Extra Uncertainty Research Articles

Bayesian Precalibration of a Large Stochastic Microsimulation Model

Calibration of stochastic traffic microsimulation models is a challenging task. This paper proposes a fast iterative probabilistic precalibration framework and demonstrates how it can be successfully applied to a real-world traffic simulation model of a section of the M40 motorway and its surrounding area in the U.K. The efficiency of the method stems from the use of emulators of the stochastic microsimulator, which provides fast surrogates of the traffic model. The use of emulators minimizes the number of microsimulator runs required, and the emulators' probabilistic construction allows for the consideration of the extra uncertainty introduced by the approximation. It is shown that automatic precalibration of this real-world microsimulator, using turn-count observational data, is possible, considering all parameters at once, and that this precalibrated microsimulator improves on the fit to observations compared with the traditional expertly tuned microsimulation.

Amplify-and-Forward Compressed Sensing as a Physical-Layer Secrecy Solution in Wireless Sensor Networks

In this paper, we assess the physical-layer secrecy performance of the amplify-and-forward compressed sensing (AF-CS) framework when malicious eavesdropping nodes are listening. In particular, we investigate the robustness of the AF-CS scheme in the presence of a group of coordinated eavesdropping nodes under the assumption that they have corrupted channel state information. In order to fulfil this assumption, we propose a channel estimation technique based on pseudorandom pilots. This technique introduces extra uncertainty only in the channel estimation of the eavesdroppers. Our simulation results evaluate the physical-layer protection as a function of the total number of coordinated eavesdroppers and the level of channel estimation distortion of the eavesdroppers. We demonstrate that a small number of eavesdroppers (small being defined later on) has a zero probability of recovering the intended signal. We also show that a very large number of eavesdropping nodes are required to perfectly recover the signal in comparison with other distributed compressed sensing schemes in the literature.

MODELING OF GREEN'S FUNCTION WITH BOTTOM REFLECTIVE PARAMETERS (P, Q) INSTEAD OF GA PARAMETERS

In shallow-water acoustic waveguide, the bottom of the sea (as the boundary condition that determines the Green's function of the sound propagation) plays an extremely important role in the sound field in water medium, especially at low frequency. Commonly the bottom is characterized by geoacoustic (GA) parameters and nearly all the existing numerical codes for sound field prediction use the GA parameters as the input of the bottom. However, the GA parameters are model based (needs a specified layered bottom model to mount the parameters in) which in practical applications may cause a series of problems such as model mismatching, extra uncertainty for field prediction and time consuming in MFP inverting. When the two bottom reflective parameters (P, Q) are used instead of GA parameters, which are model-free and directly determine the effect of the bottom on the sound field respectively in phase and strength, those problems will be solved naturally. In this paper, for range-independent waveguide using (P, Q) directly as input to construct the Green's function in terms of normal mode field is fully developed. For range-dependent waveguide, we propose an effective-equivalence based mapping between the bottom reflective parameters (P, Q) and the effective half-space (EHS) GA parameters to make (P, Q) as input parameters indirectly. Then all the existed numerical codes can still be used for the calculation of sound field without any modification except using P and Q as the input parameters of the bottom. The accuracy of this mapping is verified for both range-independent and range-dependent waveguide. At last the uncertainty analysis in GA space as well as in PQ space is briefly discussed to reveal the "extra uncertainty" due to the inter-coupling among the GA parameters.

High-Precision Bayesian Modeling of Samples Susceptible to Inbuilt Age

Radiocarbon dates on samples susceptible to inbuilt age are common in the chronological record of many archaeological and environmental sites. Indeed, fragments of charcoal and wood are sometimes the only materials sufficiently well preserved for dating. However, where high-precision estimates arc required the extra uncertainty associated with such measurements often renders them unusable. This article tests three Bayesian modeling approaches that are designed to tackle this problem. The findings of our study suggest that successful corrections can be made for the inherent age offsets. The most effective and versatile approach was based on a version of outlier analysis. It is hoped that this method will become more widely employed and enable samples susceptible to inbuilt age to be included in high-precision chronologies.

