Uncertainty Reasoning Research Articles

A Data-Driven Approach for Forecasting Current Direction With a Hybrid Model of Empirical Mode Decomposition and Warped Gaussian Process

Abstract Ocean current forecasting is essential for tidal renewable energy generation and operation. However, forecasting the current direction at multiple points along the water depth are still lacking of comprehensive studies. In this study, a data-driven approach was developed to attain short-term prediction in the current direction with reasonable uncertainty quantification. The developed approach employed empirical mode decomposition (EMD) and the warped Gaussian process (WGP) in the forecasting process. The ocean current data, which were measured by a seabed-mounted acoustic Doppler current profiler in the Haitian Strait, were used to illustrate the developed approach. The measured current direction data were preprocessed with the average shifting method to obtain the principal and random components for the improvement of the forecasting accuracy. The random components were decomposed into intrinsic mode functions (IMFs) and residuals. The principal components, IMFs, and residuals of the current direction were then forecasted by the WGP approach. The forecasting performance of the developed approach was investigated through comparisons with those of single standard GP, single WGP, and EMD + GP models. The effects of the kernel function and training input on the forecasting efficiency and precision were investigated. The extrapolation performances of the proposed model for a 1-step prediction and multistep-ahead prediction were also examined.

Random walk in random permutation set theory.

Random walk is an explainable approach for modeling natural processes at the molecular level. The random permutation set theory (RPST) serves as a framework for uncertainty reasoning, extending the applicability of Dempster-Shafer theory. Recent explorations indicate a promising link between RPST and random walk. In this study, we conduct an analysis and construct a random walk model based on the properties of RPST, with Monte Carlo simulations of such random walk. Our findings reveal that the random walk generated through RPST exhibits characteristics similar to those of a Gaussian random walk and can be transformed into a Wiener process through a specific limiting scaling procedure. This investigation establishes a novel connection between RPST and random walk theory, thereby not only expanding the applicability of RPST but also demonstrating the potential for combining the strengths of both approaches to improve problem-solving abilities.

A Monte Carlo Propagation of the Full Variance‐Covariance of GRACE‐Like Level‐2 Data With Applications in Hydrological Data Assimilation and Sea‐Level Budget Studies

AbstractUnderstanding mass (re‐)distribution within the Earth system, and addressing global challenges such as the impact of climate change on water resources requires global time‐variable terrestrial water storage (TWS) estimates along with reasonable uncertainty fields. The Gravity Recovery and Climate Experiment (GRACE) and GRACE‐FO satellite missions provide time‐variable gravity fields with full variance‐covariance information. A rigorous uncertainty propagation of these errors to TWS uncertainties is mathematically challenging and computationally inefficient. We propose a Monte Carlo Full Variance‐Covariance (MCFVC) error propagation approach to precisely compute TWS uncertainties. We also establish theoretical criteria to predict the actual convergence and accuracy of MCFVC, showing a convergence after 10,000 realizations with the relative error of 2.8% for variance and 4.7% for covariance at the confidence level of 95%. This can be achieved in few seconds using a single CPU to compute the uncertainties of each 1° resolution globally gridded TWS field. A validation against the rigorous error propagation method indicates relative differences of less than 0.8%. A global uncertainty assessment shows that neglecting the covariance of gravity coefficients can considerably bias the TWS uncertainties, that is, up to 60%, in some basins like Eyre. Flexibility of MCFVC allows the quantification of filtering impacts on the uncertainty of TWS fields, for example, up to 35% in the Tocantins River Basin. An empirical model is provided to reproduce GRACE‐like TWS uncertainty fields for hydrological studies. Finally, experiments of GRACE(‐FO) data assimilation for hydrological applications and sea‐level budget estimation are presented that indicate the importance of accounting for the full covariance information in these studies.

