CBDX: a workhorse mortality model from the Cairns–Blake–Dowd family

Information from multiple informants is frequently used to assess psychopathology. We consider marginal regression models with multiple informants as discrete predictors and a time to event outcome. We fit these models to data from the Stirling County Study; specifically, the models predict mortality from self report of psychiatric disorders and also predict mortality from physician report of psychiatric disorders. Previously, Horton et al. found little relationship between self and physician reports of psychopathology, but that the relationship of self report of psychopathology with mortality was similar to that of physician report of psychopathology with mortality. Generalized estimating equations (GEE) have been used to fit marginal models with multiple informant covariates; here we develop a maximum likelihood (ML) approach and show how it relates to the GEE approach. In a simple setting using a saturated model, the ML approach can be constructed to provide estimates that match those found using GEE. We extend the ML technique to consider multiple informant predictors with missingness and compare the method to using inverse probability weighted (IPW) GEE. Our simulation study illustrates that IPW GEE loses little efficiency compared with ML in the presence of monotone missingness. Our example data has non-monotone missingness; in this case, ML offers a modest decrease in variance compared with IPW GEE, particularly for estimating covariates in the marginal models. In more general settings, e.g., categorical predictors and piecewise exponential models, the likelihood parameters from the ML technique do not have the same interpretation as the GEE. Thus, the GEE is recommended to fit marginal models for its flexibility, ease of interpretation and comparable efficiency to ML in the presence of missing data.

본 연구는 비연속 분할함수 성장혼합모형의 접근법에 따라 계층 간 원격 결과변인 추정치에 어떠한 차이가 있는지를 확인하는 데 목적이 있다. 이를 위하여 본 연구는 3단계 ML접근법과 3단계 BCH 접근법을 적용하여 모의실험 연구를 수행하였다. 모의실험에 계층 분류정도(1.3, 2.6), 계층 혼합비율(90:10, 70:30, 50:50), 표본크기(200, 500, 1000, 2000)의 조건을 설정하였다. 분석결과, 3단계 ML접근법과 3단계 BCH접근법의 원격 결과변인에서 양호도의 차이는 미미한 것으로 나타났지만, 소표본일 때 3단계 BCH접근법이 3단계 ML접근법에 비해 상대적으로 효율성이 높은 것으로 나타났다. 본 연구는 원격 결과변인의 보조변수 접근법에 기존에 활용되지 않았던 비연속 분할함수 성장혼합모형을 적용하고, 다양한 모의실험 조건을 설정하여 모의실험 연구를 수행하였다는 점에서 의의가 있다. 본 연구가 연구자들에게 실질적인 모형 활용 방안을 제시할 수 있을 것으로 기대하며, 연구의 제한점을 바탕으로 후속연구를 제언하였다.The purpose of this study was to compare the estimates of distal outcome variable in discontinuous growth mixture model. For this purpose, this study carried out a simulation study using a three-step maximum likelihood (ML) approach and a three-step BCH approach. The manipulated conditions were the class separation (1.3, 2.6), the mixing proportions (90:10, 70:30, 50:50), and the sample size (200, 500, 1000, 2000). The differences between ML and a three-step BCH approaches were not substantial, however, the three-step BCH approach was relatively more efficient than the three-step ML approach in the conditions of relatively small sample sizes. In particular, the bias of standard error was smaller in the conditions of the relatively less mixing proportions when three-step BCH approach was used. Limitations of the current study and suggestions for future study were provided.

An eigenvector (EV) method for the determination of directional spectra from heave, pitch and roll buoy data is presented. Both a direct and an iterative form (based on an algorithm by Pawka) of this data-adaptive procedure are developed. The direct form outperforms the Longuet-Higgins et al. method, the cosine spread model and the maximum likelihood (ML) method for both simulated and real data. In the iterative form, the iterative EV method is superior to the other methods tested, including the iterative ML method for unimodal peaks when the noise-to-signal ratio is greater than 0.2 and for bimodal peaks at all noise levels. With real data, the direct EV method produced errors within an 80% confidence zone of the data cross-spectral matrix within the stopping criteria of Lawson and Long. Errors of the iterative EV and iterative ML methods were lower than for both the direct EV and ML results and were about the same magnitude when compared to each other. The iterative EV method, however, produced...

This study examines the estimation of the scale parameter of the Weibull-Power Function Distribution (WPFD) using both maximum likelihood and Bayesian approaches. Bayesian estimation is conducted under one informative Gamma prior with hyperparameters , as well as two non-informative priors: the uniform prior and Jeffreys’ prior. For each prior specification, Bayes estimators are derived under squared error, quadratic, and precautionary loss functions. Closed-form expressions for the posterior distributions and corresponding Bayes estimators are obtained. The finite-sample performance of the competing estimators is evaluated through a Monte Carlo simulation study based on 1000 replications. Estimator performance is assessed using mean squared error (MSE), bias, and coverage probability. The results indicate that all estimators are consistent, with bias and MSE decreasing as sample size increases. Across different prior specifications and parameter settings, the Bayesian estimator under the quadratic loss function consistently attains the lowest MSE, yielding reductions of approximately 10-20% relative to the maximum likelihood estimator in small and moderate samples. These findings suggest that Bayesian estimation under quadratic loss provides improved finite-sample efficiency for estimating the WPFD scale parameter, while maintaining asymptotic comparability with the maximum likelihood approach.

