Low Uncertainty Research Articles

Advancements in solar spectral irradiance measurements by the TSIS-1 spectral irradiance monitor and its role for long-term data continuity

The first implementation of NASA’s Total and Spectral Solar Irradiance Sensor (TSIS-1) launched on December 15th, 2017, and was integrated into the International Space Station (ISS) to measure both the total solar irradiance (TSI) and the solar spectral irradiance (SSI). The direct measurement of the SSI is made by the LASP Spectral Irradiance Monitor (SIM) and provides data essential to interpreting how the Earth system responds to solar spectral variability. Extensive advances in TSIS-1 SIM instrument design and new SI-traceable spectral irradiance calibration techniques have resulted in improved absolute accuracy with uncertainties of less than 0.5% over the continuous 200–2400 nm spectral range. Furthermore, improvements in the long-term spectral stability corrections provide lower trend uncertainties in SSI variability measurements. Here we present the early results of the TSIS-1 SIM measurements covering the first 5 years of operations. This time period includes the descending phase of solar cycle 24, the last solar minimum, and the ascending phase of solar cycle 25. The TSIS-1 SIM SSI results are compared to previous measurements both in the absolute scale of the solar spectrum and the time dependence of the SSI variability. The TSIS-1 SIM SSI spectrum shows lower IR irradiance (up to 6% at 2400 nm) and small visible increases (~0.5%) from some previous reference solar spectra. Finally, initial comparisons are made to current NRLSSI2 and SATIRE-S SSI model results and offer opportunities to validate model details both for short-term (solar rotation) spectral variability and, for the first time, the longer-term (near half solar cycle) spectral variability across the solar spectrum from the UV to the IR.

Regression-Based Hyperparameter Learning for Support Vector Machines.

Unification of classification and regression is a major challenge in machine learning and has attracted increasing attentions from researchers. In this article, we present a new idea for this challenge, where we convert the classification problem into a regression problem, and then use the methods in regression to solve the problem in classification. To this end, we leverage the widely used maximum margin classification algorithm and its typical representative, support vector machine (SVM). More specifically, we convert SVM into a piecewise linear regression task and propose a regression-based SVM (RBSVM) hyperparameter learning algorithm, where regression methods are used to solve several key problems in classification, such as learning of hyperparameters, calculation of prediction probabilities, and measurement of model uncertainty. To analyze the uncertainty of the model, we propose a new concept of model entropy, where the leave-one-out prediction probability of each sample is converted into entropy, and then used to quantify the uncertainty of the model. The model entropy is different from the classification margin, in the sense that it considers the distribution of all samples, not just the support vectors. Therefore, it can assess the uncertainty of the model more accurately than the classification margin. In the case of the same classification margin, the farther the sample distribution is from the classification hyperplane, the lower the model entropy. Experiments show that our algorithm (RBSVM) provides higher prediction accuracy and lower model uncertainty, when compared with state-of-the-art algorithms, such as Bayesian hyperparameter search and gradient-based hyperparameter learning algorithms.

Multistatic radar distribution geometry effects on parameter estimation accuracy

AbstractAn analysis of the parameter estimation uncertainty for the target location and velocity achievable using a single‐transmitter‐multiple‐receiver multistatic radar system is presented. A framework for establishing measures of multistatic radar parameter uncertainties by expansion of the bistatic radar parameter uncertainty measures is presented for systems containing omnidirectionally radiating nodes. The methodology uses analytical methods based on the Cramér–Rao Lower Bounds applied to scenarios in a two‐dimensional physical space with a single target exhibiting Doppler characteristics and a bistatic angle dependent radar cross‐section. A set of geometric descriptors is proposed to characterise the system, and parameter uncertainty results are reported as a function of these descriptors. The results indicate that angular separation between the transmitter and the centre of the receiver distribution is of greater importance than the quantity of receivers within the system when low uncertainty estimation capabilities are desired, though a minimum of two receivers must be available. The proportion of receivers within the system which contributed information crucial to obtaining the minimum estimation uncertainty is reported for systems containing different quantities of receivers. It was observed that, as the total number of receivers available increased, the proportion of receivers required to achieve the minimal uncertainty level reduces significantly.