A probabilistic full waveform inversion of surface waves

AbstractOver the past decades, surface wave methods have been routinely employed to retrieve the physical characteristics of the first tens of meters of the subsurface, particularly the shear wave velocity profiles. Traditional methods rely on the application of the multichannel analysis of surface waves to invert the fundamental and higher modes of Rayleigh waves. However, the limitations affecting this approach, such as the 1D model assumption and the high degree of subjectivity when extracting the dispersion curve, motivate us to apply the elastic full‐waveform inversion, which, despite its higher computational cost, enables leveraging the complete information embedded in the recorded seismograms. Standard approaches solve the full‐waveform inversion using gradient‐based algorithms minimizing an error function, commonly measuring the misfit between observed and predicted waveforms. However, these deterministic approaches lack proper uncertainty quantification and are susceptible to get trapped in some local minima of the error function. An alternative lies in a probabilistic framework, but, in this case, we need to deal with the huge computational effort characterizing the Bayesian approach when applied to non‐linear problems associated with expensive forward modelling and large model spaces. In this work, we present a gradient‐based Markov chain Monte Carlo full‐waveform inversion where we accelerate the sampling of the posterior distribution by compressing data and model spaces through the discrete cosine transform. Additionally, a proposal is defined as a local, Gaussian approximation of the target density, constructed using the local Hessian and gradient information of the log posterior. We first validate our method through a synthetic test where the velocity model features lateral and vertical velocity variations. Then we invert a real dataset from the InterPACIFIC project. The obtained results prove the efficiency of our proposed algorithm, which demonstrates to be robust against cycle‐skipping issues and able to provide reasonable uncertainty evaluations with an affordable computational cost.

Cascaded Multi-path Shortcut Diffusion Model for Medical Image Translation

Image-to-image translation is a vital component in medical imaging processing, with many uses in a wide range of imaging modalities and clinical scenarios. Previous methods include Generative Adversarial Networks (GANs) and Diffusion Models (DMs), which offer realism but suffer from instability and lack uncertainty estimation. Even though both GAN and DM methods have individually exhibited their capability in medical image translation tasks, the potential of combining a GAN and DM to further improve translation performance and to enable uncertainty estimation remains largely unexplored. In this work, we address these challenges by proposing a Cascade Multi-path Shortcut Diffusion Model (CMDM) for high-quality medical image translation and uncertainty estimation. To reduce the required number of iterations and ensure robust performance, our method first obtains a conditional GAN-generated prior image that will be used for the efficient reverse translation with a DM in the subsequent step. Additionally, a multi-path shortcut diffusion strategy is employed to refine translation results and estimate uncertainty. A cascaded pipeline further enhances translation quality, incorporating residual averaging between cascades. We collected three different medical image datasets with two sub-tasks for each dataset to test the generalizability of our approach. Our experimental results found that CMDM can produce high-quality translations comparable to state-of-the-art methods while providing reasonable uncertainty estimations that correlate well with the translation error.

National security of Ukraine: analysis of risks and challenges

The article examines the essential characteristics of Ukraine's national security, its components, role and features in the context of global security. The understanding of Ukraine's national security is presented in military, political, information, and cultural dimensions. The challenges to Ukraine's national security since the declaration of independence (1991), the mistakes of domestic and foreign policy that deprived Ukraine of the military power inherited after the collapse of the USSR are analyzed. The reasons for the prolonged uncertainty of the foreign policy and the unformed national idea are highlighted both at the level of the political authorities, which were under the strong influence of the Russian Federation, and in the context of the dynamics of public sentiment of Ukrainians and their political mentality. The influence of European values and traditions, Soviet narratives, and Russian propaganda on the identity and political mentality of Ukrainians, and how these sentiments affected the state-building process are studied. The situation of Ukraine in the military-political sphere after independence to the Revolution of Dignity is traced; the influence of European traditions on the state-building process is noted; the role of Ukrainian culture as an important factor in countering Russian expansion and a factor of national security is emphasized; Ukraine's achievements on the path to European integration are highlighted.

Thermal response tests on boreholes in multi-layered ground with geothermal gradient

The design of ground source heat pump systems requires knowledge of the properties of the ground and boreholes, which are often measured through thermal response tests (TRTs). Conventional TRT analysis methods apply for uniform ground properties and undisturbed ground temperature. These assumptions become less valid for deeper boreholes, which penetrate more ground layers while the geothermal gradient becomes more important. In multi-layered ground without a geothermal gradient, conventional methods estimate the effective ground thermal conductivity kgr near the thickness-weighted average, but a geothermal gradient adds complications. In the present study simulated TRTs with quasi-steady-state and fully transient models demonstrate that the required test duration for conventional methods may become impractically large as the borehole depth increases. In general, this occurs when the dimensionless parameter |qratio| approaches 1 or less. This parameter represents the ratio of the externally imposed heat injection/extraction rate to the natural heat rate associated with the geothermal gradient. In these cases, the conventional methods do not estimate the thickness-weighted average value of kgr. On the other hand, a fully transient multi-layered ground model can determine the thickness-weighted average value of kgr. This model requires measured fluid vertical temperature profiles to estimate individual layer values of kgr within reasonable uncertainties.