The construction of rank hierarchies based on agonistic interactions between two individuals (“dyads”) is an important component in the characterization of the social structure of groups. To this end, winner‐loser matrices are typically created, which collapse the outcome of dyadic interactions over time, resulting in the loss of all information contained in the temporal domain. Methods that track changes in the outcome of dyadic interactions (such as “Elo‐ratings”) are receiving increasing interest. Critically, individual ratings are not just based on the succession of wins and losses, but depend on the values of start ratings and a shift coefficient. Recent studies improved existing methods by introducing a point estimation of these auxiliary parameters on the basis of a maximum likelihood (ML) approach. For a sound assessment of the rank hierarchies generated this way, we argue that measures of uncertainty of the estimates, as well as a quantification of the robustness of the methods, are also needed. We introduce a Bayesian inference (BI) approach using “partial pooling”, which rests on the assumption that all start ratings are samples from the same distribution. We compare the outcome of the ML approach to that of the BI approach using real‐world data. In addition, we simulate different scenarios to explore in which way the Elo‐rating responds to social events (such as rank changes), and low numbers of observations. Estimates of the start ratings based on “partial pooling” are more robust than those based on ML, also in scenarios where some individuals have only few observations. Our simulations show that assumed rank differences may fall well within the “uncertain” range, and that low sampling density, unbalanced designs, and coalitionary leaps involving several individuals within the hierarchy may yield unreliable results. Our results support the view that Elo‐rating can be a powerful tool in the analysis of social behaviour, when the data meet certain criteria. Assessing the uncertainty greatly aids in the interpretation of results. We advocate running simulation approaches to test how well Elo‐ratings reflect the (simulated) true structure and how sensitive the rating is to true changes in the hierarchy.

A comparative study of short cut procedures for parameter estimation in differential equations

In longitudinal studies, missing data are ubiquitous. This article made a comparison of three model-based techniques for handling different types of missing data (i.e., missing at random (MAR)-based maximum likelihood (ML) approach, missing not at random (MNAR)-based Diggle–Kenward (DK) selection model and MNAR-based pattern mixture (PM) model) in longitudinal studies through a Monte Carlo simulation study. Two influential factors were considered: the dropout rates (5%, 10%, 20%, and 40%) and the sample sizes (100, 300, 500, and 1000) under MAR and MNAR missingness mechanisms respectively. The results indicated that the model selection was a crucial issue when researchers were dealing with missing data in longitudinal studies because under MNAR mechanism, DK method outperformed MAR-based ML approach, but PM method performed worse than MAR-based method did. The differences of the parameter estimation among three methods became more significant as the sample size and the dropout rate increased.

Uncertainty assessment of flow and contaminant transport in the vadose zone entails probability density functions (PDFs) of soil hydraulic parameters. An unconventional maximum likelihood (ML) approach was used in this study to estimate the PDFs of water retention parameters (e.g., van Genuchten α and m) for a situation common in field‐scale modeling where core samples are sparse and prior PDFs of the parameters are unknown. In this situation, the unconventional ML approach approximates the PDFs as multivariate Gaussian. This study developed a method of estimating the mean and covariance of the multivariate Gaussian PDF based on the results of least square methods that can be easily obtained in practice. The developed method was applied to and evaluated through numerical simulation of unsaturated flow and tracer transport at the proposed Yucca Mountain geologic repository. Another focus of this study was to investigate the effect of uncertainty in the water retention parameters on predictive uncertainty. By comparing the predictive uncertainty before and after incorporating random water retention parameters, it was found that the random water retention parameters had limited effects on the mean predictions of the state variables including percolation flux and tracer travel time from the potential repository to the water table. Incorporating the uncertainty in the water retention parameters, however, significantly increased the magnitude and spatial extent of predictive uncertainty of the state variables. In particular, incorporating the random water retention parameters significantly changed the 5th and 95th percentiles of the tracer travel time by tens of thousands of years.

A fundamental issue in knowledge-aided space-time adaptive processing (KA-STAP) is to determine the degree of accuracy of the a~priori knowledge and the optimal emphasis that should be placed on it. In KA-STAP, the a priori knowledge consists usually of an initial guess of the clutter covariance matrix. This can be obtained either by previous radar probings or by a map-based study. We consider a linear combination of the a~priori clutter covariance matrix with the sample covariance matrix obtained from secondary data, and derive an optimal weighting factor on the a priori knowledge by a maximum likelihood (ML) approach. The performance of the ML approach for KA-STAP is evaluated based on numerically simulated data.

