Parsimonious Modeling Research Articles

Parsimonious modelling of winter season rainfall incorporating reanalysis climatological data

Abstract Several Markov modulated Poisson process (MMPP) models are developed to describe winter season rainfall with parsimonious parameter use. We propose a methodology for determining the best form of seasonal model for fine-scale rainfall within a MMPP framework. Of those proposed here, a model with a fixed transition rate is shown to be superior over the other MMPP models considered. The model is expanded to include covariate data for sea-level air pressure, relative humidity, and temperature using reanalysis data over 14 years from the coordinates covering the Bracknell rainfall collection site in England. Results are compared using the likelihood ratio test and the second-order properties of aggregated rainfall.

The Curve Number Concept as a Driver for Delineating Hydrological Response Units

In this paper, a new methodology for delineating Hydrological Response Units (HRUs), based on the Curve Number (CN) concept, is presented. Initially, a semi-automatic procedure in a GIS environment is used to produce basin maps of distributed CN values as the product of the three classified layers, soil permeability, land use/land cover characteristics and drainage capacity. The map of CN values is used in the context of model parameterization, in order to identify the essential number and spatial extent of HRUs and, consequently, the number of control variables of the calibration problem. The new approach aims at reducing the subjectivity introduced by the definition of HRUs and providing parsimonious modelling schemes. In particular, the CN-based parameterization (1) allows the user to assign as many parameters as can be supported by the available hydrological information, (2) associates the model parameters with anticipated basin responses, as quantified in terms of CN classes across HRUs, and (3) reduces the effort for model calibration, simultaneously ensuring good predictive capacity. The advantages of the proposed approach are demonstrated in the hydrological simulation of the Nedontas River Basin, Greece, where parameterizations of different complexities are employed in a recently improved version of the HYDROGEIOS model. A modelling experiment with a varying number of HRUs, where the parameter estimation problem was handled through automatic optimization, showed that the parameterization with three HRUs, i.e., equal to the number of flow records, ensured the optimal performance. Similarly, tests with alternative HRU configurations confirmed that the optimal scores, both in calibration and validation, were achieved by the CN-based approach, also resulting in parameters values across the HRUs that were in agreement with their physical interpretation.

Modelling German Electricity Wholesale Spot Prices with a Parsimonious Fundamental Model Validation & Application

Increasing shares of fluctuating renewable energy, the integration of European electricity grids and markets as well as new technologies induce continuous change in the European energy system. Due to these changes, fundamental electricity system and market models that have been developed and applied in the past are dealing with an increasing number of details inducing correspondingly huge data needs. The complexity of these called parameter-rich models (cf. Weron, 2014) leads to limited transparency, also on the impact of data on results, and makes model backtesting rather cumbersome. At the same time, the validity of future scenarios based on non-validated models is dubious. To complement these highly complicated models, more reduced models may be helpful both for transparency and for backtesting. In this paper, we apply a parsimonious fundamental modelling approach to determine hourly German day-ahead power market prices and production volumes. The methodology approximates the supply stack by a piecewise linear function and considers fundamental information, e.g. power plant capacities and availabilities, fuel prices, must-run production and cross-border exchange. We reduce complexity by considering technology classes, uncoupled time periods and only one market area. Between 2011 and 2015, German day-ahead prices declined by 38% and various reasons have been identified in literature, namely a drop in emission certificate prices, the expansion of renewable energies (RES) or lower fuel prices. However, the decision of the German government to shut down nuclear power plants after the Fukushima nuclear disaster happened at the same time and received too little attention as it rather by itself could have led to an increase in prices. The parsimonious model is able to reproduce the hourly historical prices (2011-2015) with a MAE of 5.6 €/MWh and accurately reproduces the electricity production volumes for most thermal production units. In a case study, we investigate a counterfactual scenario without accelerated nuclear phase-out in Germany after the Fukushima nuclear disaster in 2011. The results indicate that German day-ahead power prices would have fallen by additional 3 €/MWh if the nuclear phase-out would have not occurred. Since coal- and gas-fired production as well as additional imports have substituted production from nuclear power plants, their usage would have dropped in the counterfactual scenario.