Computational Fluid Dynamic Analysis of Water Flow Through Nozzle of a Gravimetric Measuring Method System

The gravimetric measuring method incurs errors and uncertainties in calibration, originating from various sources, with the diverter valve being one of the most significant. For optimal operation, the output flow from the diverter valve should form a jet in a thin, rectangular sheet form to ensure a low uncertainty value. The current work explores different scenarios in the configuration of an upstream diverter valve installation to determine its effect on velocity profile and flow path line at the nozzle outlet. The analysis is conducted using CFD Fluent edition 2023, varying operational conditions and nozzle geometry. In the results section, a pressure drop along the nozzle at different velocities as well as uniformity in velocities vectors and pressure magnitude at outlet nozzle, are presented.

Need for precise nuclear structure data for reactor studies

This paper highlights the strong need for precise nuclear structure and decay data measurements in order to perform high-quality modelling on nuclear reactors and other applications. The context of nuclear data evaluation, as well as the importance of low uncertainty evaluations, will be first presented. The importance of such data for interpreting nuclear data experimental measurements is stressed throughout. To demonstrate this, we will explain how mass and charge-dependent fission yields, decay data (in particular for the purpose of residual heat calculations), and inelastic neutrons scattering cross section rely on nuclear structure and decay information and how new and higher quality in such data can lead to improved accuracy in the precision of evaluated nuclear data.

When commitment isn’t enough: The cross-cultural interactive effects of commitment-inducement and compliance-enforcement on performance

The current study contributes to the ongoing discourse in the extant literature concerning the performance effects of the commitment-inducement and the compliance-enforcement approaches to the management of people and work. We expand on two research studies conducted in China to assess if the finding that commitment-inducement and compliance-enforcement result in higher organization financial and operational performance generalizes to corporate social responsibility performance and to countries and cultures across the globe. Using the current study’s large global multi-source sample, our findings illuminate that compliance-enforcement explained significant incremental variance in both organization financial and operational performance and organization corporate social responsibility performance beyond that of the commitment-inducement approach alone. Moreover, the highest levels of both performance outcomes were obtained by organizations that simultaneously used both commitment-inducement and compliance-enforcement; that is, hybrid governance. Compliance-enforcement was also found to have a more substantive relative effect on organization financial and operational performance while commitment-inducement was found to have a more substantive relative effect on organization corporate social responsibility performance. Furthermore, as hypothesized, at the between country-level, the relationship between the commitment-inducement approach of managing people and work and corporate social responsibility performance was found to be more negative both for a high individualism than a low individualism culture and for a high uncertainty avoidance than a low uncertainty avoidance culture, respectively. Whereas, the relationship between the compliance-enforcement approach and corporate social responsibility performance was found to be more positive for a high uncertainty avoidance than a low uncertainty avoidance culture. Finally, as hypothesized, at the between country-level, commitment-inducement and compliance-enforcement were found to be substitutes and have a negative synergistic effect on corporate social responsibility performance. Implications, limitations, and avenues for future research are discussed.

Analyst herding – whether, why, and when? Two new tests for herding detection in target forecast prices

This study proposes two novel tests for security analyst herding based on binomial correlation and forecast error volatility scaling and applies it to investigate herding patterns in analyst target prices in 2008-2020 in the UK. Analysts robustly herd in their valuations, with results consistent across years, sectors, in panel fixed effect, quantile, instrumental variable regressions, and when controlled for optimism and conservatism. Herding becomes prominent for stocks followed by at least five analysts and towards the long sides of Fama-French sorts, reinforcing its non-spurious and behavioral nature. Analyst herd more strongly subject to low volatility and uncertainty.

Quantile connectedness between the climate policy and economic uncertainty: Evidence from the G7 countries

In this study, we investigate the transmission mechanism between climate policy uncertainty (CPU) and economic policy uncertainty (EPU) in the G7 countries. To account for different conditions, we use a quantile-based VAR (Q-VAR) model over the period between 2000 and 2021. Our results show high connectedness between the CPU and the EPU of G7 countries, particularly at extreme quantile orders. On the other hand, the spillover effects between climate and economic policy uncertainty differ depending on the distributional levels of the uncertainty indices. The CPU is a net receiver of uncertainty shocks, while for almost all countries, the EPU acts as a net receiver or emitter, depending on the economic situation. During times of high or low economic uncertainty, the EPU of all G7 countries is strongly affected by shocks originating from the CPU. Moreover, the results indicate that the dynamic spillover patterns between EPU and CPU vary over time, responding to different economic events and financial crises. These results call for policymakers and governments to urgently integrate climate considerations into economic planning, fiscal policies, and regulatory frameworks to promote sustainable economic growth and mitigate the impacts of climate change.

