Statistical Data Modeling Research Articles

A review study of functional autoregressive models with application to energy forecasting

AbstractIn this data‐rich era, it is essential to develop advanced techniques to analyze and understand large amounts of data and extract the underlying information in a flexible way. We provide a review study on the state‐of‐the‐art statistical time series models for univariate and multivariate functional data with serial dependence. In particular, we review functional autoregressive (FAR) models and their variations under different scenarios. The models include the classic FAR model under stationarity; the FARX and pFAR model dealing with multiple exogenous functional variables and large‐scale mixed‐type exogenous variables; the vector FAR model and common functional principal component technique to handle multiple dimensional functional time series; and the warping FAR, varying coefficient‐FAR and adaptive FAR models to handle seasonal variations, slow varying effects and the more challenging cases of structural changes or breaks respectively. We present the models’ setup and detail the estimation procedure. We discuss the models’ applicability and illustrate the numerical performance using real‐world data of high‐resolution natural gas flows in the high‐pressure gas pipeline network of Germany. We conduct 1‐day and 14‐days‐ahead out‐of‐sample forecasts of the daily gas flow curves. We observe that the functional time series models generally produce stable out‐of‐sample forecast accuracy.This article is categorized under: Statistical Models > Semiparametric Models Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data

Varying-coefficient models for dynamic networks

Dynamic networks are commonly used to model relational data that are observed over time. Statistical models for such data should capture both the temporal variation of the relational system as well as the structural dependencies within each network. As a consequence, effectively making inference on dynamic networks is a computationally challenging task, and many models are intractable even for moderately sized systems. In light of these challenges, a family of dynamic network models known as varying-coefficient exponential random graph models (VCERGMs) is proposed to characterize the evolution of network topology through smoothly varying parameters. The VCERGM provides an interpretable dynamic network model that enables the inference of temporal heterogeneity in dynamic networks. Estimation of the VCERGM is achieved via maximum pseudo-likelihood techniques, thereby providing a computationally tractable strategy for statistical inference of complex dynamic networks. Furthermore, a bootstrap hypothesis testing framework is presented for testing the temporal heterogeneity of an observed dynamic network sequence. Application to the U.S. Senate co-voting network and comprehensive simulation studies both reveal that the VCERGM provides relevant and interpretable patterns and has significant advantages over existing methods.

Probabilistic and statistical data models: a basis of applied statistics methods

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Learning Models over Relational Data Using Sparse Tensors and Functional Dependencies

Integrated solutions for analytics over relational databases are of great practical importance as they avoid the costly repeated loop data scientists have to deal with on a daily basis: select features from data residing in relational databases using feature extraction queries involving joins, projections, and aggregations; export the training dataset defined by such queries; convert this dataset into the format of an external learning tool; and train the desired model using this tool. These integrated solutions are also a fertile ground of theoretically fundamental and challenging problems at the intersection of relational and statistical data models. This article introduces a unified framework for training and evaluating a class of statistical learning models over relational databases. This class includes ridge linear regression, polynomial regression, factorization machines, and principal component analysis. We show that, by synergizing key tools from database theory such as schema information, query structure, functional dependencies, recent advances in query evaluation algorithms, and from linear algebra such as tensor and matrix operations, one can formulate relational analytics problems and design efficient (query and data) structure-aware algorithms to solve them. This theoretical development informed the design and implementation of the AC/DC system for structure-aware learning. We benchmark the performance of AC/DC against R, MADlib, libFM, and TensorFlow. For typical retail forecasting and advertisement planning applications, AC/DC can learn polynomial regression models and factorization machines with at least the same accuracy as its competitors and up to three orders of magnitude faster than its competitors whenever they do not run out of memory, exceed 24-hour timeout, or encounter internal design limitations.

Cross-tier personal gains in mixed electoral systems

ABSTRACT We extend the research on contamination effects in mixed-member electoral systems by considering the impact of “dual candidacies” in systems that combine SMD and open-list PR rules. We make three claims. First, we argue that dual-listed candidates have incentives to run campaigns that enable them to maximize their share of personal votes in both tiers. Second, the effect of a dual listing is conditioned by incumbency and party-list position. Finally, we argue that parties themselves benefit from strong dual candidates in the PR list election itself. To test our argument, we analyze the 2016 Lithuanian parliamentary election. Using elite interviews and statistical models of electoral data, our analysis supports our claims. We provide important contribution to contamination literature by demonstrating that parties received a direct, list-tier benefit from nominating SMD candidates, who successfully build personal vote coalitions.