Assessing motivations for carbon offsetting by environmentally certified tourism enterprises

This paper presents survey results on tourism operator preferences and motivations for carbon offset options by environmentally certified tourism enterprises in Queensland, Australia. It found that less than a third are involved in carbon offset programmes, whereas just over a third plan to implement offsetting in the near future. Preferred offset projects are regional tree planting or renewable energy. Motivations for offsetting are related to environmental concern, commercial benefits of climate-friendly tourism, and financially supporting offset projects. This study found motivations for offsetting by larger tourism enterprises aligning with the more general business motivations and drivers for adopting corporate social and environmental responsibility practices. However, the extra cost and uncertainty about carbon issues limited the uptake of offsetting by smaller tourism operators.

A simplified model of soakaway infiltration interaction with a shallow groundwater table

This paper presents a new and simplified modeling concept for soakaway infiltration in the presence of a shallow groundwater table, including representation of the local groundwater mound and its effects on the infiltration rate. The soil moisture retention curve is used to represent the influence of the mound on infiltration rates. The model is intended to be used in situations when distributed urban drainage models with soakaways or similar infiltration devices are coupled to distributed groundwater flow models. With this new modeling concept, the local mounding from small-scale infiltration systems, and its effects on the infiltration rate, can be represented even if the spatial resolution of the groundwater flow model is coarser than the extent of the mound. The new model has been run for a number of scenarios and soil parameters, and the results compared to the output from a two-dimensional unsaturated/saturated flow model based on Richard’s equation. The comparison shows that soakaway emptying times calculated by the new model are on average 13% higher than the emptying times of the two-dimensional model. The deviation is smaller for scenarios including a shallow groundwater table, only around 5% on average. Groundwater mounding depths are underestimated close to the soakaway and overestimated far from the soakaway. At 5 m distance from the soakaway center, the average deviation is 18% for the shallow groundwater scenarios. Mass balance errors were checked and found to be below 1% for all scenarios at all times during the simulation period. The extra uncertainty introduced by this new model is compensated for by the reduction in runtime; it is on average 600 times faster than the two-dimensional model. Furthermore, the new model is based on the same input parameters as the two-dimensional model and thus requires no extra calibration. The new modeling concept is therefore a useful tool for simulating small-scale stormwater infiltration in the presence of a shallow groundwater table with distributed models on larger scales.

Prediction of flow resistance in a compound open channel

Flooding in a river is a complex phenomenon which affects the livelihood and economic condition of the region. During flooding flow overtops the river course and spreads around the flood plain resulting in a two-course compound channel. It has been observed that the flow velocity in the flood plain is slower than that in the actual river course. This can produce a large shear layer between sections of the flow and produces turbulent structures which generate extra resistance and uncertainty in flow prediction. Researchers have adopted various numerical, analytical, and empirical models to analyze this situation. Generally, a one-dimensional empirical model is used for flow prediction assuming that the flow in the compound open channel is uniform. However, flow in a compound channel is quasi-uniform due to the transfer of momentum in sub-sections and sudden change of depths laterally. Hence, it is essential to analyze the turbulent structures prevalent in the situation. Therefore, in this study, an effort has been made to analyze the turbulent structure involved in flooding using large eddy simulation (LES) method to estimate the resistance. Further, a combination of an artificial neural network (ANN) and a fuzzy logic (FL) is considered to predict flow resistance in a compound open channel.

