Bayesian Maximum Entropy Methods Research Articles

A Bayesian maximum entropy model for predicting tsetse ecological distributions

BackgroundAfrican trypanosomiasis is a tsetse-borne parasitic infection that affects humans, wildlife, and domesticated animals. Tsetse flies are endemic to much of Sub-Saharan Africa and a spatial and temporal understanding of tsetse habitat can aid surveillance and support disease risk management. Problematically, current fine spatial resolution remote sensing data are delivered with a temporal lag and are relatively coarse temporal resolution (e.g., 16 days), which results in disease control models often targeting incorrect places. The goal of this study was to devise a heuristic for identifying tsetse habitat (at a fine spatial resolution) into the future and in the temporal gaps where remote sensing and proximal data fail to supply information.MethodsThis paper introduces a generalizable and scalable open-access version of the tsetse ecological distribution (TED) model used to predict tsetse distributions across space and time, and contributes a geospatial Bayesian Maximum Entropy (BME) prediction model trained by TED output data to forecast where, herein the Morsitans group of tsetse, persist in Kenya, a method that mitigates the temporal lag problem. This model facilitates identification of tsetse habitat and provides critical information to control tsetse, mitigate the impact of trypanosomiasis on vulnerable human and animal populations, and guide disease minimization in places with ephemeral tsetse. Moreover, this BME analysis is one of the first to utilize cluster and parallel computing along with a Monte Carlo analysis to optimize BME computations. This allows for the analysis of an exceptionally large dataset (over 2 billion data points) at a finer resolution and larger spatiotemporal scale than what had previously been possible.ResultsUnder the most conservative assessment for Kenya, the BME kriging analysis showed an overall prediction accuracy of 74.8% (limited to the maximum suitability extent). In predicting tsetse distribution outcomes for the entire country the BME kriging analysis was 97% accurate in its forecasts.ConclusionsThis work offers a solution to the persistent temporal data gap in accurate and spatially precise rainfall predictions and the delayed processing of remotely sensed data collectively in the − 45 days past to + 180 days future temporal window. As is shown here, the BME model is a reliable alternative for forecasting future tsetse distributions to allow preplanning for tsetse control. Furthermore, this model provides guidance on disease control that would otherwise not be available. These ‘big data’ BME methods are particularly useful for large domain studies. Considering that past BME studies required reduction of the spatiotemporal grid to facilitate analysis. Both the GEE-TED and the BME libraries have been made open source to enable reproducibility and offer continual updates into the future as new remotely sensed data become available.

Application of Synthetic DINCAE–BME Spatiotemporal Interpolation Framework to Reconstruct Chlorophyll–a from Satellite Observations in the Arabian Sea

Chlorophyll–a (Chl–a) concentration is an indicator of phytoplankton pigment, which is associated with the health of marine ecosystems. A commonly used method for the determination of Chl–a is satellite remote sensing. However, due to cloud cover, sun glint and other issues, remote sensing data for Chl–a are always missing in large areas. We reconstructed the Chl–a data from MODIS and VIIRS in the Arabian Sea within the geographical range of 12–28° N and 56–76° E from 2020 to 2021 by combining the Data Interpolating Convolutional Auto–Encoder (DINCAE) and the Bayesian Maximum Entropy (BME) methods, which we named the DINCAE–BME framework. The hold–out validation method was used to assess the DINCAE–BME method’s performance. The root–mean–square–error (RMSE) and the mean–absolute–error (MAE) values for the hold–out cross–validation result obtained by the DINCAE–BME were 1.8824 mg m−3 and 0.4682 mg m−3, respectively; compared with in situ Chl–a data, the RMSE and MAE values for the DINCAE–BME–generated Chl–a product were 0.6196 mg m−3 and 0.3461 mg m−3, respectively. Moreover, DINCAE–BME exhibited better performance than the DINEOF and DINCAE methods. The spatial distribution of the Chl–a product showed that Chl–a values in the coastal region were the highest and the Chl–a values in the deep–sea regions were stable, while the Chl–a values in February and March were higher than in other months. Lastly, this study demonstrated the feasibility of combining the BME method and DINCAE.