On the Analysis of New COVID-19 Cases in Pakistan Using an Exponentiated Version of the M Family of Distributions

This paper develops the exponentiated Mfamily of continuous distributions, aiming to provide new statistical models for data fitting purposes. It stands out from the other families, as it depends on two baseline distributions, with the use of ratio and power transforms in the definition of the main cumulative distribution function. Thanks to the joint action of the possibly different baseline distributions, flexible statistical models can be created, motivating a complete study in this regard. Thus, we discuss the theoretical properties of the new family, with emphasis on those of potential interest to the overall probability and statistics. Then, a new three-parameter lifetime distribution is derived, with the choices of the inverse exponential and exponential distributions as baselines. After pointing out the great flexibility of the related model, we apply it to analyze an actual dataset of current interest: the daily COVID-19 cases observed in Pakistan from 21 March to 29 May 2020 (inclusive). As notable results, we demonstrate that the proposed model is the best among the 15 top ranked models in the literature, including the inverse exponential and exponential models, several modern extensions of them depending on more parameters, and the “unexponentiated” version of the proposed model as well. As future perspectives, the proposed model can be of interest to analyze data on COVID-19 cases in other countries, for possible comparison studies.

Real Smart Home Data-Assisted Statistical Traffic Modeling for the Internet of Things

The majority of practical studies and analyses in the context of the Internet of Things (IoT) have been carried out assuming that data packet generation follows theoretical models (typically a Poisson process with exponentially distributed packet interarrival times) without previous experimental validation and supporting evidence. In contrast to this approach, this article proposes a novel experimental and mathematical framework to determine statistical models for IoT data traffic. Based on empirical data generated by common smart home devices (e.g., ambient temperature, luminous intensity, atmospheric pressure, and motion sensors) recorded over a full year using an experimental IoT subsystem, this article first shows that real IoT traffic does not follow the Poisson process model conventionally assumed in the literature, but rather depends on the type of application. Consequently, we estimate the empirical statistical distribution of the interarrival between data packets for several smart home applications. The empirical distribution of the packet interarrival times is fitted with some well-established classical statistical distributions using the method of moments as well as maximum-likelihood estimation techniques, and the goodness of fit is quantified using the Kolmogorov–Smirnov (KS) test. Moreover, we also carry out a regression analysis to provide mathematical relations between the distribution parameters and the considered physical input parameters (ambient temperature, luminous intensity, and atmospheric pressure), which is particularly useful in practical scenarios. Furthermore, an exhaustive analysis of the variation of parameters over different time scales and the autocorrelation characteristics of the data packet generation are included as well. In summary, this article provides accurate traffic models suitable for real-life IoT scenarios that can be used for an adequate design and optimization of future communication networks to efficiently support IoT services.

Meaningful Modeling of Section Bus Running Times by Time Varying Mixture Distributions of Fixed Components

Understanding the variability of bus travel time is a key issue in the optimization of schedules, transit reliability, route choice analysis, and transit simulation. The statistical modeling of bus travel time data is of increasing importance given the increasing availability of data. In this paper, we introduce a novel approach to modeling the day-to-day variability of urban bus running times on a section level. First, the explanatory power of conventionally used distributions is examined, based on likelihood and effect size. We show that a mixture model is a powerful tool to increase fitting performance, but the applied components need to be justified. To overcome this issue, we propose a novel model consisting of two individual characteristic distributions representing either off-peak or peak hour dynamics. The observed running time distribution at every hour of the day can be described as a combination (mixture) of the two dynamics. The proposed time varying model uses a small set of parameters, which are physically interpretable and capable of accurately describing running time distributions. With our modeling approach, we reduce the complexity of mixture models and increase the explanatory power and fit compared with conventional models.

Comparison of statistical and machine learning models for healthcare cost data: a simulation study motivated by Oncology Care Model (OCM) data

