Abstract: Multistate models are increasingly being used to model complex disease profiles. By modelling transitions between disease states, accounting for competing events at each transition, we can gain a much richer understanding of patient trajectories and how risk factors impact over the entire disease pathway. In this article, we concentrate on parametric multistate models, both Markov and semi-Markov, and develop a flexible framework where each transition can be specified by a variety of parametric models including exponential, Weibull, Gompertz, Royston-Parmar proportional hazards models or log-logistic, log-normal, generalised gamma accelerated failure time models, possibly sharing parameters across transitions. We also extend the framework to allow time-dependent effects. We then use an efficient and generalisable simulation method to calculate transition probabilities from any fitted multistate model, and show how it facilitates the simple calculation of clinically useful measures, such as expected length of stay in each state, and differences and ratios of proportion within each state as a function of time, for specific covariate patterns. We illustrate our methods using a dataset of patients with primary breast cancer. User-friendly Stata software is provided.

Abstract: Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.

Abstract: We study data-driven methods for community detection in graphs. This estimation problem is typically formulated in terms of the spectrum of certain operators, as well as via posterior inference under certain probabilistic graphical models. Focusing on random graph families such as the Stochastic Block Model, recent research has unified these two approaches, and identified both statistical and computational signal-to-noise detection thresholds. We embed the resulting class of algorithms within a generic family of graph neural networks and show that they can reach those detection thresholds in a purely data-driven manner, without access to the underlying generative models and with no parameter assumptions. The resulting model is also tested on real datasets, requiring less computational steps and performing significantly better than rigid parametric models.

Abstract: This paper proposes a pole-residue-based adjoint neuro-transfer function (neuro-TF) technique with electromagnetic (EM) sensitivity analysis for parametric modeling of EM behavior of microwave components with respect to changes in geometrical parameters. The purpose is to increase model accuracy by utilizing EM sensitivity information and to speed up model development by reducing the number of training data required for developing the model. The proposed parametric model consists of original and adjoint pole-residue based neuro-TF models. New formulations are derived for calculating the second-order derivatives for training the adjoint pole-residue-based neuro-TF model. An advanced pole-residue tracking technique is proposed to exploit the sensitivity information to track the splitting of poles as geometrical parameters change. This pole-residue tracking technique allows the model to bridge the differences of the orders of transfer function over different regions of the geometrical parameters, and ultimately form smooth and continuous functions between the pole/residues and the geometrical variables. The proposed technique addresses the challenges of tracking pole splitting when training data are limited. By exploiting the sensitivity information, the proposed technique can speed up the model development process over the existing pole-residue parametric modeling method which does not use sensitivity analysis.

Abstract: More than three decades of observations of tropical cyclone wind and wave fields have resulted in a detailed understanding of wave-growth dynamics, although details of the physics are still lacking. These observations are presented in a consistent manner, which provides the basis to be able to characterize the full wave spectrum in a parametric form throughout tropical cyclones. The data clearly shows that an extended fetch model can be used to represent the maximum significant wave height in such storms. The shape stabilizing influence of nonlinear interactions means that the spectral shape is remarkably similar to fetch-limited cases. As such, the tropical cyclone spectrum can also be described by using well-known parametric models. A detailed process is described to parameterize the wave spectrum at any point in a tropical cyclone.

Abstract: Under the inspiration of polar coordinates, a novel parametric modeling and optimization method for Savonius wind turbines was proposed to obtain the highest power output, in which a quadratic polynomial curve was bent to describe a blade. Only two design parameters are needed for the shape-complicated blade. Therefore, this novel method reduces sampling scale. A series of transient simulations was run to get the optimal performance coefficient (power coefficient C p) for different modified turbines based on computational fluid dynamics (CFD) method. Then, a global response surface model and a more precise local response surface model were created according to Kriging Method. These models defined the relationship between optimization objective Cp and design parameters. Particle swarm optimization (PSO) algorithm was applied to find the optimal design based on these response surface models. Finally, the optimal Savonius blade shaped like a “hook” was obtained. Cm (torque coefficient), Cp and flow structure were compared for the optimal design and the classical design. The results demonstrate that the optimal Savonius turbine has excellent comprehensive performance. The power coefficient Cp is significantly increased from 0.247 to 0.262 (6% higher). The weight of the optimal blade is reduced by 17.9%.