Application and Analysis of XCO2 Data from OCO Satellite Using a Synthetic DINEOF–BME Spatiotemporal Interpolation Framework

Carbon dioxide (CO2) is one of the main greenhouse gases leading to global warming, and the ocean is the largest carbon reservoir on the earth that plays an important role in regulating CO2 concentration on a global scale. The column-averaged dry-air mole fraction of atmospheric CO2 (XCO2) is a key parameter in describing ocean carbon content. In this paper, the Data Interpolation Empirical Orthogonal Function (DINEOF) and the Bayesian Maximum Entropy (BME) methods are combined to interpolate XCO2 data of Orbiting Carbon Observatory 2 (OCO-2) and Orbiting Carbon Observatory 3 (OCO-3) from January to December 2020 occurring within the geographical range of 15–45°N and 120–150°E. At the first stage of our proposed analysis, spatiotemporal information was used by the DINEOF method to perform XCO2 interpolation that improved data coverage; at the second stage, the DINEOF-generated interpolation results were regarded as soft data and were subsequently assimilated using the BME method to obtain improved XCO2 interpolation values. The performance of the synthetic DINEOF–BME interpolation method was evaluated by means of a five-fold cross-validation method. The results showed that the Mean Absolute Error (MAE), the Root Mean Square Error (RMSE), and the Bias of the DINEOF-based OCO-2 and OCO-3 interpolations were 2.106 ppm, 3.046 ppm, and 1.035 ppm, respectively. On the other hand, the MAE, RMSE, and Bias of the cross-validation results obtained by the DINEOF–BME were 1.285 ppm, 2.422 ppm, and −0.085 ppm, respectively, i.e., smaller than the results obtained by DINEOF. In addition, based on the in situ measured XCO2 data provided by the Total Carbon Column Observing Network (TCCON), the original OCO-2 and OCO-3 data were combined and compared with the interpolated products of the synthetic DINEOF–BME framework. The accuracy of the original OCO-2 and OCO-3 products is lower than the DINEOF–BME-generated XCO2 products in terms of MAE (1.751 ppm vs. 2.616 ppm), RMSE (2.877 ppm vs. 3.566 ppm) and Bias (1.379 ppm vs 1.622 ppm), the spatiotemporal coverage of XCO2 product also improved dramatically from 16% to 100%. Lastly, this study demonstrated the feasibility of the synthetic DINEOF–BME approach for XCO2 interpolation purposes and the ability of the BME method to be successfully combined with other techniques.

An Integrated Framework for Mapping Nationwide Daily Temperature in China

Air temperature (Ta) is an essential parameter for science research and engineering practice. While the traditional site-based approach is only able to obtain observations in limited and discrete locations, satellite remote sensing is promising to retrieve some environmental variables with spatially continuous coverage. Nowadays, land surface temperature (Ts) measurements can be obtained from some satellite sensors (e.g., MODIS), further enabling us to estimate Ta in view of the relationship between Ta and Ts. In this article, we proposed a two-phase integrated framework to estimate daily mean Ta nationwide. In the first phase, multivariate linear regression models were fitted between site-based observations of daily mean air temperature (Ta-mean) and MODIS land surface temperature products (including Terra day: TMOD-day, Terra night: TMOD-night, Aqua day: TMYD-day, and Aqua night: TMYD-night) conditional on some covariates of environmental factors. The fitted models were then used to predict Ta-mean from those covariates at unobserved locations. The predicted Ta-mean were looked on as stochastic variables, and their distributions were also obtained. In the second phase, Bayesian maximum entropy (BME) methods were used to produce spatially continuous maps of Ta-mean taking the meteorological station observations as hard data and the predicted Ta-mean in the first phase as soft data. It is shown that the proposed approach is promising to improve the interpolation accuracy significantly, comprehensively considering the prior knowledge and the context of space variability and correlation, which will enable it to compile spatially continuous air temperature products with higher accuracy.

Mapping Yearly Fine Resolution Global Surface Ozone through the Bayesian Maximum Entropy Data Fusion of Observations and Model Output for 1990-2017.