BackgroundThe Oncology Care Model (OCM) was developed as a payment model to encourage participating practices to provide better-quality care for cancer patients at a lower cost. The risk-adjustment model used in OCM is a Gamma generalized linear model (Gamma GLM) with log-link. The predicted value of expense for the episodes identified for our academic medical center (AMC), based on the model fitted to the national data, did not correlate well with our observed expense. This motivated us to fit the Gamma GLM to our AMC data and compare it with two other flexible modeling methods: Random Forest (RF) and Partially Linear Additive Quantile Regression (PLAQR). We also performed a simulation study to assess comparative performance of these methods and examined the impact of non-linearity and interaction effects, two understudied aspects in the field of cost prediction.MethodsThe simulation was designed with an outcome of cost generated from four distributions: Gamma, Weibull, Log-normal with a heteroscedastic error term, and heavy-tailed. Simulation parameters both similar to and different from OCM data were considered. The performance metrics considered were the root mean square error (RMSE), mean absolute prediction error (MAPE), and cost accuracy (CA). Bootstrap resampling was utilized to estimate the operating characteristics of the performance metrics, which were described by boxplots.ResultsRF attained the best performance with lowest RMSE, MAPE, and highest CA for most of the scenarios. When the models were misspecified, their performance was further differentiated. Model performance differed more for non-exponential than exponential outcome distributions.ConclusionsRF outperformed Gamma GLM and PLAQR in predicting overall and top decile costs. RF demonstrated improved prediction under various scenarios common in healthcare cost modeling. Additionally, RF did not require prespecification of outcome distribution, nonlinearity effect, or interaction terms. Therefore, RF appears to be the best tool to predict average cost. However, when the goal is to estimate extreme expenses, e.g., high cost episodes, the accuracy gained by RF versus its computational costs may need to be considered.

Co-evolution of work structure and process in organizations: improvisation in post-disaster debris removal operations

This study examines the performance of cognitive work—as constrained by physical, policy and resource-related factors—in the near-simultaneous design and execution of disaster response operations. The demands of the situation described here—the removal of debris from a high-value barrier island in the US state of New York after Hurricane Sandy (2012)—lay at the far boundaries of the responding organizations’ experience, making this case an excellent candidate for study. Data are analyzed on the deliberative processes of the responding organization in order to characterize the interaction between the design and operation of the debris removal network over time. Statistical data modeling of these processes reveals a number of temporal dependencies between ideation and decision-making processes, as well as between components of the system. The illumination and quantification of these processes using data produced through normal operations contributes significantly to theories of the cognitive and behavioral phenomena that underlie organizational response to highly non-routine events, thus building upon broader theories of organizational improvisation and performance.

Bayesian inference on the parameters of the truncated normal distribution and application to reverberation chamber measurement data

Assessing the performance of reverberation chambers (RCs) is a continuous problem which requires constant development and analysis. Several performance indicators exist, have been proposed and continue to be proposed in the literature. Each one of these indicators exhibits different levels of applicability, robustness or relevance towards a particular aspect of the field (statistical) behavior inside the RC. In this paper, we address this problem by introducing an alternative methodology able to estimate the distribution of the statistical parameters of interest. The methodology is based on Bayesian inference and it is applied to two different statistical models for RC measurement data and to two different loading conditions. The present paper is a significant expansion of a relevant abstract presented at the ‘Mathematical and Statistical Methods for Metrology’ Workshop, Torino, Italy, 30–31 May 2019. The corresponding abstract can be found at http://www.msmm2019.polito.it/programme.

Bayesian statistical models for community annoyance survey data

This paper demonstrates the use of two Bayesian statistical models to analyze single-event sonic boom exposure and human annoyance data from community response surveys. Each model is fit to data from a NASA pilot study. Unlike many community noise surveys, this study used a panel sample to collect multiple observations per participant instead of a single observation. Thus, a multilevel (also known as hierarchical or mixed-effects) model is used to account for the within-subject correlation in the panel sample data. This paper describes a multilevel logistic regression model and a multilevel ordinal regression model. The paper also proposes a method for calculating a summary dose-response curve from the multilevel models that represents the population. The two models' summary dose-response curves are visually similar. However, their estimates differ when calculating the noise dose at a fixed percent highly annoyed.

Intermittent Absence of Control during Reinforcement Learning Interferes with Pavlovian Bias in Action Selection.

The ability to control the occurrence of rewarding and punishing events is crucial for our well-being. Two ways to optimize performance are to follow heuristics like Pavlovian biases to approach reward and avoid loss or to rely more on slowly accumulated stimulus-action associations. Although reduced control over outcomes has been linked to suboptimal decision-making in clinical conditions associated with learned helplessness, it is unclear how uncontrollability of the environment is related to the arbitration between different response strategies. This study directly tested whether a behavioral manipulation designed to induce learned helplessness in healthy adults (intermittent loss of control over feedback in a reinforcement learning task; "yoking") would modulate the magnitude of Pavlovian bias and the neurophysiological signature of cognitive control (frontal midline theta power) in healthy adults. Using statistical analysis and computational modeling of behavioral data and electroencephalographic signals, we found stronger Pavlovian influences and alterations in frontal theta activity in the yoked group. However, these effects were not accompanied by reduced performance in experimental blocks with regained control, indicating that our behavioral manipulation was not potent enough for inducing helplessness and impaired coping ability with task demands. We conclude that the level of contingency between instrumental choices and rewards/punishments modulates Pavlovian bias during value-based decision-making, probably via interfering with the implementation of cognitive control. These findings might have implications for understanding the mechanisms underlying helplessness in various psychiatric conditions.