Revealing the mobile sensing powers of semi‐random and deterministic “drive‐by” vehicle fleets

AbstractThe utilization of mobile sensing through the deployment of sensors on third‐party vehicles that pass by an area offers notable benefits in terms of spatiotemporal coverage, precision, timeliness, and cost‐effectiveness for monitoring urban environments. However, the diverse travel behaviors exhibited by different types of vehicle fleets result in varying levels of sensing powers. Drawing inspiration from these phenomena, this study quantifies and compares the travel patterns and sensing powers of bus and taxi fleets. The experimental findings unveiled several noteworthy laws, such as a diminishing rate of increase in sensing power with the stable increasing vehicle number, the high sensing power exhibited by taxis, the comparable spatial coverage between buses, and the relatively low uncertainty associated with buses' sensing power. Furthermore, the impact of travel patterns (i.e., semi‐random behavior of taxis and deterministic behavior of buses) on the powers of mobile sensing was revealed. The aforementioned findings provide valuable insights for the development of efficient mobile sensing schemes and hold significant relevance for the implementation of smart city infrastructure.

Uncertainty Analysis and Data Fusion of Multi-Source Land Evapotranspiration Products Based on the TCH Method

Evapotranspiration (ET) is a very important variable in the global water cycle, carbon cycle, and energy cycle. However, there are still some uncertainties in existing ET products. Therefore, this paper evaluates the uncertainty of three widely used global ET products (ERA5-Land, GLDAS-Noah, and MERRA-2) based on the three-cornered hat (TCH) method, and generates a new ET product based on this. The new product is a long-series global monthly ET dataset with a spatial resolution of 0.25° × 0.25° and a time span of 21 years. The results show that ERA5-Land (8.46 mm/month) has the lowest uncertainty among the three ET products, followed by GLDAS-Noah (8.81 mm/month) and MERRA-2 (11.78 mm/month). The new product (TCH) captures ET trends in different regions as well as validating against in situ flux observations, and it exhibits better performance than the re-analysis dataset (ERA5-Land) in vegetation classifications such as evergreen needle-leaf forest, grassland, open shrubland, savanna, and woody savanna. The linear trend analysis of the new product shows a significant decreasing trend in south-eastern South America and southwestern parts of Africa, and an increasing trend in almost all other regions, including eastern North America, north-eastern South America, western Europe, north-central Africa, southern Asia, and south-eastern Oceania.

Reactor reliability modeling and reliable life analysis method for multi-state space reactor systems based on DBN and interval estimation

Space nuclear reactor power (space reactor) is of the highest energy density and the most promising long-term self-sustaining and high-power level space power source. Achieving high reliability during the years-long maintenance-free service process is one of the bottlenecks that constrain the application of space reactors, which brings a challenging task on the quantitative evaluation of reliability indicators (life and reliability) of space reactors during the design phase. On the one hand, traditional binary reliability theory cannot model the system functional structure accurately, due to diverse failure modes and complex propagation paths; on the other hand, the lack of reliability data introduces large epistemic uncertainty, resulting from high costs and time-consuming ground reliability tests. To tackle these problems, this paper takes the Stirling integrated space reactor (ACMIR) as a specific research object and proposes a general reactor reliability modeling and reliable life analysis method for space reactors with large prior epistemic uncertainty which is robust to manipulation and can obtain system reliability indicators with small confidence intervals for engineering decisions. First, based on experts’ experience, the functional logic relationship between components and system is sorted out by the failure mode and effect analysis (FMEA) and the prior failure rates of components are evaluated according to the failure grade of the industrial standard. Then, the FMEA model is mapped to a discrete-time Bayesian network (DBN) to model the system reliable life, based on which system reliability indicators with low epistemic uncertainty are analyzed by interval estimation. Finally, the practical and engineering value of the proposed method is demonstrated with the example of ACMIR in two application cases.