Estimates of ground-level ozone concentrations are necessary to determine the human health burden of ozone. To support the Global Burden of Disease Study, we produce yearly fine resolution global surface ozone estimates from 1990 to 2017 through a data fusion of observations and models. As ozone observations are sparse in many populated regions, we use a novel combination of the M3Fusion and Bayesian Maximum Entropy (BME) methods. With M3Fusion, we create a multimodel composite by bias-correcting and weighting nine global atmospheric chemistry models based on their ability to predict observations (8834 sites globally) in each region and year. BME is then used to integrate observations, such that estimates match observations at each monitoring site with the observational influence decreasing smoothly across space and time until the output matches the multimodel composite. After estimating at 0.5° resolution using BME, we add fine spatial detail from an additional model, yielding estimates at 0.1° resolution. Observed ozone is predicted more accurately (R2 = 0.81 at the test point, 0.63 at 0.1°, and 0.62 at 0.5°) than the multimodel mean (R2 = 0.28 at 0.5°). Global ozone exposure is estimated to be increasing, driven by highly populated regions of Asia and Africa, despite decreases in the United States and Russia.

A Space/Time Data Fusion Method for Accurately Estimating Wildfire Smoke Concentrations During the October 2017 California Fires to Inform Population-Level Exposure

Background. Exposure to wildfire smoke causes a range of adverse health outcomes, suggesting the importance of accurately estimating wildfire smoke concentrations. While chemical transport models (CTMs) and spatial interpolation of observations are often used to assess smoke exposure, geostatistical methods can combine surface observations with modeled and satellite-derived concentrations to produce more accurate exposure estimates.Methods. Here we estimate ground-level PM2.5 concentrations during the October 2017 California wildfires, using the Constant Air Quality Model Performance (CAMP) Method and the Bayesian Maximum Entropy (BME) Framework to bias-correct and fuse together three PM2.5 datasets: concentrations from permanent and temporary monitoring stations, a CTM, and satellite observations. Four different BME space/time (s/t) kriging and data fusion methods using these three datasets were evaluated for accuracy.Results. All four BME methods produced more accurate estimates of ground-level PM2.5 than the standalone CTM and satellite products, with the addition of temporary monitoring station data further improving accuracy. While BME s/t kriging on observations performed best near monitoring stations, the BME data fusion of observations with the CAMP-corrected CTM provided the best overall estimate, especially in smoke-impacted regions. Using these smoke concentrations, we estimate more than 60,000 people were exposed to very unhealthy air, PM2.5 concentrations greater than 150.5 µg/m3, during the 2017 wildfires.Conclusions. We show that the BME framework, used in combination with the CAMP correction method, can be used to accurately estimate ground-level PM2.5 concentrations during a wildfire event. Our results emphasize the importance of combining multiple data sources to characterize population-level exposure during extreme air pollution events.

Estimating Wildfire Smoke Concentrations during the October 2017 California Fires through BME Space/Time Data Fusion of Observed, Modeled, and Satellite-Derived PM2.5.

Exposure to wildfire smoke causes adverse health outcomes, suggesting the importance of accurately estimating smoke concentrations. Geostatistical methods can combine observed, modeled, and satellite-derived concentrations to produce accurate estimates. Here, we estimate daily average ground-level PM2.5 concentrations at a 1 km resolution during the October 2017 California wildfires, using the Constant Air Quality Model Performance (CAMP) and Bayesian Maximum Entropy (BME) methods to bias-correct and fuse three concentration datasets: permanent and temporary monitoring stations, a chemical transport model (CTM), and satellite-derived estimates. Four BME space/time kriging and data fusion methods were evaluated. All BME methods produce more accurate estimates than the standalone CTM and satellite products. Adding temporary station data increases the R2 by 36%. The data fusion of observations with the CAMP-corrected CTM and satellite-derived concentrations provides the best estimate (R2 = 0.713) in fire-impacted regions, emphasizing the importance of combining multiple datasets. We estimate that approximately 65,000 people were exposed to very unhealthy air (daily average PM2.5 ≥ 150.5 μg/m3).

