Latent Parameters Research Articles

Adaptivity in Bayesian Inverse Finite Element Problems: Learning and Simultaneous Control of Discretisation and Sampling Errors.

The local size of computational grids used in partial differential equation (PDE)-based probabilistic inverse problems can have a tremendous impact on the numerical results. As a consequence, numerical model identification procedures used in structural or material engineering may yield erroneous, mesh-dependent result. In this work, we attempt to connect the field of adaptive methods for deterministic and forward probabilistic finite-element (FE) simulations and the field of FE-based Bayesian inference. In particular, our target setting is that of exact inference, whereby complex posterior distributions are to be sampled using advanced Markov Chain Monte Carlo (MCMC) algorithms. Our proposal is for the mesh refinement to be performed in a goal-oriented manner. We assume that we are interested in a finite subset of quantities of interest (QoI) such as a combination of latent uncertain parameters and/or quantities to be drawn from the posterior predictive distribution. Next, we evaluate the quality of an approximate inversion with respect to these quantities. This is done by running two chains in parallel: (i) the approximate chain and (ii) an enhanced chain whereby the approximate likelihood function is corrected using an efficient deterministic error estimate of the error introduced by the spatial discretisation of the PDE of interest. One particularly interesting feature of the proposed approach is that no user-defined tolerance is required for the quality of the QoIs, as opposed to the deterministic error estimation setting. This is because our trust in the model, and therefore a good measure for our requirement in terms of accuracy, is fully encoded in the prior. We merely need to ensure that the finite element approximation does not impact the posterior distributions of QoIs by a prohibitively large amount. We will also propose a technique to control the error introduced by the MCMC sampler, and demonstrate the validity of the combined mesh and algorithmic quality control strategy.

Students’ satisfaction in higher education: the role of practices, needs and beliefs of teachers

PurposeThe purpose of the paper is the analysis of the evolution of students’ satisfaction over time in a large Italian university and the effects on it because of some characteristics of the teachers: didactic practices, beliefs and needs with regard to teaching and learning.Design/methodology/approachThe first step of the analysis identifies a latent construct, measured with items composing the questionnaire, and proposes a reduced set of indicators to measure satisfaction and to model its evolution over time (information collected in three consecutive academic years is available). A second step clusters teachers in homogenous groups with reference to their opinions, beliefs and needs, collected with a new survey conducted at the University of Padova, with the aim of developing strategies to support academic teachers. Then, a mixture conditional latent growth model is estimated with covariates affecting the latent parameters and class membership.FindingsModel estimation identifies a large group of university courses with a high level of satisfaction, which stays constant over time, and a small group of problematic courses with low satisfaction, moreover, that decreases over the three considered academic years. Interesting significant effects of covariates related to both the teacher and the didactic activity are estimated.Originality/valueStatistical analyses show that the implementation of innovative didactic practices and commitment to quality of teaching are important factors to be encouraged by the university management. On the contrary, the traditionalist way of teaching and a low passion for teaching do not improve students’ satisfaction.

Modeling Test-Taking Non-effort in MIRT Models.

The validity of inferences based on test scores will be threatened when examinees' test-taking non-effort is ignored. A possible solution is to add test-taking effort indicators in the measurement model after the non-effortful responses are flagged. As a new application of the multidimensional item response theory (MIRT) model for non-ignorable missing responses, this article proposed a MIRT method to account for non-effortful responses. Two simulation studies were conducted to examine the impact of non-effortful responses on item and latent ability parameter estimates, and to evaluate the performance of the MIRT method, comparing to the three-parameter logistic (3PL) model as well as the effort-moderated model. Results showed that: (a) as the percentage of non-effortful responses increased, the unidimensional 3PL model yielded poorer parameter estimates; (b) the MIRT model could obtain as accurate item parameter estimates as the effort-moderated model; (c) the MIRT model provided the most accurate ability parameter estimates when the correlation between test-taking effort and ability was high. A real data analysis was also conducted for illustration. The limitation and future research were discussed further.