Short-term stochastic multi-objective optimization scheduling of wind-solar-hydro hybrid system considering source-load uncertainties

Uncertainties in energy outputs (source side) and load side are simultaneously present and cannot be ignored in the actual operation of multi-energy systems. Adopting a reasonable uncertainty modeling method and understanding the impact of source-load uncertainties on optimization scheduling are key to formulating accurate and effective multi-energy scheduling plans. To address the uncertainties on both the source side and the load side in wind-solar-hydro hybrid systems, this paper proposes a multi-objective optimization scheduling model based on stochastic programming theory. The model aims to maximize the net profit of the system's power generation and minimize the fluctuation of the remaining load. It employs Vine-Copula coupled with Monte Carlo simulation and the deep learning method TimeGAN to generate joint wind and solar power output and load scenario sets. The generated source-load uncertainty scenarios are then reduced to representative scenarios using the K-Means clustering method, which are used as inputs for the scheduling model. The proposed model is applied to a wind-solar-hydro energy base in China, and the results show that: 1) The Vine-Copula-based source-side scenario generation method can quantitatively consider the correlations among meteorological factors. The relative errors of the generated scenarios' statistics compared to the original data are all less than 5%, and the relative errors of the correlation coefficients are less than 10%. 2) The TimeGAN-based load-side scenario generation method avoids the presupposition of the load probability distribution. Compared to the original data, the generated scenarios have R2 and Pearson correlation coefficients of 0.77 and 0.87, respectively. Additionally, TimeGAN shows significant advantages over traditional random sampling methods in simulating extreme scenarios. 3) Both source-side and load-side uncertainties significantly impact the optimization scheduling results of multi-energy systems, leading to increased fluctuation of the remaining load and decreased net profit. 4) The combined source-load uncertainties have a synergistic negative impact on the multi-objective optimization scheduling results. 5) The Pareto front of the optimization results is a concave function with low marginal benefits. Decision-makers should adopt a compromise solution as a guide for the operation of multi-energy systems.

Research on Evaluation and Prediction Method of Electrical Life of Contactor Individual

Aiming at the problem of electrical life prediction of AC contactor individual, considering that characteristic information and degradation trend of different life stages are different, a comprehensive electrical life analysis method is proposed. First, based on uncertainty reasoning, initial electrical life is qualitatively evaluated to realize an early warning for contactor with poor performance. Secondly, real‐time monitoring of performance degradation inflection point is used to realize the determination of degradation stage. With degradation stage matching mechanism, the quantitative prediction of remaining useful electrical life is realized based on performance inflection point and Elman neural network, thus forming an effective monitoring of the operation state in full life cycle. It is verified by experiment that the proposed method can accurately evaluate initial life grade and predict remaining useful life after performance inflection point. Compared with other methods, the information of electrical life for contactor individual can be accurately and comprehensively obtained. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Probabilistic fracture mechanics analyses of a reactor pressure vessel using the irradiation embrittlement evaluation based on the Bayesian nonparametric method

In the structural integrity assessment of an embrittled reactor pressure vessel (RPV) based on probabilistic fracture mechanics (PFM), it is crucial to consider both of the mean value and the uncertainty of the embrittlement prediction. Typically, the embrittlement prediction uncertainty is given by a normal distribution, and its standard deviation is determined from the residuals of the measured and predicted values of all data used to develop the embrittlement prediction method. Therefore, the same uncertainty is assumed regardless of neutron fluence and the available data. To overcome this issue, the Japan Atomic Energy Agency recently developed the embrittlement prediction method based on machine learning and Bayesian statistics, i.e., the Bayesian nonparametric (BNP) method, and introduced it to the PFM analysis code. The BNP method can predict the probability distribution according to data scarcity and provide more reasonable uncertainty because it estimates significant uncertainties where the scatter of actual measured data is large and the number of data is small. In this study, PFM analysis for a Japanese model RPV in a pressurized water reactor is conducted using the PFM analysis of structural components in aging light water reactors, where the embrittlement probability distribution calculated using the BNP method is used. Furthermore, the effects of different embrittlement prediction methods and uncertainties on the failure frequency of RPVs are investigated in the PFM analyses, and the results are presented.