Effects of dating errors on nonparametric trend analyses of speleothem time series

Abstract. A fundamental problem in paleoclimatology is to take fully into account the various error sources when examining proxy records with quantitative methods of statistical time series analysis. Records from dated climate archives such as speleothems add extra uncertainty from the age determination to the other sources that consist in measurement and proxy errors. This paper examines three stalagmite time series of oxygen isotopic composition (δ18O) from two caves in western Germany, the series AH-1 from the Atta Cave and the series Bu1 and Bu4 from the Bunker Cave. These records carry regional information about past changes in winter precipitation and temperature. U/Th and radiocarbon dating reveals that they cover the later part of the Holocene, the past 8.6 thousand years (ka). We analyse centennial- to millennial-scale climate trends by means of nonparametric Gasser–Müller kernel regression. Error bands around fitted trend curves are determined by combining (1) block bootstrap resampling to preserve noise properties (shape, autocorrelation) of the δ18O residuals and (2) timescale simulations (models StalAge and iscam). The timescale error influences on centennial- to millennial-scale trend estimation are not excessively large. We find a "mid-Holocene climate double-swing", from warm to cold to warm winter conditions (6.5 ka to 6.0 ka to 5.1 ka), with warm–cold amplitudes of around 0.5‰ δ18O; this finding is documented by all three records with high confidence. We also quantify the Medieval Warm Period (MWP), the Little Ice Age (LIA) and the current warmth. Our analyses cannot unequivocally support the conclusion that current regional winter climate is warmer than that during the MWP.

Secure FSM-based arithmetic codes

Recently, arithmetic coding has attracted the attention of many scholars because of its high compression capability. Accordingly, in this paper, a method that adds secrecy to this well-known source code is proposed. Finite state arithmetic code is used as source code to add security. Its finite state machine characteristic is exploited to insert some random jumps during source coding process. In addition, a Huffman code is designed for each state to make decoding possible even in jumps. Being prefix-free, Huffman codes are useful in tracking correct states for an authorized user when he/she decodes with correct symmetric pseudo-random key. The robustness of our proposed scheme is further reinforced by adding another extra uncertainty by swapping outputs of Huffman codes in each state. Several test images are used for inspecting the validity of the proposed Huffman finite state arithmetic coding (HFSAC). The results of several experimental key space analyses, statistical analyses, key and plaintext sensitivity tests show that HFSAC with a little effect on compression efficiency provides an efficient and secure method for real-time image encryption and transmission.

Including all individuals is not enough: lessons for intention-to-treat analysis.

Intention-to-treat (ITT) analysis requires all randomised individuals to be included in the analysis in the groups to which they were randomised. However, there is confusion about how ITT analysis should be performed in the presence of missing outcome data. To explain, justify, and illustrate an ITT analysis strategy for randomised trials with incomplete outcome data. We consider several methods of analysis and compare their underlying assumptions, plausibility, and numbers of individuals included. We illustrate the ITT analysis strategy using data from the UK700 trial in the management of severe mental illness. Depending on the assumptions made about the missing data, some methods of analysis that include all randomised individuals may be less valid than methods that do not include all randomised individuals. Furthermore, some methods of analysis that include all randomised individuals are essentially equivalent to methods that do not include all randomised individuals. This work assumes that the aim of analysis is to obtain an accurate estimate of the difference in outcome between randomised groups and not to obtain a conservative estimate with bias against the experimental intervention. Clinical trials should employ an ITT analysis strategy, comprising a design that attempts to follow up all randomised individuals, a main analysis that is valid under a stated plausible assumption about the missing data, and sensitivity analyses that include all randomised individuals in order to explore the impact of departures from the assumption underlying the main analysis. Following this strategy recognises the extra uncertainty arising from missing outcomes and increases the incentive for researchers to minimise the extent of missing data.

A Bayesian Log-Normal Model for Multivariate Loss Reserving

The correlation among multiple lines of business plays an important role in quantifying the uncertainty of loss reserves for insurance portfolios. To accommodate correlation, most multivariate loss-reserving methods focus on the pairwise association between corresponding cells in multiple run-off triangles. However, such practice usually relies on the independence assumption across accident years and ignores the calendar year effects that could affect all open claims simultaneously and induce dependencies among loss triangles. To address this issue, we study a Bayesian log-normal model in the prediction of outstanding claims for dependent lines of business. In addition to the pairwise correlation, our method allows for an explicit examination of the correlation due to common calendar year effects. Further, different specifications of the calendar year trend are considered to reflect valuation actuaries’ prior knowledge of claim development. In a case study, we analyze an insurance portfolio of personal and commercial auto lines from a major U.S. property-casualty insurer. It is shown that the incorporation of calendar year effects improves model fit significantly, though it contributes substantively to the predictive variability. The availability of the realizations of predicted claims permits us to perform a retrospective test, which suggests that extra prediction uncertainty is indispensable in modern risk management practices.