Efficiency analysis of thermoelectric generators

The negative environmental and economic impact, derived from the use of fossil fuels – oil, coal, gas, and other non-renewable sources of energy – has stimulated scientific research on clean and economically viable sources. Photovoltaics and wind power are intermittent sources which stimulates the quest for other energy sources. In this sense, a promising source of energy is made up of Thermoelectric Generators (TEGs), which have the property of converting thermal energy into electrical energy, through the well-known Seebeck Effect. A new methodology for the characterization of these devices is presented in this work. For a robust analysis of the measures, the extraction of parameters is done through the meta-heuristic Self-Adaptive differential evolution method. This is made possible by simultaneous fitting of three equations and five parameters in a consistent autonomous fashion. Besides a robust experimental setup which allows the generation and precise control of the temperature variable as electrical measurements, in a controlled environment, and a thorough statistical analysis is carried for eight TEGs, model SP-184827145 which gives the mean performance of the manufactured devices. The results obtained with low uncertainties indicates that this methodology is a reliable and low-cost option for the characterization of thermoelectric devices.

Application of traceable calibration for gaseous oxidized mercury in air

BackgroundThe current speciation methods for mercury (Hg) measurements are fraught with considerable uncertainty, from sample collection to calibration. High reactivity of gaseous oxidized Hg (GOM) species and their ultra-trace level presence makes them difficult to sample and calibrate. Given that improper calibration may lead to measurement biases, reliable and metrologically traceable calibration methods are required for accurately quantifying GOM in air. In the present study, we applied the recently developed calibration method based on non-thermal plasma oxidation of elemental Hg, to a commercially available Hg air speciation system for actual environmental measurements of GOM for the first time. ResultsHg species such as HgO, HgCl2, and HgBr2 were produced with trace amounts of reactant gases (oxygen and electrolytically produced chlorine and bromine) and the production was driven by plasma-assisted oxidation. The plasma oxidation efficiency of elemental Hg with oxygen was 98.5 ± 7.5 % (k = 2), while that for chlorine and bromine was 96.8 ± 6.9 % (k = 2) and 97.4 ± 9.6 % (k = 2), respectively. The calibration method was tested against the internal permeation (Hg0) source of the Tekran 2537B Hg analyzer on-field by loading HgO to different KCl-coated denuders using the plasma. GOM concentrations were measured using the Tekran speciation system. With internal calibration, concentrations were up to 9.1 % lower than those in plasma calibration, thereby emphasizing the importance of the calibration strategy. Measurement uncertainty (k = 2) further emphasizes this distinction. Internal calibration measurement uncertainty was 36.8 %, while plasma calibration boasted lower uncertainty at 13.8 %. SignificanceThe non-thermal plasma calibration strategy, as a unique and discrete calibration method traceable to the NIST SRM 3133 for ambient air GOM measurements, provide a higher level of confidence in the accuracy of GOM measurements with several advantages over other methods. Calibrations at extreme low concentrations (<100 pg) are possible with this method relevant to ambient air GOM concentrations.

Inequality, premium and the timing of resolution of uncertainty

We incorporate Epstein-Zin preferences in an exchange economy with income uncertainty and examine the effect of inequality on the equity risk premium. When agents have preference for late resolution of uncertainty, inequality increases the premium for low income uncertainty and decreases the premium for large income uncertainty. When agents have preference for early resolution of uncertainty, inequality increases the equity premium even when the level of income uncertainty is large. Our results suggest that the time preference for resolution of uncertainty has an important effect on income uncertainty, which subsequently affects the relationship of inequality with the equity risk premium.