Machine Learning and Information Theory Concepts towards an AI Mathematician

The current state of the art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. What could be missing? Can we learn something useful about that gap from how the brains of mathematicians go about their craft? This essay builds on the idea that current deep learning mostly succeeds at system 1 abilities—which correspond to our intuition and habitual behaviors—but still lacks something important regarding system 2 abilities—which include reasoning and robust uncertainty estimation. It takes an information-theoretical posture to ask questions about what constitutes an interesting mathematical statement, which could guide future work in crafting an AI mathematician. The focus is not on proving a given theorem but on discovering new and interesting conjectures. The central hypothesis is that a desirable body of theorems better summarizes the set of all provable statements, for example, by having a small description length while at the same time being close (in terms of number of derivation steps) to many provable statements.

Simultaneous U–Pb and U–Th Dating Using LA-ICP-MS for Young (<0.4 Ma) Minerals: A Reappraisal of the Double Dating Approach

Simultaneous U–Pb and U–Th dating using laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) was performed on the ca. 0.1 Ma Toya tephra and the ca. 0.08 Ma SS14-28 U–Th zircon reference material. In U–Pb dating, both Th/U and Pa/U partitioning between magma and minerals were considered. In U–Th dating, both abundance sensitivity and molecular interferences on 230Th were reevaluated. As a result, the Toya tephra yielded an accurate weighted mean U–Pb age of 0.103 ± 0.029 Ma (2σ) using zircon and monazite. Conversely, the SS14-28 zircon yielded an inaccurate U–Pb age (0.25 ± 0.10 Ma), which was attributed to low 206Pb signal intensity. Both the Toya tephra zircon and the SS14-28 zircon yielded accurate U–Th model ages of 0.108 ± 0.014 Ma and 0.078 ± 0.007 Ma, respectively. The agreement of U–Pb and U–Th ages for Toya indicates that simultaneous U–Pb and U–Th dating is possible and viable. The inappropriate age of SS14-28 U–Pb age and appropriate U–Th model age also indicates it is preferable to apply both U–Pb and U–Th dating simultaneously for young (<0.4 Ma) zircons to check internal consistency. The proposed double dating approach may be especially useful for small grains when it otherwise would be impossible to obtain multiple ages from a single grain. By adopting simultaneous U–Pb and U–Th dating using LA-ICP-MS, zircon crystallization ages as old as 4.5 Ga to as young as 0.1 Ma (or even younger) can be obtained in a quick and cost-effective manner with a reasonable (~5% at 1σ) uncertainty.

Distance metric learning-based multi-granularity neighborhood rough sets for attribute reduction

Attribute reduction is a hot research topic in data mining, in which rough set theory-based attribute reduction methods have been widely focused. The neighborhood rough set (NRS) model has good generalization performance and practicality in uncertainty reasoning, so it is often used for attribute reduction in recent years. Calculating the distance between samples in different attribute spaces is a key step in the NRS-based attribute reduction methods, which directly affects the performance of the reduction algorithm. However, the NRS model uses a fixed computational paradigm in calculating the distance between samples and does not consider the influence of labels in the attribute spaces on the distance calculation, which is not conducive to improving the performance of the reduction algorithm. Distance metric learning takes full account of the labels information in the multi-dimensional attribute space, and it can learn the distance between samples by taking into account the integrated principle that samples with the same label are closer and samples with different labels are further away, which helps to reduce the classification uncertainty. Inspired by this, this paper firstly incorporates distance metric learning into the NRS model from the perspective of multi-dimensional attribute space and proposes a distance metric learning-based multi-granularity neighborhood rough set (DmlMNRS) model. The related properties of the DmlMNRS model are also introduced and proved. Then, the DmlMNRS-based attribute reduction criterion and the significance of the attributes are defined. A DmlMNRS-based heuristic attribute reduction (DMNHAR) algorithm is designed based on this. Finally, experiments are performed on fifteen publicly datasets, and the experimental results show that the proposed algorithm has better robustness and classification performance.