Mixture inner product spaces and their application to functional data analysis

We introduce the concept of mixture inner product spaces associated with a given separable Hilbert space, which feature an infinite-dimensional mixture of finite-dimensional vector spaces and are dense in the underlying Hilbert space. Any Hilbert valued random element can be arbitrarily closely approximated by mixture inner product space valued random elements. While this concept can be applied to data in any infinite-dimensional Hilbert space, the case of functional data that are random elements in the $L^{2}$ space of square integrable functions is of special interest. For functional data, mixture inner product spaces provide a new perspective, where each realization of the underlying stochastic process falls into one of the component spaces and is represented by a finite number of basis functions, the number of which corresponds to the dimension of the component space. In the mixture representation of functional data, the number of included mixture components used to represent a given random element in $L^{2}$ is specifically adapted to each random trajectory and may be arbitrarily large. Key benefits of this novel approach are, first, that it provides a new perspective on the construction of a probability density in function space under mild regularity conditions, and second, that individual trajectories possess a trajectory-specific dimension that corresponds to a latent random variable, making it possible to use a larger number of components for less smooth and a smaller number for smoother trajectories. This enables flexible and parsimonious modeling of heterogeneous trajectory shapes. We establish estimation consistency of the functional mixture density and introduce an algorithm for fitting the functional mixture model based on a modified expectation-maximization algorithm. Simulations confirm that in comparison to traditional functional principal component analysis the proposed method achieves similar or better data recovery while using fewer components on average. Its practical merits are also demonstrated in an analysis of egg-laying trajectories for medflies.

Pricing bond options in emerging markets: A case study

We propose two methodologies to price sovereign bond options in emerging markets. The motivation is to provide hedging protection against price fluctuations, departing from the not liquid data provided by the stock exchange. Taking this into account, we first compute prices provided by the Jamshidian formula, when modeling the interest rate through Vasicek model, with parameters estimated with the help of the Kalman filter. The second methodology is the pricing strategy provided by the Black-Derman-Toy tree model. A numerical comparison is carried out. The first equilibrium approach provides parsimonious modeling, is less sensitive to daily changes and more robust, while the second non-arbitrage approach provides more fluctuating but also what can be considered more accurate option prices.

FlexCWM: A Flexible Framework for Cluster-Weighted Models

Cluster-weighted models (CWMs) are mixtures of regression models with random covariates. However, besides having recently become rather popular in statistics and data mining, there is still a lack of support for CWMs within the most popular statistical suites. In this paper, we introduce flexCWM, an R package specifically conceived for fitting CWMs. The package supports modeling the conditioned response variable by means of the most common distributions of the exponential family and by the t distribution. Covariates are allowed to be of mixed-type and parsimonious modeling of multivariate normal covariates, based on the eigenvalue decomposition of the component covariance matrices, is supported. Furthermore, either the response or the covariates distributions can be omitted, yielding to mixtures of distributions and mixtures of regression models with fixed covariates, respectively. The expectation-maximization (EM) algorithm is used to obtain maximum-likelihood estimates of the parameters and likelihood-based information criteria are adopted to select the number of groups and/or a parsimonious model. For the component regression coefficients, standard errors and significance tests are also provided. Parallel computation can be used on multicore PCs and computer clusters, when several models have to be fitted. To exemplify the use of the package, applications to artificial and real datasets, included in the package, are presented.

High-Dimensional Mixture Models for Unsupervised Image Denoising (HDMI)

This work addresses the problem of patch-based image denoising through the unsupervised learning of a probabilistic high-dimensional mixture model on the noisy patches. The model, called HDMI, proposes a full modeling of the process that is supposed to have generated the noisy patches. To overcome the potential estimation problems due to the high dimension of the patches, the HDMI model adopts a parsimonious modeling which assumes that the data live in group-specific subspaces of low dimensionalities. This parsimonious modeling allows us in turn to get a numerically stable computation of the conditional expectation of the image which is applied for denoising. The use of such a model also permits us to rely on model selection tools, such as BIC, to automatically determine the intrinsic dimensions of the subspaces and the variance of the noise. This yields a denoising algorithm that can be used both when the noise level is known and is unknown.