Projections of Greenland climate change from CMIP5 and CMIP6

As the Arctic continues to warm faster than the global average, the Greenland ice sheet faces a warmer future without restrictions on greenhouse gas emissions. In this study, 24 CMIP5 and 21 CMIP6 models were used to analyze projections of precipitation, 2 m or near-surface air temperature (T2m), and 500 hPa geopotential height (Z500) over Greenland under medium and high emission scenarios. The multi-model ensemble means indicate that CMIP6 is a warmer output with more precipitation in Greenland under medium and high emission scenarios relative to CMIP5. At the end of the 21st century (2071–2100), annual integrated precipitation in Greenland under RCP8.5 (SSP58.5) is projected to increase by 277.9 (281.3) Gt relative to the 1986–2005 climatological mean, with a significant positive trend of 38.5 (42.9) Gt/dec (p < 0.05) post-2020, approximately twice that under RCP4.5 (SSP24.5). Under high emission scenarios, T2m will steadily increase by 5.2 (5.7) °C at the end of the 21st century and the northern amplifying effect of warming is more intense. In this context, northeast Greenland will increase the highest precipitation, with a trend of >30 mm/dec during 2020–2100. The Z500 rises higher from southeast to northwest Greenland due to global warming under medium and high emission scenarios. Model and scenario uncertainties are major sources of uncertainty at the end of the 21st century. Compared to CMIP5, the model uncertainty of CMIP6 decreases more but remained higher at the end of this century. The projections of northern Greenland are more reliable than those of other regions, with a lower total fractional uncertainty and a greater signal-to-noise ratio. Furthermore, we did not find an additional T2m increase due to internal variability. Under medium and high emission scenarios, Greenland near surface air warming is major owed to global warming. Considering the importance of current circulation anomalies and after removing the artificial increase in Z500, the decrease in ΔZ500 indicates that future warming has been underestimated under medium and high emission scenarios.

Decreasing trends of ammonia emissions over Europe seen from remote sensing and inverse modelling

Abstract. Ammonia (NH3), a significant precursor of particulate matter, affects not only biodiversity, ecosystems, and soil acidification but also climate and human health. In addition, its concentrations are constantly rising due to increasing feeding needs and the large use of fertilization and animal farming. Despite the significance of ammonia, its emissions are associated with large uncertainties, while its atmospheric abundance is difficult to measure. Nowadays, satellite products can effectively measure ammonia with low uncertainty and a global coverage. Here, we use satellite observations of column ammonia in combination with an inversion algorithm to derive ammonia emissions with a high resolution over Europe for the period 2013–2020. Ammonia emissions peak in northern Europe due to agricultural application and livestock management, in western Europe (industrial activity), and over Spain (pig farming). Emissions have decreased by −26 % since 2013 (from 5431 Gg in 2013 to 3994 Gg in 2020), showing that the abatement strategies adopted by the European Union have been very efficient. The slight increase (+4.4 %) in 2015 is also reproduced here and is attributed to some European countries exceeding annual emission targets. Ammonia emissions are low in winter (286 Gg) and peak in summer (563 Gg) and are dominated by the temperature-dependent volatilization of ammonia from the soil. The largest emission decreases were observed in central and eastern Europe (−38 %) and in western Europe (−37 %), while smaller decreases were recorded in northern (−17 %) and southern Europe (−7.6 %). When complemented with ground observations, modelled concentrations using the posterior emissions showed improved statistics, also following the observed seasonal trends. The posterior emissions presented here also agree well with respective estimates reported in the literature and inferred from bottom-up and top-down methodologies. These results indicate that satellite measurements combined with inverse algorithms constitute a robust tool for emission estimates and can infer the evolution of ammonia emissions over large timescales.

Metaheuristic learning algorithms for accurate prediction of hydraulic performance of porous embankment weirs

A porous weir is an environmentally friendly structure with minimal negative environmental impact. Due to the complex flow mechanism around porous weirs, it is difficult to provide a general empirical relationship to estimate the free and submerged discharge coefficients and threshold submergence or modular limit. Hence, the current study attempts to introduce an efficient alternative approach leveraging on multilayer perceptron (MLP) coupled with generalized normal distribution optimization (GNDO), Runge-Kutta optimization algorithm (RUN), slime mould algorithm (SMA), whale optimization algorithm (WOA), and grey wolf optimizer (GWO). These models' robustness and accuracy are investigated to solve the free discharge coefficient (FDC), modular limit index (MLI), and submerge discharge reduction factor (SDRF) of the porous embankment weirs (PEWs) modeling problem where 6514 datasets are studied experimentally for free, modular limit, and submerged flow conditions. The performance of developed metaheuristic-MLP models is compared with a gradient algorithm-based MLP, namely Levenberg-Marquardt (LM) model. The obtained results from analysis of different performance indicators demonstrate that the GNDO-MLP outperforms other developed MLP models. The results demonstrate that the metaheuristic-based MLP models are more reliable in forecasting FDC, MLI, and SDRF of PEWs than the ML-MLP model. To measure how much the MLP model improved when combined with meta-heuristic algorithms, an aggregated statistical index called objective function was applied. The results of this index showed that the MLP model with GNDO performed better than the MLP models with WOA, SMA, GWO, RUN, and LM by 82%, 66%, 69%, 69%, and 96% for FDC, by 41%, 13%, 9%, 8%, and 48% for MLI, and by 64%, 20%, 8%, 4%, and 69% for SDRF condition, respectively. Furthermore, the results of the uncertainty analysis, using the P-factor and R-factor, demonstrated that GNDO-MLP had lower uncertainty compared to other models. The robustness of the GNDO-MLP model indicates that it can be used for further research on the probabilistic analysis of the PEWs.