Defining specialism and functional species groups in birds: First steps toward a farmland bird indicator

Although farmland birds are used extensively in Europe as an indicator group to assess agricultural impacts on ecosystems, no such group has been formally identified in North America. Here we present a hierarchical framework to identify a suite of farmland bird species in Ontario, Canada by consolidating and validating classifications derived from literature review and empirical modelling. First, we reviewed literature to compile candidate farmland bird species in Ontario and assigned species to four guilds (row crop specialists, pasture specialists, farmstead specialists, and farmland edge generalists). Second, we used regression trees (RTs) to test whether these species could be classified into the same literature-based guilds or different guilds, based on modelled relationships between breeding bird atlas abundance data and Census of Agriculture statistics. We consolidated both classifications using a decision tree into a final list of 45 farmland bird species, comprising 11 farmstead specialists, 13 pasture specialists, 5 row crop specialists, 12 farmland edge generalists, and 4 farmland generalists flagged for classification uncertainty. To validate the distinctness of the assigned farmland bird guilds, we used pairwise permANOVA to test for differences in species composition among guilds, based on 34 species with sufficient occurrence data. We found significant compositional differences between almost all guilds, except for the farmstead specialist and row crop specialist guilds which could not be differentiated. We also validated species’ guild assignments using canonical analysis of principal coordinates (CAP) to group 35 species according to ecological resemblance which were then compared to our proposed guild classifications. CAP validated guild assignments for 78.2% of the evaluated farmland specialists, particularly for farmstead specialists and pasture specialists, while 50% of evaluated farmland edge generalists were grouped differently than our final classification. Each final classification was associated with low, moderate, or high uncertainty according to concordance between classification methods and support from CAP groupings to highlight species with uncertainly assigned guilds. For some such species, mismatches between their literature-based and empirically-derived classifications might be due to the predictor variables being measured at too large a scale to reflect associations between their abundance distributions and agricultural landscape characteristics. We recommend that these farmland bird species be further verified using statistical models of bird count data, satellite imagery, and climate variables, and a trait-based approach to bolster confidence in the proposed list. When confirmed and expanded, this list can be used to inform a farmland bird indicator to monitor agroecosystem health in Ontario, and perhaps elsewhere in eastern North America.

Statistical Modeling of Longitudinal Data with Non-ignorable Non-monotone Missingness with Semiparametric Bayesian and Machine Learning Components.

In longitudinal studies, outcomes are measured repeatedly over time and it is common that not all the patients will be measured throughout the study. For example patients can be lost to follow-up (monotone missingness) or miss one or more visits (non-monotone missingness); hence there are missing outcomes. In the longitudinal setting, we often assume the missingness is related to the unobserved data, which is non-ignorable. Pattern-mixture models (PMM) analyze the joint distribution of outcome and patterns of missingness in longitudinal data with non-ignorable nonmonotone missingness. Existing methods employ PMM and impute the unobserved outcomes using the distribution of observed outcomes, conditioned on missing patterns. We extend the existing methods using latent class analysis (LCA) and a shared-parameter PMM. The LCA groups patterns of missingness with similar features and the shared-parameter PMM allows a subset of parameters to be different between latent classes when fitting a model. We also propose a method for imputation using distribution of observed data conditioning on latent class. Our model improves existing methods by accommodating data with small sample size. In a simulation study our estimator had smaller mean squared error than existing methods. Our methodology is applied to data from a phase II clinical trial that studies quality of life of patients with prostate cancer receiving radiation therapy.

Parametric prediction of finite population total under Informative sampling and nonignorable nonresponse

Abstract In this paper, we combine two methodologies used in the model-based survey sampling, namely the prediction of the finite population total, named T, under informative sampling and full response, see Sverchkov and Pfeffermann (2004), and the prediction of T with a noninformative sampling design and the nonignorable nonresponse mechanism, see Eideh (2012). The former approach involves the dependence of the first order inclusion probabilities on the study variable, while the latter involves the dependence of the probability of nonresponse on unobserved or missing observations. The main aim of the paper is to consider how to account for the joint effects of informative sampling designs and not-missing-at-random response mechanism in statistical models for complex survey data. For this purpose, theoretically, we use the response distribution and relationships between the moments of the superpopoulation, the sample, sample-complement, response, and nonresponse distributions for the prediction of finite population totals, see Eideh (2016). The derived parametric predictors of T use the observation for the response set of the study variable or variable of interest, values of auxiliary variables and their population totals, sampling weights, and propensity scores. An interesting outcome of the T study is that most predictors known from model-based survey sampling can be derived as a special case from this general theory, see Chambers and Clark (2012).