Negative Binomial Models for Visual Fixation Counts on Test Items.

With the development of technology-enhanced learning platforms, eye-tracking biometric indicators can be recorded simultaneously with students item responses. In the current study, visual fixation, an essential eye-tracking indicator, is modeled to reflect the degree of test engagement when a test taker solves a set of test questions. Three negative binomial regression models are proposed for modeling visual fixation counts of test takers solving a set of items. These models follow a similar structure to the lognormal response time model and the two-parameter logistic item response model. The proposed modeling structures include individualized latent person parameters reflecting the level of engagement of each test taker and two item parameters indicating the visual attention intensity and discriminating power of each test item. A Markov chain Monte Carlo estimation method is implemented for parameter estimation. Real data are fitted to the three proposed models, and the results are discussed.

Counterfactuals with Latent Information

We describe a methodology for making counterfactual predictions when the information held by strategic agents is a latent parameter. The analyst observes behavior which is rationalized by a Bayesian model in which agents maximize expected utility, given partial and differential information about payoff-relevant states of the world. A counterfactual prediction is desired about behavior in another strategic setting, under the hypothesis that the distribution of and agents’ information about the state are held fixed. When the data and the desired counterfactual prediction pertain to environments with finitely many states, players, and actions, there is a finite dimensional description of the sharp counterfactual prediction, even though the latent parameter, the type space, is infinite dimensional.

Modeling Aedes aegypti trap data with unobserved components

Several models have been proposed to describe the population dynamics of Aedes aegypti. Intuitive interpretation of model parameters and simplicity are some of the main characteristics of mechanistic models. Another possibility is the use of statistical models, which have their advantages but are not easy to interpret. The state-space model (SSM), also known as a mechanistic time series model, incorporates the beneficial aspects of both mechanistic and statistical models. This study introduces a SSM for Ae. aegypti ovitrap data to estimate latent state and static parameters, making suitable analysis of the data. The estimation of static and state parameters is easy to achieve in this framework. A simulation study is performed to study some properties of the estimators for the parameters. The model is also applied to Ae. aegypti trap data and highlights its importance and potential for the real trap data sets. The results show that the proposed SSM has good performance and the parameters can be reasonably estimated.

Learning Latent Parameters without Human Response Patterns: Item Response Theory with Artificial Crowds.

Incorporating Item Response Theory (IRT) into NLP tasks can provide valuable information about model performance and behavior. Traditionally, IRT models are learned using human response pattern (RP) data, presenting a significant bottleneck for large data sets like those required for training deep neural networks (DNNs). In this work we propose learning IRT models using RPs generated from artificial crowds of DNN models. We demonstrate the effectiveness of learning IRT models using DNN-generated data through quantitative and qualitative analyses for two NLP tasks. Parameters learned from human and machine RPs for natural language inference and sentiment analysis exhibit medium to large positive correlations. We demonstrate a use-case for latent difficulty item parameters, namely training set filtering, and show that using difficulty to sample training data outperforms baseline methods. Finally, we highlight cases where human expectation about item difficulty does not match difficulty as estimated from the machine RPs.

‘The Company We Keep:’ Endogenous Network Formation and Peer Effects in Customer Churn