Dirichlet Bayesian network scores and the maximum relative entropy principle

A classic approach for learning Bayesian networks from data is to identify a maximum a posteriori (MAP) network structure. In the case of discrete Bayesian networks, MAP networks are selected by maximising one of several possible Bayesian–Dirichlet (BD) scores; the most famous is the Bayesian–Dirichlet equivalent uniform (BDeu) score from Heckerman et al. (Mach Learn 20(3):197–243, 1995). The key properties of BDeu arise from its uniform prior over the parameters of each local distribution in the network, which makes structure learning computationally efficient; it does not require the elicitation of prior knowledge from experts; and it satisfies score equivalence. In this paper we will review the derivation and the properties of BD scores, and of BDeu in particular, and we will link them to the corresponding entropy estimates to study them from an information theoretic perspective. To this end, we will work in the context of the foundational work of Giffin and Caticha (Proceedings of the 27th international workshop on Bayesian inference and maximum entropy methods in science and engineering, pp 74–84, 2007), who showed that Bayesian inference can be framed as a particular case of the maximum relative entropy principle. We will use this connection to show that BDeu should not be used for structure learning from sparse data, since it violates the maximum relative entropy principle; and that it is also problematic from a more classic Bayesian model selection perspective, because it produces Bayes factors that are sensitive to the value of its only hyperparameter. Using a large simulation study, we found in our previous work [Scutari in J Mach Learn Res (Proc Track PGM 2016) 52:438–448, 2016] that the Bayesian–Dirichlet sparse (BDs) score seems to provide better accuracy in structure learning; in this paper we further show that BDs does not suffer from the issues above, and we recommend to use it for sparse data instead of BDeu. Finally, will show that these issues are in fact different aspects of the same problem and a consequence of the distributional assumptions of the prior.

Inference of reaction rate parameters based on summary statistics from experiments

We present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate parameters of the rate coefficient of the H2/O2-mechanism chain branching reaction H+O2→OH+O. Available published data is summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shock-tube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the given summary statistics, using Approximate Bayesian Computation methods and a Markov chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Padé and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use in the Bayesian inference procedure. We also utilize Gauss–Hermite quadrature with Gaussian proposal probability density functions for moment computation resulting in orders of magnitude speedup in data likelihood evaluation. Despite the strong non-linearity in the model, the consistent data sets all result in nearly Gaussian conditional parameter probability density functions. The technique also accounts for nuisance parameters in the form of Arrhenius parameters of other rate coefficients with prescribed uncertainty. The resulting pooled parameter probability density function is propagated through stoichiometric hydrogen–air auto-ignition computations to illustrate the need to account for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions.

Spatiotemporal Approaches to Analyzing Pedestrian Fatalities: The Case of Cali, Colombia

Objective: Injuries among pedestrians are a major public health concern in Colombian cities such as Cali. This is one of the first studies in Latin America to apply Bayesian maximum entropy (BME) methods to visualize and produce fine-scale, highly accurate estimates of citywide pedestrian fatalities. The purpose of this study is to determine the BME method that best estimates pedestrian mortality rates and reduces statistical noise. We further utilized BME methods to identify and differentiate spatial patterns and persistent versus transient pedestrian mortality hotspots.Methods: In this multiyear study, geocoded pedestrian mortality data from the Cali Injury Surveillance System (2008 to 2010) and census data were utilized to accurately visualize and estimate pedestrian fatalities. We investigated the effects of temporal and spatial scales, addressing issues arising from the rarity of pedestrian fatality events using 3 BME methods (simple kriging, Poisson kriging, and uniform model Bayesian maximum entropy). To reduce statistical noise while retaining a fine spatial and temporal scale, data were aggregated over 9-month incidence periods and censal sectors. Based on a cross-validation of BME methods, Poisson kriging was selected as the best BME method. Finally, the spatiotemporal and urban built environment characteristics of Cali pedestrian mortality hotspots were linked to intervention measures provided in Mead et al.'s (2014) pedestrian mortality review.Results: The BME space–time analysis in Cali resulted in maps displaying hotspots of high pedestrian fatalities extending over small areas with radii of 0.25 to 1.1 km and temporal durations of 1 month to 3 years. Mapping the spatiotemporal distribution of pedestrian mortality rates identified high-priority areas for prevention strategies. The BME results allow us to identify possible intervention strategies according to the persistence and built environment of the hotspot; for example, through enforcement or long-term environmental modifications.Conclusions: BME methods provide useful information on the time and place of injuries and can inform policy strategies by isolating priority areas for interventions, contributing to intervention evaluation, and helping to generate hypotheses and identify the preventative strategies that may be suitable to those areas (e.g., street-level methods: pedestrian crossings, enforcement interventions; or citywide approaches: limiting vehicle speeds). This specific information is highly relevant for public health interventions because it provides the ability to target precise locations.