A novel quantum Dempster's rule of combination for pattern classification

Dempster's rule of combination (DRC) is widely used for uncertainty reasoning in intelligent information system, which is generalized to complex domain recently. However, as the increase of identification framework elements, the computational complexity of Dempster's rule of combination increases exponentially. To address this issue, we propose a novel quantum Dempster's rule of combination (QDRC) by means of Toffoli gate. The QDRC combination process is completely implemented using quantum circuits. To validate the efficiency of the proposed QDRC, we conduct simulation experiments on IBM and IonQ quantum cloud platforms. Besides, we implement the QDRC algorithm to the real quantum computer of IonQ Harmony. The experiment results show that the result of QDRC is getting more and more accurate as the number of measurements increases. In addition, we propose a quantum multisource information fusion method on the basis of QDRC. Finally, we demonstrate its effectiveness to solve pattern classification problem under several diverse real UCI datasets.

The photon content of the neutron

In this work, we complete our CT18qed study with the neutron’s photon parton distribution function (PDF), which is essential for the nucleus scattering phenomenology. Two methods, CT18lux and CT18qed, based on the LUXqed formalism and the DGLAP evolution, respectively, to determine the neutron’s photon PDF have been presented. Various low-Q2 non-perturbative variations have been carefully examined, which are treated as additional uncertainties on top of those induced by quark and gluon PDFs. The impacts of the momentum sum rule as well as isospin symmetry violation have been explored and turned out to be negligible. A detailed comparison with other neutron’s photon PDF sets has been performed, which shows a great improvement in the precision and a reasonable uncertainty estimation. Finally, two phenomenological implications are demonstrated with photon-initiated processes: neutrino-nucleus W-boson production, which is important for the near-future TeV–PeV neutrino observations, and the axion-like particle production at a high-energy muon beam-dump experiment.

Ensemble learning for predicting average thermal extraction load of a hydrothermal geothermal field: A case study in Guanzhong Basin, China

Accurate prediction of the average thermal extraction load (ATEL) in hydrothermal heating systems optimizes energy recovery, though numerical models are constrained by modeling accuracy and computational time costs. Data-driven modeling can efficiently screen alternative production plans and enhance daily operational decisions. However, ensemble learning applications for forecasting ATEL lack comprehensive comparisons and appropriate algorithm selection. This study evaluates six ensemble learning algorithms: random forest (RF), adaptive boosting (AdaBoost), gradient boosting decision trees (GBDT), extreme gradient boosting (XGBoost), light gradient boosting machine (LightBGM) and categorical boosting (CatBoost) on 1159 data points from a homogeneous thermal-hydraulic coupling numerical model. The superior performance of the CatBoost is characterized by the highest accuracy (with the lowest root mean square error (RMSE) of 150.6 kW–170.7 kW, minimal mean absolute percentage error (MAPE) of 0.66%–0.73%, and exceptional R2 values of 0.999), commendable stability, reasonable computational cost and low uncertainty. LightGBM, XGBoost, and GBDT are identified as suitable substitutes, whereas RF is a possible substitute. Moreover, the production rate is identified as the most significant factor contributing to the ATEL, followed by the well spacing and injection temperature. While perforation depth has the least influence on heat recovery.

Integrating transient pressure and flow data for determination of hydraulic permeability and specific storage of a shale sample: Experimental tests and sensitivity analysis

This paper describes a comprehensive investigation to accurately determine the hydraulic permeability k and the specific storage Ss of a shale sample. One-dimensional pressure transient tests were conducted on a cylindrical sample under various levels of pore and confining pressures. For the boundary conditions, the upstream pressure was kept constant using a syringe pump, and the downstream storage was minimized for reducing the test duration. Both the downstream pressure and the upstream fluid flow into the sample were continuously recorded throughout the transient period. To estimate the hydraulic properties, the curve fitting technique was applied to the pressure and flow data using theoretical curves. We found that the pressure curve was sensitive to the ratio of hydraulic permeability to the specific storage (k/Ss), but not sufficient to determine the individual components (k and Ss). The upstream flow curve was sensitive to the specific storage but less sensitive to the permeability. Based on our sensitivity analysis, we present a combination of two objective functions of flow and pressure data to optimize both hydraulic properties with reasonable uncertainty. An alternative is to first use the flow data to determine Ss and then use pressure data with the predetermined Ss to obtain the remaining k.