Large‐Scale Experiments in Microbially Induced Calcite Precipitation (MICP): Reactive Transport Model Development and Prediction

AbstractDesign of in situ microbially induced calcite precipitation (MICP) strategies relies on a predictive capability. To date much of the mathematical modeling of MICP has focused on small‐scale experiments and/or one‐dimensional flow in porous media, and successful parameterizations of models in these settings may not pertain to larger scales or to nonuniform, transient flows. Our objective in this article is to report on modeling to test our ability to predict behavior of MICP under controlled conditions in a meter‐scale tank experiment with transient nonuniform transport in a natural soil, using independently determined parameters. Flow in the tank was controlled by three wells, via a complex cycle of injection/withdrawals followed by no‐flow intervals. Different injection solution recipes were used in sequence for transport characterization, biostimulation, cementation, and groundwater rinse phases of the 17 day experiment. Reaction kinetics were calibrated using separate column experiments designed with a similar sequence of phases. This allowed for a parsimonious modeling approach with zero fitting parameters for the tank experiment. These experiments and data were simulated using PHT3‐D, involving transient nonuniform flow, alternating low and high Damköhler reactive transport, and combined equilibrium and kinetically controlled biogeochemical reactions. The assumption that microbes mediating the reaction were exclusively sessile, and with constant activity, in conjunction with the foregoing treatment of the reaction network, provided for efficient and accurate modeling of the entire process leading to nonuniform calcite precipitation. This analysis suggests that under the biostimulation conditions applied here the assumption of steady state sessile biocatalyst suffices to describe the microbially mediated calcite precipitation.

Predicting disease Risk by Transformation Models in the Presence of Unspecified Subgroup Membership.

Some biomedical studies lead to mixture data. When a discrete covariate defining subgroup membership is missing for some of the subjects in a study, the distribution of the outcome follows a mixture distribution of the subgroup-specific distributions. Taking into account the uncertain distribution of the group membership and the covariates, we model the relation between the disease onset time and the covariates through transformation models in each sub-population, and develop a nonparametric maximum likelihood based estimation implemented through EM algorithm along with its inference procedure. We further propose methods to identify the covariates that have different effects or common effects in distinct populations, which enables parsimonious modeling and better understanding of the difference across populations. The methods are illustrated through extensive simulation studies and a real data example.

Quantitative predictions from competition theory with an incomplete knowledge of model parameters tested against experiments across diverse taxa

The capacity of community ecology for making quantitative predictions is often limited by incomplete empirical information which precludes obtaining reasonable estimates of model parameters. This is particularly the case for communities with large species richness S since it is practically impossible to perform the S monoculture experiments (to obtain the species carrying capacities) plus the S×(S−1)/2 pairwise experiments (required to estimate the entire set of interspecific interaction coefficients of the interaction or community matrix). However quantitative predictive tools are vital for understanding the fate of ecological communities.Here we derive an analytical approximation for predicting the relative yield total (or equivalently the mean relative yield) as a function of the mean intensity of the interspecific competition and the species richness. The rationale is that with incomplete information on model parameters it seems more reasonable to attempt to predict “macroscopic” or mean quantities, defined for the whole community of competing species, rather than making detailed “microscopic” predictions, like species abundances.This method, with only a fraction of the model parameters (carrying capacities and competition coefficients), is able to predict accurately empirical measurements covering a wide variety of taxa −algae, plants, protozoa, etc.Our aim with this approach is to contribute in making community ecology a more quantitative and predictive science. We argue that such parsimonious modeling is preferable than more realistic/complex theories involving additional parameters which can be very difficult to measure.

Impact of rainfall patterns and frequency on the export of pesticides and heavy-metals from agricultural soils