Abstract: One of the major challenges in computational science is to determine the uncertainty of a virtual measurement, that is the prediction of an observable based on calculations. As highly accurate first-principles calculations are in general unfeasible for most physical systems, one usually resorts to parameteric property models of observables, which require calibration by incorporating reference data. The resulting predictions and their uncertainties are sensitive to systematic errors such as inconsistent reference data, parametric model assumptions, or inadequate computational methods. Here, we discuss the calibration of property models in the light of bootstrapping, a sampling method that can be employed for identifying systematic errors and for reliable estimation of the prediction uncertainty. We apply bootstrapping to assess a linear property model linking the 57Fe Mossbauer isomer shift to the contact electron density at the iron nucleus for a diverse set of 44 molecular iron compounds. The contact ele...

Abstract: In complicated/nonlinear parametric models, it is generally hard to know whether the model parameters are point identified. We provide computationally attractive procedures to construct confidence sets (CSs) for identified sets of full parameters and of subvectors in models defined through a likelihood or a vector of moment equalities or inequalities. These CSs are based on level sets of optimal sample criterion functions (such as likelihood or optimally-weighted or continuously-updated GMM criterions). The level sets are constructed using cutoffs that are computed via Monte Carlo (MC) simulations directly from the quasi-posterior distributions of the criterions. We establish new Bernstein-von Mises (or Bayesian Wilks) type theorems for the quasi-posterior distributions of the quasi-likelihood ratio (QLR) and profile QLR in partially-identified regular models and some non-regular models. These results imply that our MC CSs have exact asymptotic frequentist coverage for identified sets of full parameters and of subvectors in partially-identified regular models, and have valid but potentially conservative coverage in models with reduced-form parameters on the boundary. Our MC CSs for identified sets of subvectors are shown to have exact asymptotic coverage in models with singularities. We also provide results on uniform validity of our CSs over classes of DGPs that include point and partially identified models. We demonstrate good finite-sample coverage properties of our procedures in two simulation experiments. Finally, our procedures are applied to two non-trivial empirical examples: an airline entry game and a model of trade flows.

Abstract: We study the framework for semi-parametric estimation and statistical inference for the sample average treatment-specific mean effects in observational settings where data are collected on a single network of connected units (e.g., in the presence of interference or spillover). Despite recent advances, many of the current statistical methods rely on estimation techniques that assume a particular parametric model for the outcome, even though some of the most important statistical assumptions required by these models are most likely violated in the observational network settings, often resulting in invalid and anti-conservative statistical inference. In this manuscript, we rely on the recent methodological advances for the targeted maximum likelihood estimation (TMLE) of causal effects in a network of causally connected units, to describe an estimation approach that permits for more realistic classes of data-generative models and provides valid statistical inference in the context of network-dependent data. The approach is applied to an observational setting with a single time point stochastic intervention. We start by assuming that the true observed data-generating distribution belongs to a large class of semi-parametric statistical models. We then impose some restrictions on the possible set of the data-generative distributions that may belong to our statistical model. For example, we assume that the dependence among units can be fully described by the known network, and that the dependence on other units can be summarized via some known (but otherwise arbitrary) summary measures. We show that under our modeling assumptions, our estimand is equivalent to an estimand in a hypothetical iid data distribution, where the latter distribution is a function of the observed network data-generating distribution. With this key insight in mind, we show that the TMLE for our estimand in dependent network data can be described as a certain iid data TMLE algorithm, also resulting in a new simplified approach to conducting statistical inference. We demonstrate the validity of our approach in a network simulation study. We also extend prior work on dependent-data TMLE towards estimation of novel causal parameters, e.g., the unit-specific direct treatment effects under interference and the effects of interventions that modify the initial network structure.