Bayesian sensitivity models for missing covariates in the analysis of survival data

This paper presents a Bayesian approach using WinBUGS for analysing survival data in which observations have missing information on some covariates. Modelling the joint density of the survival time and the covariates allows for the missing covariate data to be missing at random (MAR), as opposed to the more restrictive assumptions imposed by a complete case analysis. Here, the survival times are modelled by the accelerated failure time model and the joint covariate density is factorized as a series of conditional densities, each modelled by logistic regression. We propose a class of models to examine MAR assumption by using Bayesian informative priors or auxiliary data. In the example considered, the complete case analysis underestimates the proportion of severely impaired cases. Furthermore, models evaluating sensitivity to the MAR assumption suggest that median life expectancies could be increased. Gains in precision are small in the application considered, possibly a reflection of extra uncertainty because of the inclusion of all cases, including those of unknown severity. Through simple Bayesian models, more realistic assumptions concerning the nature of the missing data can be made. Implementation in WinBUGS means that this model is accessible to practicing statisticians.

Confidence intervals for random effects meta-analysis and robustness to publication bias

The DerSimonian-Laird confidence interval for the average treatment effect in meta-analysis is widely used in practice when there is heterogeneity between studies. However, it is well known that its coverage probability (the probability that the interval actually includes the true value) can be substantially below the target level of 95 per cent. It can also be very sensitive to publication bias. In this paper, we propose a new confidence interval that has better coverage than the DerSimonian-Laird method, and that is less sensitive to publication bias. The key idea is to note that fixed effects estimates are less sensitive to such biases than random effects estimates, since they put relatively more weight on the larger studies and relatively less weight on the smaller studies. Whereas the DerSimonian-Laird interval is centred on a random effects estimate, we centre our confidence interval on a fixed effects estimate, but allow for heterogeneity by including an assessment of the extra uncertainty induced by the random effects setting. Properties of the resulting confidence interval are studied by simulation and compared with other random effects confidence intervals that have been proposed in the literature. An example is briefly discussed.

Bayesian Method for Improving Logistic Regression Estimates under Group-Based Exposure Assessment with Additive Measurement Errors

ABSTRACT The group-based exposure assessment has been widely used in occupational epidemiology. When the sample size used to estimate group means is “large”, this leads to negligible attenuation in the estimation of odds ratio. However, the bias is proportional to the between-subject variability and is affected by the difference in true group means. We explore a Bayesian method, which adjusts in a natural way for the extra uncertainty in the outcome model associated with using the predicted values as exposures. We aim to improve the estimate obtained in naïve analysis by exploiting the properties of Berkson type error structure. We consider cases where differences in the proximity of group means and the between-subject variance are both large. The results of the simulations show that our Bayesian measurement error adjustment method that follows group-based exposure assessment improves estimates of odds ratios when the between-subject variance is large and group means are far apart.

A Few More Useful 8-valued Logics for Reasoning with Tetralattice EIGHT 4

In their useful logic for a computer network Shramko and Wansing generalize initial values of Belnap’s 4-valued logic to the set 16 to be the power-set of Belnap’s 4. This generalization results in a very specific algebraic structure — the trilattice SIXTEEN3 with three orderings: information, truth and falsity. In this paper, a slightly different way of generalization is presented. As a base for further generalization a set 3 is chosen, where initial values are a — incoming data is asserted, d — incoming data is denied, and u — incoming data is neither asserted nor denied, that corresponds to the answer “don’t know”. In so doing, the power-set of 3, that is the set 8 is considered. It turns out that there are not three but four orderings naturally defined on the set 8 that form the tetralattice EIGHT4. Besides three ordering relations mentioned above it is an extra uncertainty ordering. Quite predictably, the logics generated by a–order (truth order) and d–order (falsity order) coincide with first-degree entailment. Finally logic with two kinds of operations (a–connectives and d–connectives) and consequence relation defined via a–ordering is considered. An adequate axiomatization for this logic is proposed.