Online connectivity and other technologies provide academic researchers and practitioners with unprecedented access to data on social interactions between consumers in the process of adoption and consumption of products, services, and ideas. In many cases, the social connections that can be recovered from such data are fundamentally endogenous. This paper addresses the endogeneity in social connections in empirical measurement of peer effects in customer churn. Understanding peer effect in churn decisions is of paramount importance in many industries where products or services are consumed in a socially connected manner, both online and offline, as lost customers hurt revenue streams and are expensive to replenish. Equipped with knowledge of causality, managers can craft effective retention campaigns. To tackle the peer network endogeneity issue, we directly model the process of social network formation based on observed consumer interactions during product use. After accounting for the choice of peers, we model the interdependence of agents' churn decisions and estimate the causal peer effect in churn. Modeling the network formation process first allows us to recover the unobserved individual-specific parameters that might affect both peer network formation and individuals' decisions to churn. The recovered latent individual-specific parameters correct for tie endogeneity in the peer effect model. We use data from the popular massively multiplayer online game World of Warcraft. We find significant evidence of the network formation outcome being largely explained by the latent characteristics of gamers. We also find a strong peer effect in churn decisions after controlling for the network endogeneity. Based on our estimation results, we run counterfactual simulation studies to investigate how churn dynamic in the network is affected by composition of gamers that determines the generated network structure. We provide recommendations to inform a company’s policy of inducing formation of guilds that suffer less from peer effect in churn.

Stochastic Approach to the Analysis of Latent Parameters of Objects of Electric Power Industry

Stochastic Approach to the Analysis of Latent Parameters of Objects of Electric Power Industry

Pseudo-Marginal Hamiltonian Monte Carlo with Efficient Importance Sampling

The joint posterior of latent variables and parameters in Bayesian hierarchical models often has a strong nonlinear dependence structure, thus making it a challenging target for standard Markov-chain Monte-Carlo methods. Pseudo-marginal methods aim at effectively exploring such target distributions, by marginalizing the latent variables using Monte-Carlo integration and directly targeting the marginal posterior of the parameters. We follow this approach and propose a generic pseudo-marginal algorithm for efficiently simulating from the posterior of the parameters. It combines efficient importance sampling, for accurately marginalizing the latent variables, with the recently developed pseudo-marginal Hamiltonian Monte Carlo approach. We illustrate our algorithm in applications to dynamic state space models, where it shows a very high simulation efficiency even in challenging scenarios with complex dependence structures.

Using of mathematical models for analyzing of the results in psychological Guilford test

Results of the survey, conducted using Joy Guilford methodology, of 800 servicemen regarding their professional competence was analyzed with IRT models. In particular, Rasch model and 1-PL, 2-PL and 3-PL models were used. All computations were performed with R statistical software along with ltm package. Latent parameters for both respondents and corresponding indicators (survey questions) were obtained. It was found that there exists signifi cant discrepancy between the models and results of the survey. Analysis of this discrepancy has shown that the major cause of their existence are inadequate conditions under which the survey was conducted.

Latent Parameter Estimation in Fusion Networks Using Separable Likelihoods

Multisensor state-space models underpin fusion applications in networks of sensors. Estimation of latent parameters in these models has the potential to provide highly desirable capabilities such as network self-calibration. Conventional solutions to the problem pose difficulties in scaling with the number of sensors due to the joint multisensor filtering involved when evaluating the parameter likelihood. In this paper, we propose a separable pseudo-likelihood which is a more accurate approximation compared to a previously proposed alternative under typical operating conditions. In addition, we consider using separable likelihoods in the presence of many objects and ambiguity in associating measurements with objects that originated them. To this end, we use a state-space model with a hypothesis-based parameterization, and develop an empirical Bayesian perspective in order to evaluate separable likelihoods on this model using local filtering. Bayesian inference with this likelihood is carried out using belief propagation on the associated pairwise Markov random field. We specify a particle algorithm for latent parameter estimation in a linear Gaussian state-space model and demonstrate its efficacy for network self-calibration using measurements from noncooperative targets in comparison with alternatives.