Abstract: We address the issue of reliably detecting and quantifying cross-frequency coupling (CFC) in neural time series. Based on non-linear auto-regressive models, the proposed method provides a generative and parametric model of the time-varying spectral content of the signals. As this method models the entire spectrum simultaneously, it avoids the pitfalls related to incorrect filtering or the use of the Hilbert transform on wide-band signals. As the model is probabilistic, it also provides a score of the model "goodness of fit" via the likelihood, enabling easy and legitimate model selection and parameter comparison; this data-driven feature is unique to our model-based approach. Using three datasets obtained with invasive neurophysiological recordings in humans and rodents, we demonstrate that these models are able to replicate previous results obtained with other metrics, but also reveal new insights such as the influence of the amplitude of the slow oscillation. Using simulations, we demonstrate that our parametric method can reveal neural couplings with shorter signals than non-parametric methods. We also show how the likelihood can be used to find optimal filtering parameters, suggesting new properties on the spectrum of the driving signal, but also to estimate the optimal delay between the coupled signals, enabling a directionality estimation in the coupling.

Abstract: A new parametric model is developed to describe the wind field asymmetry commonly observed in tropical cyclones or hurricanes in a reference frame fixed at its center. Observations from 21 hurricanes from the North Atlantic basin and TC Roger (1993) in the Coral Sea are analyzed to determine the azimuthal and radial asymmetry typical in these mesoscale systems after removing the forward speed. On the basis of the observations, a new asymmetric directional wind model is proposed which adjusts the widely used Holland (1980) axisymmetric wind model to account for the action of blocking high-pressure systems, boundary layer friction, and forward speed. The model is tested against the observations and demonstrated to capture the physical features of asymmetric cyclones and provides a better fit to observed winds than the Holland model. Optimum values and distributions of the model parameters are derived for use in statistical modeling. Finally, the model is used to investigate the asymmetric character of TC systems, including the azimuth of the maximum wind speed, the degree of asymmetry, and the relationship between asymmetry and forward speed.

Abstract: In this paper, we introduce the system operational dependency analysis methodology. Its purpose is to assess the effect of dependencies between components in a monolithic complex system, or between systems in a system-of-systems, and to support design decision making. We propose a parametric model of the behavior of the system. This approach results in a simple, intuitive model, whose parameters give a direct insight into the causes of observed, and possibly emergent, behavior. Using the proposed method, designers, and decision makers can quickly analyze and explore the behavior of complex systems and evaluate different architecture under various working conditions. Thus, the system operational dependency analysis method supports educated decision making both in the design and in the update process of systems architecture, without the need to execute extensive simulations. In particular, in the phase of concept generation and selection, the information given by the method can be used to identify promising architectures to be further tested and improved, while discarding architectures that do not show the required level of global features. Application of the proposed method to a small example is used to demonstrate both the validation of the parametric model, and the capabilities of the method for system analysis, design and architecture.

Abstract: Marginal structural models (MSMs) are a general class of causal models for specifying the average effect of treatment on an outcome. These models can accommodate discrete or continuous treatments, as well as treatment effect heterogeneity (causal effect modification). The literature on estimation of MSM parameters has been dominated by semiparametric estimation methods, such as inverse probability of treatment weighted (IPTW). Likelihood-based methods have received little development, probably in part due to the need to integrate out confounders from the likelihood and due to reluctance to make parametric modeling assumptions. In this article we develop a fully Bayesian MSM for continuous and survival outcomes. In particular, we take a Bayesian nonparametric (BNP) approach, using a combination of a dependent Dirichlet process and Gaussian process to model the observed data. The BNP approach, like semiparametric methods such as IPTW, does not require specifying a parametric outcome distribution. Moreover, by using a likelihood-based method, there are potential gains in efficiency over semiparametric methods. An additional advantage of taking a fully Bayesian approach is the ability to account for uncertainty in our (uncheckable) identifying assumption. To this end, we propose informative prior distributions that can be used to capture uncertainty about the identifying "no unmeasured confounders" assumption. Thus, posterior inference about the causal effect parameters can reflect the degree of uncertainty about this assumption. The performance of the methodology is evaluated in several simulation studies. The results show substantial efficiency gains over semiparametric methods, and very little efficiency loss over correctly specified maximum likelihood estimates. The method is also applied to data from a study on neurocognitive performance in HIV-infected women and a study of the comparative effectiveness of antihypertensive drug classes.