Monitoring of Social Network and Change Detection by Applying Statistical Process: ERGM

The statistical modeling of social network data needs much effort because of the complex dependence structure of the tie variables. In order to formulate such dependences, the statistical exponential families of distributions can provide a flexible structure. In this regard, the statistical characteristics of the network is provided to be encapsulated within an Exponential Random Graph Model (ERGM). Applying the ERGM, in this paper, we follow to design a statistical process control through network behavior. The results demonstrated the superiority of the designed chart over the existing change detection methods in controlling the states. Additionally, the detection process is formulated for the social networks and the results are statistically analyzed.

Malignancy prediction among tissues from Oral SCC patients including neck invasions: a 1H HRMAS NMR based metabolomic study.

Oral cancer is a sixth commonly occurring cancer globally. The use of tobacco and alcohol consumption are being considered as the major risk factors for oral cancer. The metabolic profiling of tissue specimens for developing carcinogenic perturbations will allow better prognosis. To profile and generate precise 1H HRMAS NMR spectral and quantitative statistical models of oral squamous cell carcinoma (OSCC) in tissue specimens including tumor, bed, margin and facial muscles. To apply the model in blinded prediction of malignancy among oral and neck tissues in an unknown set of patients suffering from OSCC along with neck invasion. Statistical models of 1H HRMAS NMR spectral data on 180 tissues comprising tumor, margin and bed from 43 OSCC patients were performed. The combined metabolites, lipids spectral intensity and concentration-based malignancy prediction models were proposed. Further, 64 tissue specimens from twelve patients, including neck invasions, were tested for malignancy in a blinded manner. Forty-eight metabolites including lipids have been quantified in tumor and adjacent tissues. All metabolites other than lipids were found to be upregulated in malignant tissues except for ambiguous glucose. All of three prediction models have successfully identified malignancy status among blinded set of 64 tissues from 12 OSCC patients with an accuracy of above 90%. The efficiency of the models in malignancy prediction based on tumor induced metabolic perturbations supported by histopathological validation may revolutionize the OSCC assessment. Further, the results may enable machine learning to trace tumor induced altered metabolic pathways for better pattern recognition. Thus, it complements the newly developed REIMS-MS iKnife real time precession during surgery.

Prediction of compressive strength of mortar near sodium chloride by artificial neural network

The compressive strength value of cement mortar is usually affected by the amount of sodium chloride, chemical admixture and cement grade. Therefore, the artificial neural network model is used to predict the mortar strength values of different cement grades and sodium chloride (NaCl) content. In order to predict the compressive strength of the mortar, an artificial neural network model of cement grade, different water-cement ratio, sodium chloride solution content, an output neuron and four input neurons was established. After immersion in 0%, 5%, and 10% sodium trichloride solution for 60 days, the compressive strength was measured using 12 different ratios. Artificial neural network (ANN) analysis shows that ANN as a nonlinear statistical data modeling tool can establish a strong correlation between sodium chloride content and compressive strength of cement mortar. In addition, modeling tools have a greater impact on different cement grades (42.5, 32.5 MPa).

Objective prior distributions for Jolly-Seber models of zero-augmented data.

Statistical models of capture-recapture data that are used to estimate the dynamics of a population are known collectively as Jolly-Seber (JS) models. State-space versions of these models have been developed for the analysis of zero-augmented data that include the capture histories of the observed individuals and an arbitrarily large number of all-zero capture histories. The number of all-zero capture histories must be sufficiently large to include the unknown number N of individuals in the population that were ever alive during all sampling periods. This definition of N is equivalent to the "superpopulation" of individuals described in several JS models. To fit JS models of zero-augmented data, practitioners often assume a set of independent, uniform prior distributions for the recruitment parameters. However, if the number of capture histories is small compared to N, these uniform priors can exert considerable influence on the posterior distributions of N and other parameters because the uniform priors induce a highly skewed prior on N. In this article, I derive a class of prior distributions for the recruitment parameters of the JS model that can be used to specify objective prior distributions for N, including the discrete-uniform and the improper scale priors as special cases. This class of priors also may be used to specify prior knowledge about recruitment while still preserving the conditions needed to induce an objective prior on N. I use analyses of simulated and real data to illustrate the inferential benefits of this class of prior distributions and to identify circumstances where these benefits are most likely to berealized.