Co-clustering addresses the problem of simultaneous clustering of both dimensions of a data matrix. When dealing with high dimensional sparse data, co-clustering turns out to be more beneficial than one-sided clustering even if one is interested in clustering along one dimension only. Aside from being high dimensional and sparse, some datasets, such as document-term matrices, exhibit directional characteristics, and the $$L_2$$ normalization of such data, so that it lies on the surface of a unit hypersphere, is useful. Popular co-clustering assumptions such as Gaussian or Multinomial are inadequate for this type of data. In this paper, we extend the scope of co-clustering to directional data. We present Diagonal Block Mixture of Von Mises–Fisher distributions (dbmovMFs), a co-clustering model which is well suited for directional data lying on a unit hypersphere. By setting the estimate of the model parameters under the maximum likelihood (ML) and classification ML approaches, we develop a class of EM algorithms for estimating dbmovMFs from data. Extensive experiments, on several real-world datasets, confirm the advantage of our approach and demonstrate the effectiveness of our algorithms.

Building forecasting models for tropical cyclone intensity is one of the most challenging area in tropical cyclone research. Most, if not all, of the existing models have been built using variants of Maximum Likelihood (ML) approach. The need to partition data into two sets for model development is seen to be one of the drawbacks of ML approach in the face of limited available data. This paper proposes a way to build forecasting model using a number of model selection criteria which take the penalized-likelihood approach, namely MML, MDL, CAICF, SRM. These criteria claim to have the mechanism to balance between model complexity and goodness of fit. The models selected are then compared with the benchmark models being used in operation.

We propose a localization method based on an enhanced maximum likelihood (ML) method, which uses the probability density function of radio signal strength indicators (RSSIs). ML is a method used for estimating node location with high accuracy. However, it often requires a large number of anchor nodes, which results in a high cost. To solve this problem, we introduce two key features into the ordinary ML method: iterative multilateration and certainty weight. The former enables the localization of nodes, which cannot directly obtain sufficient information from anchors to estimate their own location, by using the neighboring nodes with already estimated locations as pseudo-anchors (PAs). The latter provides high accuracy by weighting the location of the PA depending on its certainty. The proposed method performs localization in a distributed manner and has high scalability. The evaluation results show that our method can estimate many node locations with a higher accuracy than the original ML.

Node self-localization is a key research topic for wireless sensor networks (WSNs). There are two main algorithms, the triangulation method and the maximum likelihood (ML) estimator, for angle of arrival (AOA) based self-localization. The ML estimator requires a good initialization close to the true location to avoid divergence, while the triangulation method cannot obtain the closed-form solution with high efficiency. Here, we develop a set of efficient closed-form AOA based self-localization algorithms using auxiliary variables based methods. First, we formulate the self-localization problem as a linear least squares problem using auxiliary variables. Based on its closed-form solution, a new auxiliary variables based pseudo-linear estimator (AVPLE) is developed. By analyzing its estimation error, we present a bias compensated AVPLE (BCAVPLE) to reduce the estimation error. Then we develop a novel BCAVPLE based weighted instrumental variable (BCAVPLE-WIV) estimator to achieve asymptotically unbiased estimation of locations and orientations of unknown nodes based on prior knowledge of the AOA noise variance. In the case that the AOA noise variance is unknown, a new AVPLE based WIV (AVPLE-WIV) estimator is developed to localize the unknown nodes. Also, we develop an autonomous coordinate rotation method to overcome the tangent instability of the proposed algorithms when the orientation of the unknown node is near <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\pi/2$</tex> </formula> . We also derive the Cramér-Rao lower bound of the ML estimator. Extensive simulations demonstrate the new algorithms achieve much higher localization accuracy than the triangulation method and avoid local minima and divergence in iterative ML estimators.

We pose the estimation of the parameters of multiple superimposed exponential signals in additive Gaussian noise problem as a maximum likelihood (ML) estimation problem. The ML problem is non linear and hard to solve. Some previous works focused on finding alternative estimation procedures, for example by denoising. In contrast, we tackle the ML estimation problem directly. First, we use the same transformation as the first step of iterative quadratic maximum likelihood (IQML) and transform the ML problem into another optimization problem that gets rid of the amplitude coefficients. Second, we solve the remaining optimization problem with a gradient descent approach ("pseudo-quadratic maximum likelihood"). We also use this algorithm for ultra-wideband channel estimation and estimate ranging in non-line of sight environment.

Industrial revolution leads to the manufacturing of multicomponent products; to guarantee the sufficiency of the product and consumer satisfaction, the producer has to study the lifetime of the products. This leads to the use of bivariate and multivariate lifetime distributions in reliability engineering. The most popular and applicable is Marshall–Olkin family of distributions. In this paper, a new bivariate lifetime distribution which is the bivariate inverted Kumaraswamy (BIK) distribution is found and its properties are illustrated. Estimation using both maximum likelihood and Bayesian approaches is accomplished. Using different selection criteria, it is found that BIK provides the best performance compared with other bivariate distributions like bivariate exponential and bivariate inverse Weibull distributions. As a generalization, the multivariate inverted Kumaraswamy (MIK) distribution is derived. Few studies have been conducted on the multivariate Marshall–Olkin lifetime distributions. To the best of our knowledge, none of them handle estimation process. In this paper, we developed an algorithm to show how to estimate the unknown parameters of MIK using both maximum likelihood and Bayesian approaches. This algorithm could be applied in estimating other Marshall–Olkin multivariate lifetime distributions.