The combined influence of soil characteristics, pollutant aging and rainfall patterns on the export of pollutants from topsoils is poorly understood. We used laboratory experiments and parsimonious modeling to evaluate the impact of rainfall characteristics on the ponding and the leaching of a pollutant mixture from topsoils. The mixture included the fungicide metalaxyl, the herbicide S-metolachlor, as well as copper (Cu) and zinc (Zn). Four rainfall patterns, which differed in their durations and intensities, were applied twice successively with a 7days interval on each soil type. To evaluate the influence of soil type and aging, experiments included crop and vineyard soils and two stages of pollutant aging (0 and 10days). The global export of pollutants was significantly controlled by the rainfall duration and frequency (P<0.01). During the first rainfall event, the longest and most intense rainfall pattern yielded the largest export of metalaxyl (44.5±21.5% of the initial mass spiked in the soils), S-metolachlor (8.1±3.1%) and Cu (3.1±0.3%). Soil compaction caused by the first rainfall reduced in the second rainfall the leaching of remaining metalaxyl, S-metolachlor, Cu and Zn by 2.4-, 2.9-, 30- and 50-fold, respectively. In contrast, soil characteristics and aging had less influence on pollutant mass export. The soil type significantly influenced the leaching of Zn, while short-term aging impacted Cu leaching. Our results suggest that rainfall characteristics predominantly control export patterns of metalaxyl and S-metolachlor, in particular when the aging period is short. We anticipate our study to be a starting point for more systematic evaluation of the dissolved pollutant ponding/leaching partitioning and the export of pollutant mixtures from different soil types in relation to rainfall patterns.

Semiparametric Dynamic Max-Copula Model for Multivariate Time Series

SummaryThe paper presents a novel non-linear framework for the construction of flexible multivariate dependence structure (i.e. copulas) from existing copulas based on a straightforward ‘pairwise max-’rule. The newly constructed max-copula has a closed form and has strong interpretability. Compared with the classical ‘linear symmetric’ mixture copula, the max-copula can be viewed as a ‘non-linear asymmetric’ framework. It is capable of modelling asymmetric dependence and joint tail behaviour while also offering good performance in non-extremal behaviour modelling. Max-copulas that are based on single-factor and block factor models are developed to offer parsimonious modelling for structured dependence, especially in high dimensional applications. Combined with semiparametric time series models, the max-copula can be used to develop flexible and accurate models for multivariate time series. A new semiparametric composite maximum likelihood method is proposed for parameter estimation, where the consistency and asymptotic normality of estimators are established. The flexibility of the max-copula and the accuracy of the proposed estimation procedure are illustrated through extensive numerical experiments. Real data applications in value-at-risk estimation and portfolio optimization for financial risk management demonstrate the max-copula's promising ability to capture accurately joint movements of high dimensional multivariate stock returns under both normal and crisis regimes of the financial market.

Decomposing core energy factor structure of U.S. commercial buildings through clustering around latent variables with Random Forest on large-scale mixed data

Accurate selection of explanatory factors is critical for precise quantitative energy analysis (e.g. benchmarking and predicting) to support the sustainability strategy in commercial building sector. Nevertheless, the generic guiding information on factor selection lacks. This paper addresses the research gap to decompose building energy factor structure (i.e. the interaction structure among the factors which affect building energy performance) particularly at a nation level for factor selection. Specifically, an iterative approach is developed by integrating the technical strengths of Variable Clustering and Random Forest to remove collinearity, redundancy and nonrelevance. Based on a comprehensive source database extracted from a multiframe country-wide survey, the core energy factor space is revealed for 2779 commercial buildings in the U.S. In particular, 36 principal factors are identified to reliably explain building energy efficiency variations. These factors are of sufficient independence and heterogeneity which may benefit the development of parsimonious energy modeling frameworks. The robustness of the deciphered factor structure and the representativeness of the recognized critical factors are numerically validated. These acquired results can be useful for informed decision analysis and rational policy design in commercial building sector with a lighter data burden.

On estimation in some reduced rank extended growth curve models

The general multivariate analysis of variance model has been extensively studied in the statistical literature and successfully applied in many different fields for analyzing longitudinal data. In this article, we consider the extension of this model having two sets of regressors constituting a growth curve portion and a multivariate analysis of variance portion, respectively. Nowadays, the data collected in empirical studies have relatively complex structures though often demanding a parsimonious modeling. This can be achieved for example through imposing rank constraints on the regression coefficient matrices. The reduced rank regression structure also provides a theoretical interpretation in terms of latent variables. We derive likelihood based estimators for the mean parameters and covariance matrix in this type of models. A numerical example is provided to illustrate the obtained results.

