups. In Chapter 5 we summarise the results and provide suggestions for further work. Our main contribution is the use of simulation and experimental methodologies to explain the collective behaviour generated by customers' and managers' decisions in queueing systems as well as the analysis of the individual behaviour of these agents. In this way, we differ from the typical literature related to queueing systems which focuses on optimising performance measures and the analysis of equilibrium solutions. Our work can be seen as a first step towards understanding the interaction between customer behaviour and the capacity adjustment process in queueing systems. This framework is still in its early stages and accordingly there is a large potential for further work that spans several research topics. Interesting extensions to this work include incorporating other characteristics of queueing systems which affect the customers' experience (e.g. balking, reneging and jockeying); providing customers and managers with additional information to take their decisions (e.g. service price, quality, customers' profile); analysing different decision rules and studying other characteristics which determine the profile of customers and managers.

Risk aversion and embedding bias

In Selten (1967) ?Strategy Method,? the second mover in the game submits a complete strategy. This basic idea has been exported to nonstrategic experiments, where a participant reports a complete list of contingent decisions, one for each situation or state in a given sequence, out of which one and only one state, randomly selected, will be implemented.In general, the method raises the following concern. If S0 and S1 are two differentsequences of states, and state s is in both S0 and S1, would the participant make the same decision in state s when confronted with S0 as when confronted with S1? If not, the experimental results are suspect of suffering from an ?embedding bias.?We check for embedding biases in elicitation methods of Charles Holt and Susan Laury(Laury and Holt, 2000, and Holt and Laury, 2002), and of the present authors (Bosch-Dom?nech and Silvestre, 1999, 2002, 2006a, b) by appropriately chosen replications of the original experiments. We find no evidence of embedding bias in our work. But in Holt and Laury?s method participants tend to switch earlier to the riskier option when later pairs of lotteries are eliminated from the sequence, suggesting the presence of some embedding bias.

When physician-expressed uncertainty leads to patient dissatisfaction: a gender study.

CONTEXT: Communication guidelines often advise physicians to disclose to their patients medical uncertainty regarding the diagnosis, origin of the problem, and treatment. However, the effect of the expression of such uncertainty on patient outcomes (e.g. satisfaction) has produced conflicting results in the literature that indicate either no effect or a negative effect. The differences in the results of past studies may be explained by the fact that potential gender effects on the link between physician-expressed uncertainty and patient outcomes have not been investigated systematically. OBJECTIVES: On the basis of previous research documenting indications that patients may judge female physicians by more severe criteria than they do male physicians, and that men are more prejudiced than women towards women, we predicted that physician-expressed uncertainty would have more of a negative impact on patient satisfaction when the physician in question was female rather than male, and especially when the patient was a man. METHODS: We conducted two studies with complementary designs. Study 1 was a randomised controlled trial conducted in a simulated setting (120 analogue patients Analogue patients are healthy participants asked to put themselves in the shoes of real medical patients by imagining being the patients of physicians shown on videos); Study 2 was a field study conducted in real medical interviews (36 physicians, 69 patients). In Study 1, participants were presented with vignettes that varied in terms of the physician's gender and physician-expressed uncertainty (high versus low). In Study 2, physicians were filmed during real medical consultations and the level of uncertainty they expressed was coded by an independent rater according to the videos. In both studies, patient satisfaction was assessed using a questionnaire. RESULTS: The results confirmed that expressed uncertainty was negatively related to patient satisfaction only when the physician was a woman (Studies 1 and 2) and when the patient was a man (Study 2). CONCLUSIONS: We believe that patients have the right to be fully informed of any medical uncertainties. If our results are confirmed in further research, the question of import will refer not to whether female physicians should communicate uncertainty, but to how they should communicate it. For instance, if it proves true that uncertainty negatively impacts on (male) patients' satisfaction, female physicians might want to counterbalance this impact by emphasizing other communication skills.