Improving Bayesian maximum entropy and ordinary Kriging methods for estimating precipitations in a large watershed: a new cluster-based approach

The main purpose of this research is to investigate spatial variations of mean annual precipitation in a watershed. As a case study, the research focused on the Namak Lake watershed in Iran. Literature provides various techniques for studying spatial patterns of precipitation in a watershed. These techniques often require a large dataset. On the other hand, nonuniform data distribution in a watershed can reduce the accuracy and reliability of the predictions. To overcome these problems, this research applied the cluster method coupled with ordinary Kriging and Bayesian maximum entropy techniques. An estimated point was modified based on the distance from the point to the cluster center. The research considered elevation variations as a secondary variable. A cross-validation technique was used for evaluating the results of mean annual precipitations. The research compared the results of ordinary Kriging and Bayesian maximum entropy methods with and without the application of the clustering method. The research concluded that the cluster-based method can estimate the dynamics of long-term mean annual precipitation more reliably and accurately. The research also revealed more informative results for the cluster-based method.

Evaluation of spatial and spatiotemporal estimation methods in simulation of precipitation variability patterns

Identification of spatial and spatiotemporal precipitation variations plays an important role in different hydrological applications such as missing data estimation. In this paper, the results of Bayesian maximum entropy (BME) and ordinary kriging (OK) are compared for modeling spatial and spatiotemporal variations of annual precipitation with and without incorporating elevation variations. The study area of this research is Namak Lake watershed located in the central part of Iran with an area of approximately 90,000 km2. The BME and OK methods have been used to model the spatial and spatiotemporal variations of precipitation in this watershed, and their performances have been evaluated using cross-validation statistics. The results of the case study have shown the superiority of BME over OK in both spatial and spatiotemporal modes. The results have shown that BME estimates are less biased and more accurate than OK. The improvements in the BME estimates are mostly related to incorporating hard and soft data in the estimation process, which resulted in more detailed and reliable results. Estimation error variance for BME results is less than OK estimations in the study area in both spatial and spatiotemporal modes.

Bayesian maximum entropy data fusion of field-observed leaf area index (LAI) and Landsat Enhanced Thematic Mapper Plus-derived LAI

Accurate high-resolution leaf area index (LAI) reference maps are necessary for the validation of coarser-resolution satellite-derived LAI products. In this article, we propose an efficient method based on the Bayesian Maximum Entropy (BME) paradigm to combine field observations and Landsat Enhanced Thematic Mapper Plus (ETM+)-derived LAI surfaces in order to produce more accurate LAI reference maps. This method takes into account the uncertainties associated with field observations and with the regression relationship between ETM+-derived LAI and field measurements to perform a non-linear prediction of LAI, the variable of interest. In order to demonstrate the difference by soft data and hard data, we estimate the LAI reference maps by three BME interpolation methods, BME1, BME2, and BME3. BME1 and BME2 perform maximum estimation and mean estimation, respectively, by taking the ETM+-derived LAI as interval soft data and the field LAI measurements as hard data. BME3 is utilized when ETM+-derived LAI surfaces are processed as uniform probability soft data and field measurements are processed as Gaussian probability soft data. Three study sites are selected from the BigFoot project (NASA's Earth Observing System validation programme) (http://www.fsl.orst.edu/larse/bigfoot/index.html). In regard to the mean and standard deviation of LAI surfaces, standard deviation predicted by BME methods has lower values than that derived by ETM+. The mean value of the BME-predicted LAI, which takes into account the uncertainties of field measurements, is lower than that of ETM+-derived LAI at each study site. A comparison with field measurements shows that BME1, BME2, and BME3 have root mean square errors (RMSE) of 0.455, 0.485, and 0.517 and average biases of −0.017, −0.010, and −0.304, respectively. The RMSEs and biases of the predicted LAI surfaces are less when compared to the ETM+-derived LAI, which has the average RMSE and bias of 0.642 and −0.080. When the field measurements are processed as soft data, the predicted LAI by BME3 has more bias than those of the predictions by BME1 and BME2, but has less RMSE than that of the ETM+-derived LAI by 0.125. In summary, BME is capable of incorporating the spatial autocorrelation and the uncertainties in the field LAI measurements into the LAI surface estimation to produce a more accurate LAI surface with less RMSE in validation. The maximum estimation has relatively better accuracy than the mean estimation. The results indicate that the BME is a promising method for fusing point-scale and area-scale data.