Novel approach for streamflow forecasting using a hybrid ANFIS-FFA model

The present study proposes a new hybrid evolutionary Adaptive Neuro-Fuzzy Inference Systems (ANFIS) approach for monthly streamflow forecasting. The proposed method is a novel combination of the ANFIS model with the firefly algorithm asan optimizer tool to construct a hybrid ANFIS-FFA model. The results of the ANFIS-FFA model is compared with the classical ANFIS model, which utilizes the fuzzy c-means (FCM) clustering method in the Fuzzy Inference Systems (FIS) generation. The historical monthly streamflow data for Pahang River, which is a major river system in Malaysia that characterized by highly stochastic hydrological patterns, is used in the study. Sixteen different input combinations with one to five time-lagged input variables are incorporated into the ANFIS-FFA and ANFIS models to consider the antecedent seasonal variations in historical streamflow data. The mean absolute error (MAE), root mean square error (RMSE) and correlation coefficient (r) are used to evaluate the forecasting performance of ANFIS-FFA model. In conjunction with these metrics, the refined Willmott’s Index (Drefined), Nash-Sutcliffe coefficient (ENS) and Legates and McCabes Index (ELM) are also utilized as the normalized goodness-of-fit metrics. Comparison of the results reveals that the FFA is able to improve the forecasting accuracy of the hybrid ANFIS-FFA model (r=1; RMSE=0.984; MAE=0.364; ENS=1; ELM=0.988; Drefined=0.994) applied for the monthly streamflow forecasting in comparison with the traditional ANFIS model (r=0.998; RMSE=3.276; MAE=1.553; ENS=0.995; ELM=0.950; Drefined=0.975). The results also show that the ANFIS-FFA is not only superior to the ANFIS model but also exhibits a parsimonious modelling framework for streamflow forecasting by incorporating a smaller number of input variables required to yield the comparatively better performance. It is construed that the FFA optimizer can thus surpass the accuracy of the traditional ANFIS model in general, and is able to remove the false (inaccurately) forecasted data in the ANFIS model for extremely low flows. The present results have wider implications not only for streamflow forecasting purposes, but also for other hydro-meteorological forecasting variables requiring only the historical data input data, and attaining a greater level of predictive accuracy with the incorporation of the FFA algorithm as an optimization tool in an ANFIS model.

Modeling and Upscaling Plot-Scale Soil Erosion under Mediterranean Climate Variability

Soil erosion is an issue in the Mediterranean slopes. Erosion plots are useful to quantify erosion rates, but data are difficult to scale up to a slope level. Moreover, short observational frameworks are generally established, making it difficult to represent multi-year fluctuations. This paper deals with the potential of parsimonious modelling to upscale plot erosion (~23 m2) at Monte Pino Met European Research Observatory (South Italy) from 2001 to 2006. Under the assumption that the slope is fractal and contains plots, monthly gross soil erosion was modeled by lumping together the erosivity factor (runoff component), Normalized Difference Vegetation Index (vegetation cover factor), and the spatial scale dependence (slope length factor). This model was applied to reconstruct monthly gross soil erosion rates for the period of 1986–2006, for which hydrological inputs were available with sufficient detail. Pronounced interannual variations, with two distinct patterns, were observed: increasing rates of erosion were visible in 1995–2006 (peaking in November 1997, 50 Mg·ha−1·month−1), while in previous years only a few peaks slightly exceeded the average of the whole period (1 Mg·ha−1·month−1). Hydrological conditions indicate that important erosional processes have been triggered during low-frequency, short rainfall events occurring in spring–summer (e.g., May 2001, June 2003), or during longer, less intense events occurring in autumn–winter (e.g., November 1997) seasons. It is likely that increased precipitation amounts associated with more frequent convective storms created conditions for higher energy events triggering erosion. For the recent warm period, investigations at a higher than monthly resolution are required to better assess the seasonal changes of erosion rates and their relationship with soil conservation.

Modeling the isotopic evolution of snowpack and snowmelt: Testing a spatially distributed parsimonious approach.