Model-based analysis of latent factors

Abstract. The detection of community or population structure through analysis of explicit cause–effect modeling of given observations has received considerable attention. The complexity of the task is mirrored by the large number of existing approaches and methods, the applicability of which heavily depends on the design of efficient algorithms of data analysis. It is occasionally even difficult to disentangle concepts and algorithms. To add more clarity to this situation, the present paper focuses on elaborating the system analytic framework that probably encompasses most of the common concepts and approaches by classifying them as model-based analyses of latent factors. Problems concerning the efficiency of algorithms are not of primary concern here. In essence, the framework suggests an input–output model system in which the inputs are provided as latent model parameters and the output is specified by the observations. There are two types of model involved, one of which organizes the inputs by assigning combinations of potentially interacting factor levels to each observed object, while the other specifies the mechanisms by which these combinations are processed to yield the observations. It is demonstrated briefly how some of the most popular methods (Structure, BAPS, Geneland) fit into the framework and how they differ conceptually from each other. Attention is drawn to the need to formulate and assess qualification criteria by which the validity of the model can be judged. One probably indispensable criterion concerns the cause–effect character of the model-based approach and suggests that measures of association between assignments of factor levels and observations be considered together with maximization of their likelihoods (or posterior probabilities). In particular the likelihood criterion is difficult to realize with commonly used estimates based on Markov chain Monte Carlo (MCMC) algorithms. Generally applicable MCMC-based alternatives that allow for approximate employment of the primary qualification criterion and the implied model validation including further descriptors of model characteristics are suggested.

Bayesian Joint Modelling of Survival Time and Longitudinal CD4 Cell Counts Using Accelerated Failure Time and Generalized Error Distributions

Survival of HIV/AIDS patients is crucially dependent on comprehensive and targeted medical interventions such as supply of antiretroviral therapy and monitoring disease progression with CD4 T-cell counts. Statistical modelling approaches are helpful towards this goal. This study aims at developing Bayesian joint models with assumed generalized error distribution (GED) for the longitudinal CD4 data and two accelerated failure time distributions, Lognormal and loglogistic, for the survival time of HIV/AIDS patients. Data are obtained from patients under antiretroviral therapy follow-up at Shashemene referral hospital during January 2006-January 2012 and at Bale Robe general hospital during January 2008-March 2015. The Bayesian joint models are defined through latent variables and association parameters and with specified non-informative prior distributions for the model parameters. Simulations are conducted using Gibbs sampler algorithm implemented in the WinBUGS software. The results of the analyses of the two different data sets show that distributions of measurement errors of the longitudinal CD4 variable follow the generalized error distribution with fatter tails than the normal distribution. The Bayesian joint GED loglogistic models fit better to the data sets compared to the lognormal cases. Findings reveal that patients’ health can be improved over time. Compared to the males, female patients gain more CD4 counts. Survival time of a patient is negatively affected by TB infection. Moreover, increase in number of opportunistic infection implies decline of CD4 counts. Patients’ age negatively affects the disease marker with no effects on survival time. Improving weight may improve survival time of patients. Bayesian joint models with GED and AFT distributions are found to be useful in modelling the longitudinal and survival processes. Thus we recommend the generalized error distributions for measurement errors of the longitudinal data under the Bayesian joint modelling. Further studies may investigate the models with various types of shared random effects and more covariates with predictions.