Jon Williamson, Bayesian Nets and Causality: Philosophical and Computational Foundations

Jon Williamson is currently located at the Department of Philosophy, Logic, and Scientific Method, London School of Economics, London. Within this volume, Williamson seeks to address the age-old question of how we reason about causal relationships. From a philosophical perspective, this book explores the ontology and epistemology of probability and causality, whereas from a computational point of view, it investigates the relationship between Bayesian nets and maximum entropy methods. Williamson’s positions argued within this book, including objective Bayesianism and epistemic causality, are part of a coherent scientific framework in which entities are neither physical, mind-independent features of the world, nor arbitrary and subjective entities varying according to the individual. The aim of this book is to present coherent foundations to recent work hypothesizing that Bayesian nets provide a calculus for causal reasoning, and that one can learn actual causal relationships by the automated learning of Bayesian nets from observational data (i.e. inductively). The predictive features of Bayesian Systems’ products are based on a fundamental principal of logic known as Bayes’ theorem. This principle was discovered in 1761 by the Englishman Thomas Bayes, and brought into its modern form shortly thereafter by the great French mathematician Pierre Simon de Laplace. Properly understood, the theorem is the fundamental mathematical law governing the process of logical inference determining what degree of confidence we may have in various possible conclusions, based on the body of evidence available. Chapter one gives a coherent and concise overview of the entirety of the book. Chapter two gives one a foundational understanding of probability and its interpretations. Chapter three introduces the reader to Bayesian nets, and thereafter gives an erudite summary of them as well. Chapter four relates the problems that are accompanied by the attempt to apply Bayesian nets to causal reasoning, which leads

Cost‐effective water quality assessment through the integration of monitoring data and modeling results

Sparse monitoring data and error inherent in water quality models make the identification of waters not meeting regulatory standards uncertain. Additional monitoring can be implemented to reduce this uncertainty, but it is often expensive. These costs are currently a major concern, since developing total maximum daily loads, as mandated by the Clean Water Act, will require assessing tens of thousands of water bodies across the United States. This work uses the Bayesian maximum entropy (BME) method of modern geostatistics to integrate water quality monitoring data together with model predictions to provide improved estimates of water quality in a cost‐effective manner. This information includes estimates of uncertainty and can be used to aid probabilistic‐based decisions concerning the status of a water (i.e., impaired or not impaired) and the level of monitoring needed to characterize the water for regulatory purposes. This approach is applied to the Catawba River reservoir system in western North Carolina as a means of estimating seasonal chlorophyll a concentration. Mean concentration and confidence intervals for chlorophyll a are estimated for 66 reservoir segments over an 11‐year period (726 values) based on 219 measured seasonal averages and 54 model predictions. Although the model predictions had a high degree of uncertainty, integration of modeling results via BME methods reduced the uncertainty associated with chlorophyll estimates compared with estimates made solely with information from monitoring efforts. Probabilistic predictions of future chlorophyll levels on one reservoir are used to illustrate the cost savings that can be achieved by less extensive and rigorous monitoring methods within the BME framework. While BME methods have been applied in several environmental contexts, employing these methods as a means of integrating monitoring and modeling results, as well as application of this approach to the assessment of surface water monitoring networks, represent unexplored areas of research.

Entropic criterion for model selection

Model or variable selection is usually achieved through ranking models according to the increasing order of preference. One of methods is applying Kullback–Leibler distance or relative entropy as a selection criterion. Yet that will raise two questions, why use this criterion and are there any other criteria. Besides, conventional approaches require a reference prior, which is usually difficult to get. Following the logic of inductive inference proposed by Caticha [Relative entropy and inductive inference, in: G. Erickson, Y. Zhai (Eds.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, AIP Conference Proceedings, vol. 707, 2004 (available from arXiv.org/abs/physics/0311093)], we show relative entropy to be a unique criterion, which requires no prior information and can be applied to different fields. We examine this criterion by considering a physical problem, simple fluids, and results are promising.