Use of stable water isotopes has become increasingly popular in quantifying water flow paths and travel times in hydrological systems using tracer‐aided modeling. In snow‐influenced catchments, snowmelt produces a traceable isotopic signal, which differs from original snowfall isotopic composition because of isotopic fractionation in the snowpack. These fractionation processes in snow are relatively well understood, but representing their spatiotemporal variability in tracer‐aided studies remains a challenge. We present a novel, parsimonious modeling method to account for the snowpack isotope fractionation and estimate isotope ratios in snowmelt water in a fully spatially distributed manner. Our model introduces two calibration parameters that alone account for the isotopic fractionation caused by sublimation from interception and ground snow storage, and snowmelt fractionation progressively enriching the snowmelt runoff. The isotope routines are linked to a generic process‐based snow interception‐accumulation‐melt model facilitating simulation of spatially distributed snowmelt runoff. We use a synthetic modeling experiment to demonstrate the functionality of the model algorithms in different landscape locations and under different canopy characteristics. We also provide a proof‐of‐concept model test and successfully reproduce isotopic ratios in snowmelt runoff sampled with snowmelt lysimeters in two long‐term experimental catchment with contrasting winter conditions. To our knowledge, the method is the first such tool to allow estimation of the spatially distributed nature of isotopic fractionation in snowpacks and the resulting isotope ratios in snowmelt runoff. The method can thus provide a useful tool for tracer‐aided modeling to better understand the integrated nature of flow, mixing, and transport processes in snow‐influenced catchments.

Flexible Mediation Analysis With Multiple Mediators.

The advent of counterfactual-based mediation analysis has triggered enormous progress on how, and under what assumptions, one may disentangle path-specific effects upon combining arbitrary (possibly nonlinear) models for mediator and outcome. However, current developments have largely focused on single mediators because required identification assumptions prohibit simple extensions to settings with multiple mediators that may depend on one another. In this article, we propose a procedure for obtaining fine-grained decompositions that may still be recovered from observed data in such complex settings. We first show that existing analytical approaches target specific instances of a more general set of decompositions and may therefore fail to provide a comprehensive assessment of the processes that underpin cause-effect relationships between exposure and outcome. We then outline conditions for obtaining the remaining set of decompositions. Because the number of targeted decompositions increases rapidly with the number of mediators, we introduce natural effects models along with estimation methods that allow for flexible and parsimonious modeling. Our procedure can easily be implemented using off-the-shelf software and is illustrated using a reanalysis of the World Health Organization's Large Analysis and Review of European Housing and Health Status (WHO-LARES) study on the effect of mold exposure on mental health (2002-2003).

A food demand framework for International Food Security Assessment

We present a parsimonious demand modeling approach developed for the annual USDA-ERS International Food Security Assessment, a large-scale prospective assessment focusing on chronic food insecurity in 76 countries. The approach incorporates price effects, food quality variation across income deciles, and consistent aggregation over income deciles and food qualities. The approach is based on a simple demand approach for four food categories. It relies on data on food availability, complemented by own-price and income elasticities and food price data. Beyond consistent aggregation, the framework exhibits desirable characteristics: food quality is increasing with income; price and income responses become less sensitive with income; and increasing income inequality decreases average per capita food consumption. The proposed approach is illustrated for Tanzania. We assess future food insecurity in Tanzania using the calibrated model and evaluate the impact of safety net policies and their budgetary costs. Food-insecure population is estimated as well as the implied food gap expressed in calorie per day per food-insecure person as well as in total annual food volume in grain equivalent. The food gap measure gauges the depth of the chronic food insecurity.

Emergent archetype patterns of coupled hydrologic and biogeochemical responses in catchments

AbstractRelationships between in‐stream dissolved solute concentrations (C) and discharge (Q) are useful indicators of catchment‐scale processes. We combine a synthesis of observational records with a parsimonious stochastic modeling approach to test how C‐Q relationships arise from spatial heterogeneity in catchment solute sources coupled with different timescales of reactions. Our model indicates that the dominant driver of emergent archetypical dilution, enrichment, and constant C‐Q patterns was structured heterogeneity of solute sources implemented as correlation of source concentration to travel time. Regardless of the C‐Q pattern, with weak correlation between solute‐source concentration and travel time, we consistently find lower variability in C than in Q, such that the predominant solute export regime is chemostatic. Consequently, the variance in exported loads is determined primarily by variance of Q. Efforts to improve stream water quality and ecological integrity in intensely managed catchments should lead away from landscape homogenization by introducing structured source heterogeneity.