Abstract: An accurate probability distribution model of wind speed is critical to the assessment of reliability contribution of wind energy to power systems. Most of current models are built using the parametric density estimation (PDE) methods, which usually assume that the wind speed are subordinate to a certain known distribution (e.g. Weibull distribution and Normal distribution) and estimate the parameters of models with the historical data. This paper presents a kernel density estimation (KDE) method which is a nonparametric way to estimate the probability density function (PDF) of wind speed. The method is a kind of data-driven approach without making any assumption on the form of the underlying wind speed distribution, and capable of uncovering the statistical information hidden in the historical data. The proposed method is compared with three parametric models using wind data from six sites. The results indicate that the KDE outperforms the PDE in terms of accuracy and flexibility in describing the long-term wind speed distributions for all sites. A sensitivity analysis with respect to kernel functions is presented and Gauss kernel function is proved to be the best one. Case studies on a standard IEEE reliability test system (IEEE-RTS) have verified the applicability and effectiveness of the proposed model in evaluating the reliability performance of wind farms.

Abstract: The extended illness-death model is a useful tool to study the risks and consequences of hospital-acquired infections (HAIs). The statistical quantities of interest are the transition-specific hazard rates and the transition probabilities as well as attributable mortality (AM) and the population-attributable fraction (PAF). In the most general case calculation of these expressions is mathematically complex. When assuming time-constant hazards calculation of the quantities of interest is facilitated. In this situation the transition probabilities can be expressed in closed mathematical forms. The estimators for AM and PAF can be easily derived from these forms. In this paper, we show how to explicitly calculate all the transition probabilities of an extended-illness model with constant hazards. Using a parametric model to estimate the time-constant transition specific hazard rates of a data example, the transition probabilities, AM and PAF can be directly calculated. With a publicly available data example, we show how the approach provides first insights into principle time-dynamics and data structure. Assuming constant hazards facilitates the understanding of multi-state processes. Even in a non-constant hazards setting, the approach is a helpful first step for a comprehensive investigation of complex data.

Abstract: Unlike parametric regression, machine learning (ML) methods do not generally require precise knowledge of the true data generating mechanisms. As such, numerous authors have advocated for ML methods to estimate causal effects. Unfortunately, ML algorithms can perform worse than parametric regression. We demonstrate the performance of ML-based single- and double-robust estimators. We use 100 Monte Carlo samples with sample sizes of 200, 1200, and 5000 to investigate bias and confidence interval coverage under several scenarios. In a simple confounding scenario, confounders were related to the treatment and the outcome via parametric models. In a complex confounding scenario, the simple confounders were transformed to induce complicated nonlinear relationships. In the simple scenario, when ML algorithms were used, double-robust estimators were superior to single-robust estimators. In the complex scenario, single-robust estimators with ML algorithms were at least as biased as estimators using misspecified parametric models. Double-robust estimators were less biased, but coverage was well below nominal. The use of sample splitting, inclusion of confounder interactions, reliance on a richly specified ML algorithm, and use of doubly robust estimators was the only explored approach that yielded negligible bias and nominal coverage. Our results suggest that ML based singly robust methods should be avoided.

Abstract: Binaural sound source localization is an important technique for speech enhancement, video conferencing, and human-robot interaction, etc. However, in realistic scenarios, the reverberation and environmental noise would degrade the precision of sound direction estimation. Therefore, reliable sound localization is essential to practical applications. To deal with these disturbances, this paper presents a novel binaural sound source localization approach based on reverberation weighting and generalized parametric mapping. First, the reverberation weighting as a preprocessing stage, is used to separately suppress the early and late reverberation, while preserving interaural cues. Then, two binaural cues, i.e., interaural time and intensity differences, are extracted from the frequency-domain representations of dereverberated binaural signals for the online localization. Their corresponding templates are established using the training data. Furthermore, the generalized parametric mapping is proposed to build a generalized parametric model for describing relationships between azimuth and binaural cues analytically. Finally, a two-step sound localization process is introduced to refine azimuth estimation based on the generalized parametric model and template matching. Experiments in both simulated and real scenarios validate that the proposed method can achieve better localization performance compared to state-of-the-art methods.