ІМІТАЦІЙНЕ МОДЕЛЮВАННЯ Й АНАЛІЗ МАТРИЦЬ ПЕРВИННИХ БАЛІВ ПЕДАГОГІЧНОГО ТЕСТУВАННЯ ЗА ДОПОМОГОЮ МОВИ R

The article researches methods of imitational modeling of matrixes containing primary grading obtained in educational testing by the means of statistical programming language R. Unique algorithms and functions were developed to allow generating of matrix of the primary grades according to corresponding test of the defined structure. The importance of this approach is defined by several reasons, specifically the needs to: create reference samples; analyze primary grades by means of CTT (Clasic Test Theory) and IRT; predict basic statistical test characteristics; clarify parameters for the calibrated tasks; model independent parameters for the test takers; increase and development educator’s competency. It should be noted that input parameters could be generated or set up manually. Comparable analysis was conducted for created functions against already existing function packages, such as eRm, ltm, mcIRT, as well as statistical analysis of the generated matrixes. This analysis took into consideration the following procedures: verification of hypothesis about compatibility between generated matrixes and set parameters for the testing tasks per criteria; verification of hypothesis about equivalence of average grades in entire matrix according Student criteriа; verification of hypothesis about equality for vectors of correct answers relative frequencies by columns according to Hotteling criteriа; comparison of theoretical characteristic curves with empirical probabilities; comparison of set parameters for task complexity and parameters graded by generated matrixes with consideration of errors in grading. An experimental system of imitational modeling and analysis for testing results was created. Such system combines contemporary methods of IRT and methods of Classical Testing Theory (CTT). It allows generating matrixes of primary testing grades and performing test results analysis; permits computation of basic statistical characteristics of the test, estimation of the latent parameters, construction of characteristic curves and informational functions. The system graphic shell was generated with the help of the package Shiny. The system utilizes modeling and analysis for testing results according to basic IRT models: Rasch, Birnbaum, Suh-Bolt, Rasch-Masters. A performance verification for algorithms and functions implemented into the system has been done by utilizing several noted statistical methods and procedures; and correct execution of these algorithms has been confirmed.

Joint Modeling of Multivariate Longitudinal Data and Competing Risks Using Multiphase Sub-models

In many clinical studies that involve follow-up, it is common to observe one or more sequences of longitudinal measurements, as well as one or more time to event outcomes. A competing risks situation arises when the probability of occurrence of one event is altered/hindered by another time to event. Recently, there has been much attention paid to the joint analysis of a single longitudinal response and a single time to event outcome, when the missing data mechanism in the longitudinal process is non-ignorable. We, in this paper, propose an extension where multiple longitudinal responses are jointly modeled with competing risks (multiple time to events). Our shared parameter joint model consists of a system of multiphase non-linear mixed effects sub-models for the multiple longitudinal responses, and a system of cause-specific non-proportional hazards frailty sub-models for competing risks, with associations among multiple longitudinal responses and competing risks modeled using latent parameters. The joint model is applied to a data set of patients who are on mechanical circulatory support and are awaiting heart transplant, using readily available software. While on the mechanical circulatory support, patient liver and renal functions may worsen and these in turn may influence one of the two possible competing outcomes: (i) death before transplant; (ii) transplant. In one application, we propose a system of multiphase cause-specific non-proportional hazard sub-model where frailty can be time varying. Performance under different scenarios was assessed using simulation studies. By using the proposed joint modeling of the multiphase sub-models, one can identify: (i) non-linear trends in multiple longitudinal outcomes; (ii) time-varying hazards and cumulative incidence functions of the competing risks; (iii) identify risk factors for the both types of outcomes, where the effect may or may not change with time; and (iv) assess the association between multiple longitudinal and competing risks outcomes, where the association may or may not change with time.

Exploring population responses to environmental change when there is never enough data: a factor analytic approach

Abstract Temporal variability in the environment drives variation in vital rates, with consequences for population dynamics and life‐history evolution. Integral projection models (IPMs) are data‐driven structured population models widely used to study population dynamics and life‐history evolution in temporally variable environments. However, many datasets have insufficient temporal replication for the environmental drivers of vital rates to be identified with confidence, limiting their use for evaluating population level responses to environmental change. Parameter selection, where the kernel is constructed at each time step by randomly selecting the time‐varying parameters from their joint probability distribution, is one approach to including stochasticity in IPMs. We consider a factor analytic (FA) approach for modelling the covariance matrix of time‐varying parameters, whereby latent variable(s) describe the covariance among vital rate parameters. This decreases the number of parameters to estimate and, where the covariance is positive, the latent variable can be interpreted as a measure of environmental quality. We demonstrate this using simulation studies and two case studies. The simulation studies suggest the FA approach provides similarly accurate estimates of stochastic population growth rate to estimating an unstructured covariance matrix. We demonstrate how the latent parameter can be perturbed to show how selection on reproductive delays in the monocarp Carduus nutans changes under different environmental conditions. We develop a demographic model of the fire dependent herb Eryngium cuneifolium to show how a putative driver of the variation in environmental quality can be incorporated with the addition of a single parameter. Using perturbation analyses we determine optimal management strategies for this species. This approach estimates fewer parameters than previous approaches and allows novel eco‐evolutionary insights. Predictions on population dynamics and life‐history evolution under different environmental conditions can be made without necessarily identifying causal factors. Putative environmental drivers can be incorporated with relatively few parameters, allowing for predictions on how populations will respond to changes in the environment.