Uncertainty and validation of health economic decision models

Health economic decision models are based on specific assumptions relating to model structure and parameter estimation. Validation of these models is recommended as an indicator of reliability, but is not commonly reported. Furthermore, models derived from different data and employing different assumptions may produce a variety of results.A Markov model for evaluating the long-term cost-effectiveness of screening for abdominal aortic aneurysm is described. Internal, prospective and external validations are carried out using individual participant data from two randomised trials. Validation is assessed in terms of total numbers and timings of key events, and total costs and life-years. Since the initial model validates well only internally, two further models are developed that better fit the prospective and external validation data. All three models are then extrapolated to a life-time horizon, producing cost-effectiveness estimates ranging from pound1600 to pound4200 per life-year gained.Parameter uncertainty is now commonly addressed in health economic decision modelling. However, the derivation of models from different data sources adds another level of uncertainty. This extra uncertainty should be recognised in practical decision-making and, where possible, specifically investigated through independent model validation.

A Fast Three-Dimensional Approximation for the Calculation of Surface Irradiance in Large-Eddy Simulation Models

Abstract Cloud-resolving models—in particular, large-eddy simulation (LES) models—are important tools to improve the understanding of cloud–radiation interactions. A method is presented for accurate, yet fast, three-dimensional calculation of surface shortwave irradiance within an LES model using the tilted independent column approximation with smoothing of the diffuse irradiance. The algorithm calculates a tilted optical thickness for each surface pixel that is then used as input to a one-dimensional radiative transfer code. In a sensitivity analysis, it is shown that this calculation can even be replaced by a simple precalculated lookup table that tabulates surface irradiance as a function of only solar zenith angle and cloud optical thickness. Because the vertical variability of the cloud is of little relevance for the surface irradiance, this approximation introduces little extra uncertainty. In a final step, surface irradiance is smoothed to account for horizontal photon transport between individual columns. The algorithm has been optimized for parallelization, which enhances its applicability in LES models. In this implementation, the total computational time of the LES model increased by only 3% relative to the reference run without radiation. Comparisons between the fast approximation and detailed three-dimensional radiative transfer calculations showed very good agreement for different cloud conditions and several solar zenith and azimuth angles, with a root-mean-square difference of 6%.

Performance analysis of a folding flow micromixer

The performance of a folding flow micromixer in the Stokes flow regime is investigated computationally and experimentally. Consistency with a previously derived general scaling relation is demonstrated and the geometric parameters in the scaling relation are determined for this mixer. Measured data from a second similar mixer are correctly predicted using the scaling relation, thus showing that the approach allows quantitative prediction of mixing. This paper focuses on the errors associated with such predictions. Basic errors, expressed as variations in the standard deviation of the concentration profile, were estimated to be −10% for the computation and −30% for the experiment at the highest values of Peclet number considered. It is shown that this experimental error was mostly due to depth averaging of the spectroscopic technique used for concentration measurement at the high Peclet numbers. However, extra uncertainty is associated with chip fabrication tolerances and this was investigated further. Measurements at the outlet of nine different mixer chips of notionally identical design revealed variations in mixing of ±26%. This variation was attributed to misalignment of the glass layers determining the geometry of the mixer in the chip. Thus, the combination of measurement error and misalignment means predictions of the concentration standard deviation for the mixer may get non-uniformity wrong by up to 50%. Ensuring a required uniformity, however, simply requires adding a few further elements to the mixer to allow for this uncertainty. Application of the scaling relation to mixer design is highlighted by a discussion of the options available for improving the performance of the experimental mixer.