Impact of microwave observations on the estimation of Arctic sea surface temperatures

The frequent and persistent cloud cover in the Arctic limits the extent to which sea surface temperature (SST) can be retrieved from thermal infrared (IR) satellite sensors. Passive microwave (PMW) observations provide highly complementary information to IR, enabling measurements through non-precipitating clouds, although at a coarser spatial resolution. The differences in coverage, accuracy, footprint size, spatial resolution and error characteristics between IR and PMW SSTs require a systematic assessment of how to best combine IR and PMW SST retrievals. This is provided in this study on the basis of the ESA-CCI PMW SST climate data record (CDR) and an existing IR-based gap-free SST and sea ice surface temperature CDR covering the Arctic (>58°N), where cloud cover is a serious limitation to IR sensors. An important step towards a combined IR and PMW SST CDR is to correct for systematic biases in the PMW and IR SST datasets relative to each other. The PMW SSTs show reduced biases against in situ SSTs compared to the IR SSTs, but for consistency with time periods when no Arctic PMW SSTs were available, the PMW SSTs have been adjusted to the IR SSTs in this study. This is done using a dynamic bias correction to generate a consistent combined IR and PMW Arctic SST CDR for the period 2002–2017. Including PMW SSTs reduces the standard deviations from 0.54 °C, 0.55 °C and 0.47 °C to 0.47 °C, 0.54 °C and 0.41 °C against drifters, moorings and Argo floats, respectively. The improved performance is seen in almost all regions (including those already covered by IR observations), with the largest improvement in IR data sparse regions. The average theoretical uncertainty reduces by 0.08 °C, which is in good agreement with the observed improvement in the standard deviation against drifters. The results are very promising and expected to improve even further in the future with the launch of the Copernicus Imaging Microwave Radiometer (CIMR), which will enable PMW SST retrievals with lower uncertainties and much closer to coasts and sea ice (where the largest uncertainties arise) than what is possible with previous and current PMW radiometers.

Quantitative delineation of water sources in the river Ganga using stable water isotopes

AbstractQuantitative delineation of water sources in a large river system is essential for the sustainable use of water. In the present study, we have tested two different methodologies to estimate the contribution from different water sources in the river Ganga. The first model uses stable isotopes and physicochemical parameters of water to delineate the contribution of glacier‐melt, groundwater, and surface runoff in different stretches of the river Ganga. The end member‐based mixing model provides glacier‐melt contribution of ~31.2%, ~5.5%, and ~0.5% in the upper, middle, and lower stretch of the river Ganga. The model showed maximum contribution from groundwater (~66.3%) in the middle stretch and surface runoff (~57.2%) in the lower stretch of the river Ganga. However, the uncertainties in the estimates from the three‐component mixing model were significantly high due to temporal variability in the end member values. To provide estimates with lower uncertainty, an alternate method (discharge dependent budget estimation [DDBE]) has been proposed which delineates the contribution of groundwater and surface runoff in small segments of the river. The DDBE model confines the calculation for budget estimates to smaller segments of the river and hence leads to lower uncertainties in the results, providing improved systematic estimation of water budget for large river systems. In the present study, estimates from the DDBE model suggest that groundwater contributes ~79% of the additional water whereas the contribution from surface runoff is ~21% in the middle and lower stretch of the river Ganga. The DDBE model was successfully applied in 5 small segments along the stretch of the river Ganga and the methodology used shows great potential for systematic delineation of water sources in large river system.

Independent versus collective expertise

We consider the problem of a decision-maker who seeks for advice from several experts. The experts have reputation concerns which generate incentives to herd on the prior belief about the state of the world. We address the following question: Should the experts be allowed to exchange their information before providing advice (“collective expertise”) or not (“independent expertise”)? We show that collective expertise is more informative than independent expertise under low prior uncertainty about the state and less informative otherwise. We also argue that collective expertise gains advantage as the number of experts grows.