Changes in the latent parameters during perceptual decision making related to disease progression of the Alzheimer’s disease continuum

Changes in the latent parameters during perceptual decision making related to disease progression of the Alzheimer’s disease continuum

Thermodynamic Analysis of Irreversible Desiccant Systems.

A new general thermodynamic mapping of desiccant systems’ performance is conducted to estimate the potentiality and determine the proper application field of the technology. This targets certain room conditions and given outdoor temperature and humidity prior to the selection of the specific desiccant material and technical details of the system configuration. This allows the choice of the operative state of the system to be independent from the limitations of the specific design and working fluid. An expression of the entropy balance suitable for describing the operability of a desiccant system at steady state is obtained by applying a control volume approach, defining sensible and latent effectiveness parameters, and assuming ideal gas behaviour of the air-vapour mixture. This formulation, together with mass and energy balances, is used to conduct a general screening of the system performance. The theoretical advantage and limitation of desiccant dehumidification air conditioning, maximum efficiency for given conditions constraints, least irreversible configuration for a given operative target, and characteristics of the system for a target efficiency can be obtained from this thermodynamic mapping. Once the thermo-physical properties and the thermodynamic equilibrium relationship of the liquid desiccant mixture or solid coating material are known, this method can be applied to a specific technical case to select the most appropriate working medium and guide the specific system design to achieve the target performance.

Investigating hot-Jupiter inflated radii with hierarchical Bayesian modelling

Context.As of today, hundreds of hot Jupiters have been found, yet the inflated radii of a large fraction of them remain unexplained. A number of mechanisms have been proposed to explain these anomalous radii, however most of these can only work under certain conditions and may not be sufficient to explain the most extreme cases. It is still unclear whether a single mechanism can sufficiently explain the entire distribution of radii, or whether a combination of these mechanisms is needed.Aims.We seek to understand the relationship of radius with stellar irradiation and mass and to find the range of masses over which hot Jupiters are inflated. We also aim to find the intrinsic physical scatter in their radii, caused by unobservable parameters, and to constrain the fraction of hot Jupiters that exhibit inflation.Methods.By constructing a hierarchical Bayesian model, we inferred the probabilistic relation between planet radius, mass, and incident flux for a sample of 286 gas giants. We separately incorporated the observational uncertainties of the data and the intrinsic physical scatter in the population. This allowed us to treat the intrinsic physical scatter in radii, due to latent parameters such as the heavy element fraction, as a parameter to be inferred.Results.We find that the planetary mass plays a key role in the inflation extent and that planets in the range ~0.37−0.98 MJshow the most inflated radii. At higher masses, the radius response to incident flux begins to decrease. Below a threshold of 0.37 ± 0.03 MJwe find that giant exoplanets as a population are unable to maintain inflated radii ≿1.4 RJbut instead exhibit smaller sizes as the incident flux is increased beyond 106W m−2. We also find that below 1 MJ, there is a cut-off point at high incident flux beyond which we find no more inflated planets, and that this cut-off point decreases as the mass decreases. At incident fluxes higher than ~1.6 × 106W m−2and in a mass range 0.37−0.98 MJ, we find no evidence for a population of non-inflated hot Jupiters. Our study sheds a fresh light on one of the key questions in the field and demonstrates the importance of population-level analysis to grasp the underlying properties of exoplanets.