Converter thickness optimisation using Monte Carlo simulations of Fluorescent Nuclear Track Detectors for neutron dosimetry

Secondary neutrons generated during ion beam radiotherapy present a concern due to the potential dose deposition beyond the treatment volume, thereby elevating the risk of inducing secondary tumours. These neutrons can possess energies comparable to those of the primary ions, reaching magnitudes of several hundred MeV, posing a challenge for neutron detectors. Fluorescent Nuclear Track Detectors (FNTDs) are promising detectors for high-energy neutron dosimetry given their capability to detect particles with a low linear energy transfer. In this work, the sensitivity of FNTDs to neutron energies reaching 20MeV was analysed by experiments and Monte Carlo (MC) simulations, quantifying the recoil proton yield of FNTDs combined with polyethylene (PE) converters of different thicknesses. The FNTDs were read out using a dedicated FNTD reader, demonstrating a reasonable uncertainty by analysing a detector area of 0.1mm2. Investigations of different converter thicknesses reveal optimal detector sensitivity between 0.5mm to 1.0mm for a 241AmBe source, yielding a maximum sensitivity of (22.7±3.4) tracksmSv-1mm-2. Similar converter-FNTD configurations were assessed through MC simulations using FLUKA, yielding a correlation between detector sensitivity and converter thickness. Furthermore, an enhanced detector sensitivity for neutron energies up to 20MeV was found for the PE converter thickness of 4.0mm. The MC simulations can be used to optimise FNTD detector configurations for measuring higher neutron energies by maximising the recoil proton yield.

Correcting model misspecification in physics-informed neural networks (PINNs)

Data-driven discovery of governing equations in computational science has emerged as a new paradigm for obtaining accurate physical models and as a possible alternative to theoretical derivations. The recently developed physics-informed neural networks (PINNs) have also been employed to learn governing equations given data across diverse scientific disciplines, e.g., in biology and fluid dynamics. Despite the effectiveness of PINNs for discovering governing equations, the physical models encoded in PINNs may be misspecified in complex systems as some of the physical processes may not be fully understood, leading to the poor accuracy of PINN predictions. In this work, we present a general approach to correct the misspecified physical models in PINNs for discovering governing equations, given some sparse and/or noisy data. Specifically, we first encode the assumed physical models, which may be misspecified in PINNs, and then employ other deep neural networks (DNNs) to model the discrepancy between the imperfect models and the observational data. Due to the expressivity of DNNs, the proposed method is capable of reducing the computational errors caused by the model misspecification and thus enables the applications of PINNs in complex systems where the physical processes are not exactly known. Furthermore, we utilize the Bayesian physics-informed neural networks (B-PINNs) and/or ensemble PINNs to quantify uncertainties arising from noisy and/or gappy data in the discovered governing equations. A series of numerical examples including reaction-diffusion systems and non-Newtonian channel and cavity flows demonstrate that the added DNNs are capable of correcting the model misspecification in PINNs and thus reduce the discrepancy between the physical models encoded in PINNs and the observational data. In addition, the B-PINNs and ensemble PINNs can provide reasonable uncertainty bounds in the discovered physical models, which makes the predictions more reliable. We also demonstrate that we can seamlessly combine the present approach with the symbolic regression to obtain the explicit governing equations upon the training of PINNs. We envision that the proposed approach will extend the applications of PINNs for discovering governing equations in problems where the physico-chemical or biological processes are not well understood.

On Traces, Clues, and Fiction: Carlo Ginzburg and the Practice of Archaeology

Abstract In recent years, archaeological research has relied on large datasets, both temporally and geographically, with some archaeologists discussing that there should be a shift towards a more scientific form of conducting archaeological research called “macroarchaeology.” Ironically, and contradictorily, this shift towards large-scale research has involved the use of inductive approaches, which means that archaeological material needs to be converted into universal quantitative values. The inductive approaches used by archaeologists today, as argued by Karl Popper, and other authors in recent years, cannot be considered scientific in the strict sense of the word, since there is always a degree of uncertainty in inductive reasoning. This study suggests that archaeological data can be considered as traces of the past, clues that allow us to reconstruct past phenomena. As Carlo Ginzburg’s evidential paradigm demonstrates, thinking of the past in terms of traces and clues is much more scientific than appears at first. In addition to traces and clues, a second interpretative procedure can be conducted on data. Based on Ginzburg’s conjectural paradigm and discussion on fiction, we can recognize the past as real, while at the same time, conjecture the several ways past agents could have acted otherwise.