Abstract: We present and validate a global parametric model of potential evapotranspiration (PET) with two parameters that are estimated through calibration, using as explanatory variables temperature and extraterrestrial radiation. The model is tested over the globe, taking advantage of the Food and Agriculture Organization (FAO CLIMWAT) database that provides monthly averaged values of meteorological inputs at 4300 locations worldwide. A preliminary analysis of these data allows for explaining the major drivers of PET over the globe and across seasons. The model calibration against the given Penman-Monteith values was carried out through an automatic optimization procedure. For the evaluation of the model, we present global maps of optimized model parameters and associated performance metrics, and also contrast its performance against the well-known Hargreaves-Samani method. Also, we use interpolated values of the optimized parameters to validate the predictive capacity of our model against monthly meteorological time series, at several stations worldwide. The results are very encouraging, since even with the use of abstract climatic information for model calibration and the use of interpolated parameters as local predictors, the model generally ensures reliable PET estimations. Exceptions are mainly attributed to irregular interactions between temperature and extraterrestrial radiation, as well as because the associated processes are influenced by additional drivers, e.g., relative humidity and wind speed. However, the analysis of the residuals shows that the model is consistent in terms of parameters estimation and model validation. The parameter maps allow for the direct use of the model wherever in the world, providing PET estimates in case of missing data, that can be further improved even with a short term acquisition of meteorological data.

Abstract: Distance estimation and proximity classification techniques are essential for numerous IoT applications and in providing efficient services in smart cities. Bluetooth Low Energy (BLE) is designed for IoT devices, and its received signal strength indicator (RSSI) has been used in distance and proximity estimation, though they are noisy and unreliable. In this study, we leverage the BLE TX power level in BLE models.We adopt a comparative analysis framework that utilizes our extensive data library of measurements. It considers commonly used state-of-the-art model, in addition to our data-driven proposed approach. The RSSI and TX power are integrated into several parametric models such as log shadowing and Android Beacon library models, and machine learning models such as linear regression, decision trees, random forests and neural networks. Specific mobile apps are developed for the study experiment. We have collected more than 1.8 millions of BLE records between encounters with various distances that range from 0.5 to 22 meters in an indoor environment. Interestingly, considering TX power when estimating the distance reduced the mean errors by up to 46% in parametric models and by up to 35% in machine learning models. Also, the proximity classification accuracy increased by up to 103% and 70% in parametric and machine learning models, respectively. This work is one of the first studies (if not the first) that analyze in depth the TX power variations in improving the distance estimation and classification.

Abstract: Since early in robotics the performance of odometry techniques has been of constant research for mobile robots. This is due to its direct influence on localization. The pose error grows unbounded in dead-reckoning systems and its uncertainty has negative impacts in localization and mapping (i.e. SLAM). The dead-reckoning performance in terms of residuals, i.e. the difference between the expected and the real pose state, is related to the statistical error or uncertainty in probabilistic motion models. A novel approach to model odometry errors using Gaussian processes (GPs) is presented. The methodology trains a GP on the residual between the non-linear parametric motion model and the ground truth training data. The result is a GP over odometry residuals which provides an expected value and its uncertainty in order to enhance the belief with respect to the parametric model. The localization and mapping benefits from a comprehensive GP-odometry residuals model. The approach is applied to a planetary rover in an unstructured environment. We show that our approach enhances visual SLAM by efficiently computing image frames and effectively distributing keyframes.

Abstract: Copulas are used to specify dependence between two or more random variables. The last few years have seen a surge of developments of parametric models for copulas. Here, we provide an up-to-date and a comprehensive review of known parametric copulas as well as applications and open problems. This review is believed to be the first of its kind.