Evaluation of margining algorithms in commercial treatment planning systems

Introduction During commissioning of the Pinnacle (Philips) treatment planning system (TPS) the margining algorithm was investigated and was found to produce larger PTVs than Plato (Nucletron) for identical GTVs. Subsequent comparison of PTV volumes resulting from the QA outlining exercise for the CHHIP (Conventional or Hypofractionated High Dose IMRT for Prostate Ca.) trial confirmed that there were differences in TPS’s margining algorithms. Margining and the clinical impact of the different PTVs in seven different planning and virtual simulation systems (Pinnacle, Plato, Prosoma (MedCom), Eclipse (7.3 and 7.5) (Varian), MasterPlan (Nucletron), Xio (CMS) and Advantage Windows (AW) (GE)) is investigated, and a simple test for 3D margining consistency is proposed. Methods Using each TPS, two different sets of prostate GTVs on 2.5 mm and 5 mm slices were margined according to the CHHIP protocol to produce PTV3 (prostate + 5 mm/0 mm post), PTV2 (PTV3 + 5 mm) and PTV1 (prostate and seminal vesicles + 10 mm). GTVs and PTVs were imported into Pinnacle for volume calculation. DVHs for 5 mm slice plans, created using the smallest PTVs, were recalculated on the largest PTV dataset and vice versa. Since adding a margin of 50 mm to a structure should give the same result as adding five margins of 10 mm, this was tested for each TPS (consistency test) using an octahedron as the GTV and CT datasets with 2.5 mm and 5 mm slices. Results The CHHIP PTV3 and PTV1 volumes had a standard deviation, across the seven systems, of 5% and PTV2 (margined twice) 9%, on the 5 mm slices. For 2.5 mm slices the standard deviations were 4% and 6%. The ratio of the Pinnacle and the Eclipse 7.3 PTV2 volumes was 1.25. Rectal doses were significantly increased when encompassing Pinnacle PTVs ( V 50 = 42.8%), compared to Eclipse 7.3 PTVs ( V 50 = 36.4%). Conversely, fields that adequately treated an Eclipse 7.3 PTV2 were inadequate for a Pinnacle PTV2. AW and Plato PTV volumes were the most consistent (0.3%) and (−0.4%). However, the 1 × 50 mm margin in Pinnacle produced a 15.9% larger volume than 5 × 10 mm margins, while for Eclipse 7.3 the single margined volume was 14.3% smaller. These inconsistencies were reduced to ∼5% by adjusting the superior/inferior margins. Conclusions Accurate margin algorithms are necessary to ensure that volume expansion does not add extra uncertainty to the radiotherapy planning process. We have found significant differences in the 3D margining algorithms of TPSs, devised a simple test to predict inconsistency and suggested corrective action to minimise the variation.

Multiple imputation for national public‐use datasets and its possible application for gestational age in United States Natality files

Multiple imputation (MI) is a technique that can be used for handling missing data in a public-use dataset. With MI, two or more completed versions of the dataset are created, containing possibly different but reasonable replacements for the missing data. Users analyse the completed datasets separately with standard techniques and then combine the results using simple formulae in a way that allows the extra uncertainty due to missing data to be assessed. An advantage of this approach is that the resulting public-use data can be analysed by a variety of users for a variety of purposes, without each user needing to devise a method to deal with the missing data. A recent example for a large public-use dataset is the MI of the family income and personal earnings variables in the National Health Interview Survey. We propose an approach to utilise MI to handle the problems of missing gestational ages and implausible birthweight-gestational age combinations in national vital statistics datasets. This paper describes MI and gives examples of MI for public-use datasets, summarises methods that have been used for identifying implausible gestational age values on birth records, and combines these ideas by setting forth scenarios for identifying and then imputing missing and implausible gestational age values multiple times. Because missing and implausible gestational age values are not missing completely at random, using multiple imputations and, thus, incorporating both the existing relationships among the variables and the uncertainty added from the imputation, may lead to more valid inferences in some analytical studies than simply excluding birth records with inadequate data.