Search Results (6)

Cognitive diagnostic models (CDMs) are increasingly being used in various assessment contexts to identify cognitive processes and provide tailored feedback. However, the most commonly used estimation method for CDMs, marginal maximum likelihood estimation with Expectation–Maximization (MMLE-EM), can present difficulties when sample sizes are small. This study compares the results of different estimation methods for CDMs under varying sample sizes using simulated and empirical data. The methods compared include MMLE-EM, Bayes modal, Markov chain Monte Carlo, a non-parametric method, and a parsimonious parametric model such as Restricted DINA. We varied the sample size, and assessed the bias in the estimation of item parameters, the precision in attribute classification, the bias in the reliability estimate, and computational cost. The findings suggest that alternative estimation methods are preferred over MMLE-EM under low sample-size conditions, whereas comparable results are obtained under large sample-size conditions. Practitioners should consider using alternative estimation methods when working with small samples to obtain more accurate estimates of CDM parameters. This study aims to maximize the potential of CDMs by providing guidance on the estimation of the parameters. Full article

The generation of synthetic time series is important in contemporary water sciences for their wide applicability and ability to model environmental uncertainty. Hydroclimatic variables often exhibit highly skewed distributions, intermittency (that is, alternating dry and wet intervals), and spatial and temporal dependencies that pose a particular challenge to their study. Vine copula models offer an appealing approach to generate synthetic time series because of their ability to preserve any marginal distribution while modeling a variety of probabilistic dependence structures. In this work, we focus on the stochastic modeling of hydroclimatic processes using vine copula models. We provide an approach to model intermittency by coupling Markov chains with vine copula models. Our approach preserves first-order auto- and cross-dependencies (correlation). Moreover, we present a novel framework that is able to model multiple processes simultaneously. This method is based on the coupling of temporal and spatial dependence models through repetitive sampling. The result is a parsimonious and flexible method that can adequately account for temporal and spatial dependencies. Our method is illustrated within the context of a recent reliability assessment of a historical hydraulic structure in central Mexico. Our results show that by ignoring important characteristics of probabilistic dependence that are well captured by our approach, the reliability of the structure could be severely underestimated. Full article

This paper reviews a conceptual rainfall-runoff model called Tank which has been widely used over the last 20 years in Korea as a part of a water resource modelling framework for assessing and developing long-term water resource polices. In order to examine the uncertainty of model predictions and the sensitivity of model’s parameters, Monte Carlos and Markov chain-based approaches are applied to five catchments of various Korean geographical and climatic conditions where the catchment sizes are ranged from 83 to 4786 km². In addition, three optimization algorithms—dynamically dimensioned search (DDS), robust parameter estimation (ROPE), and shuffled complex evolution (SCE)—are selected to test whether the model parameters can be optimized consistently within a narrower range than the uncertainty bounds. From the uncertainty analysis, it is found that there is limited success in refining the priori distributions of the model parameters, indicating there is a high degree of equifinality for some parameters or at least there are large numbers of parameter combinations leading to good solutions within model’s uncertainty bounds. Out of the three optimization algorithms, SCE meets the criteria of the consistency best. It is also found that there are still some parameters that even the SCE method struggles to refine the priori distributions. It means that their contribution to model results is minimal and can take a value within a reasonable range. It suggests that the model may be reconceptualized to be parsimonious and to rationalize some parameters without affecting model’s capacity to replicate historical flow characteristics. Cross-validation indicates that sensitive parameters to catchment characteristics can be transferred when geophysical similarity exists between two catchments. Regionalization can be further improved by using a regression or geophysical similarity-based approach to transfer model parameters to ungauged catchments. It may be beneficial to categorize the model parameters depending on the level of their sensitivities, and a different approach to each category may be applied to regionalize the calibrated parameters. Full article

Smart grid operation schemes can integrate prosumers by offering economic rewards in exchange for the desired response. In order to activate prosumers appropriately, such operation schemes require models of the dynamic uncertain price-response relationships. In this study, we combine the system identification of nonlinear dynamics with control (SINDyc) algorithm with Bayesian inference techniques based on Markov-chain Monte-Carlo sampling. We demonstrate this combination of two algorithms on an exemplary system in order to obtain parsimonious models alongside parameter uncertainty estimates. The precision of the identified models depends on the identification experiment and the parameterization of the algorithms. Such models may characterize the prosumer response and its uncertainty, thereby facilitating the integration of such entities into smart grid operation schemes. Full article

For the modeling of categorical time series, both nominal or ordinal time series, an extension of the basic discrete autoregressive moving-average (ARMA) models is proposed. It uses an observation-driven regime-switching mechanism, leading to the family of RS-DARMA models. After having discussed the stochastic properties of RS-DARMA models in general, we focus on the particular case of the first-order RS-DAR model. This RS-DAR $\left(1\right)$ model constitutes a parsimoniously parameterized type of Markov chain, which has an easy-to-interpret data-generating mechanism and may also handle negative forms of serial dependence. Approaches for model fitting are elaborated on, and they are illustrated by two real-data examples: the modeling of a nominal sequence from biology, and of an ordinal time series regarding cloudiness. For future research, one might use the RS-DAR $\left(1\right)$ model for constructing parsimonious advanced models, and one might adapt techniques for smoother regime transitions. Full article

This paper presents and discusses the use of a Mixture Transition Distribution-like model (MTD) to account for covariates in Markovian models. The MTD was introduced in 1985 by Raftery as an approximation of higher order Markov chains. In the MTD, each lag is estimated separately using an additive model, which introduces a kind of symmetrical relationship between the past and the present. Here, using an MTD-based approach, we consider each covariate separately, and we combine the effects of the lags and of the covariates by means of a mixture model. This approach has three main advantages. First, no modification of the estimation procedure is needed. Second, it is parsimonious in terms of freely estimated parameters. Third, the weight parameters of the mixture can be used as an indication of the relevance of the covariate in explaining the time dependence between states. An illustrative example taken from life course studies using a 3-state hidden Markov model and a covariate with three levels shows how to interpret the results of such models. Full article