Functional error modeling for uncertainty quantification in hydrogeology

Approximate models (proxies) can be employed to reduce the computational costs of estimating uncertainty. The price to pay is that the approximations introduced by the proxy model can lead to a biased estimation. To avoid this problem and ensure a reliable uncertainty quantification, we propose to combine functional data analysis and machine learning to build error models that allow us to obtain an accurate prediction of the exact response without solving the exact model for all realizations. We build the relationship between proxy and exact model on a learning set of geostatistical realizations for which both exact and approximate solvers are run. Functional principal components analysis (FPCA) is used to investigate the variability in the two sets of curves and reduce the dimensionality of the problem while maximizing the retained information. Once obtained, the error model can be used to predict the exact response of any realization on the basis of the sole proxy response. This methodology is purpose-oriented as the error model is constructed directly for the quantity of interest, rather than for the state of the system. Also, the dimensionality reduction performed by FPCA allows a diagnostic of the quality of the error model to assess the informativeness of the learning set and the fidelity of the proxy to the exact model. The possibility of obtaining a prediction of the exact response for any newly generated realization suggests that the methodology can be effectively used beyond the context of uncertainty quantification, in particular for Bayesian inference and optimization.

Political market and regulatory uncertainty: Insights and implications for integrated strategy

Managers can craft effective integrated strategy by properly assessing regulatory uncertainty. Leveraging the existing political markets literature, we predict regulatory uncertainty from the novel interaction of demand and supply side rivalries across a range of political markets. We argue for two primary drivers of regulatory uncertainty: ideology-motivated interests opposed to the firm and a lack of competition for power among political actors supplying public policy. We align three, previously disparate dimensions of nonmarket strategy - profile level, coalition breadth, and pivotal target - to levels of regulatory uncertainty. Through this framework, we demonstrate how and when firms employ different nonmarket strategies. To illustrate variation in nonmarket strategy across levels of regulatory uncertainty, we analyze several market entry decisions of foreign firms operating in the global telecommunications sector.

CITRICULTURE ECONOMIC AND FINANCIAL EVALUATION UNDER CONDITIONS OF UNCERTAINTY

ABSTRACT The citriculture consists in several environmental risks, as weather changes and pests, and also consists in considerable financial risk, mainly due to the period ofreturn on the initial investment. This study was motivated by the need to assess the risks of a business activity such as citriculture. Our objective was to build a stochastic simulation model to achieve the economic and financial analysis of an orange producer in the Midwest region of the state of Sao Paulo, under conditions of uncertainty. The parameters used were the Net Present Value (NPV), the Modified Internal Rate of Return(MIRR), and the Discounted Payback. To evaluate the risk conditions we built a probabilistic model of pseudorandom numbers generated with Monte Carlo method. The results showed that the activity analyzed provides a risk of 42.8% to reach a NPV negative; however, the yield assessed by MIRR was 7.7%, higher than the yield from the reapplication of the positive cash flows. The financial investment pays itself after the fourteenth year of activity.

Uncertainty associated with Monte Carlo radiation transport in radionuclide metrology

In radionuclide metrology, Monte Carlo (MC) simulation is widely used to compute parameters associated with primary measurements or calibration factors. Although MC methods are used to estimate uncertainties, the uncertainty associated with radiation transport in MC calculations is usually difficult to estimate. Counting statistics is the most obvious component of MC uncertainty and has to be checked carefully, particularly when variance reduction is used. However, in most cases fluctuations associated with counting statistics can be reduced using sufficient computing power. Cross-section data have intrinsic uncertainties that induce correlations when apparently independent codes are compared. Their effect on the uncertainty of the estimated parameter is difficult to determine and varies widely from case to case. Finally, the most significant uncertainty component for radionuclide applications is usually that associated with the detector geometry. Recent 2D and 3D x-ray imaging tools may be utilized, but comparison with experimental data as well as adjustments of parameters are usually inevitable.