We investigate use of two or more linked registers, or lists, for both population size estimation and to investigate the relationship between variables appearing on all or only some registers. This relationship is usually not fully known because some individuals appear in only some registers, and some are not in any register. These two problems have been solved simultaneously using the EM algorithm. We extend this approach to estimate the size of the indigenous Māori population in New Zealand, leading to several innovations: (1) the approach is extended to four registers (including the population census), where the reporting of Māori status differs between registers; (2) some individuals in one or more registers have missing ethnicity, and we adapt the approach to handle this additional missingness; (3) some registers cover subsets of the population by design. We discuss under which assumptions such structural undercoverage can be ignored and provide a general result; (4) we treat the Māori indicator in each register as a variable measured with error, and embed a latent class model in the multiple system estimation to estimate the population size of a latent variable, interpreted as the true Māori status. Finally, we discuss estimating the Māori population size from administrative data only. Supplementary materials for our article are available online.
Columbia University（哥伦比亚大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
The recently proposed identifiable variational autoencoder (iVAE) framework provides a promising approach for learning latent independent components (ICs). iVAEs use auxiliary covariates to build an identifiable generation structure from covariates to ICs to observations, and the posterior network approximates ICs given observations and covariates. Though the identifiability is appealing, we show that iVAEs could have local minimum solution where observations and the approximated ICs are independent given covariates.-a phenomenon we referred to as the posterior collapse problem of iVAEs. To ov…
Numerous approaches are proposed in the literature for non-stationarity marginal extreme value inference, including different model parameterisations with respect to covariate, and different inference schemes. The objective of this article is to compare some of these procedures critically. We generate sample realisations from generalised Pareto distributions, the parameters of which are smooth functions of a single smooth periodic covariate, specified to reflect the characteristics of actual samples from the tail of the distribution of significant wave height with direction, considered in the …
Aalto University（阿尔托大学）；University of Helsinki（赫尔辛基大学）；Bayer Pharmaceuticals（拜耳制药）
Conditional variational autoencoders (CVAEs) are versatile deep generative models that extend the standard VAE framework by conditioning the generative model with auxiliary covariates. The original CVAE model assumes that the data samples are independent, whereas more recent conditional VAE models, such as the Gaussian process (GP) prior VAEs, can account for complex correlation structures across all data samples. While several methods have been proposed to learn standard VAEs from partially observed datasets, these methods fall short for conditional VAEs. In this work, we propose a method to …
The analysis of high dimensional survival data is challenging, primarily due to the problem of overfitting which occurs when spurious relationships are inferred from data that subsequently fail to exist in test data. Here we propose a novel method of extracting a low dimensional representation of covariates in survival data by combining the popular Gaussian Process Latent Variable Model (GPLVM) with a Weibull Proportional Hazards Model (WPHM). The combined model offers a flexible non-linear probabilistic method of detecting and extracting any intrinsic low dimensional structure from high dimen…
University of Oxford（牛津大学）；University of British Columbia（不列颠哥伦比亚大学）；BC Cancer Agency（不列颠哥伦比亚癌症机构）；UBC Data Science Institute（不列颠哥伦比亚大学数据科学研究所）；The Alan Turing Institute（艾伦·图灵研究所）；University of Birmingham（伯明翰大学）
The interpretation of complex high-dimensional data typically requires the use of dimensionality reduction techniques to extract explanatory low-dimensional representations. However, in many real-world problems these representations may not be sufficient to aid interpretation on their own, and it would be desirable to interpret the model in terms of the original features themselves. Our goal is to characterise how feature-level variation depends on latent low-dimensional representations, external covariates, and non-linear interactions between the two. In this paper, we propose to achieve this…
In the attention-deficit hyperactivity disorder (ADHD) study, children are prescribed different stimulant medications. The height measurements are recorded longitudinally along with the medication time. Differences among the patients are captured by the parameters suggested the Superimposition by Translation and Rotation (SITAR) model using three subject-specific parameters to estimate their deviation from the mean growth curve. In this paper, we generalize the SITAR model in a Bayesian way with time-invariant covariates. The time-invariant model allows us to predict latent growth factors. Sin…
We develop a stochastic modeling approach based on spatial point processes of log-Gaussian Cox type for a collection of around 5000 landslide events provoked by a precipitation trigger in Sicily, Italy. Through the embedding into a hierarchical Bayesian estimation framework, we can use the Integrated Nested Laplace Approximation methodology to make inference and obtain the posterior estimates. Several mapping units are useful to partition a given study area in landslide prediction studies. These units hierarchically subdivide the geographic space from the highest grid-based resolution to the s…
Gaussian processes (GPs) are widely used as distributions of random effects in linear mixed models, which are fit using the restricted likelihood or the closely-related Bayesian analysis. This article addresses two problems. First, we propose tools for understanding how data determine estimates in these models, using a spectral basis approximation to the GP under which the restricted likelihood is formally identical to the likelihood for a gamma-errors GLM with identity link. Second, to examine the data's support for a covariate and to understand how adding that covariate moves variation in th…
Researchers continue to be interested in exploring the effects that covariates have on the heterogeneity in trajectories. The inclusion of covariates associated with latent classes allows for a more clear understanding of individual differences and a more meaningful interpretation of latent class membership. Many theoretical and empirical studies have focused on investigating heterogeneity in change patterns of a univariate repeated outcome and examining the effects on baseline covariates that inform the cluster formation. However, developmental processes rarely unfold in isolation; therefore,…
Missing covariates in regression or classification problems can prohibit the direct use of advanced tools for further analysis. Recent research has realized an increasing trend towards the usage of modern Machine Learning algorithms for imputation. It originates from their capability of showing favourable prediction accuracy in different learning problems. In this work, we analyze through simulation the interaction between imputation accuracy and prediction accuracy in regression learning problems with missing covariates when Machine Learning based methods for both, imputation and prediction a…
The strength of evidence provided by epidemiological and observational studies is inherently limited by the potential for unmeasured confounding. Researchers should present a quantified sensitivity to unmeasured confounding analysis that is contextualized by the study's observed covariates. VanderWeele and Ding's E-value provides an easily calculated metric for the magnitude of the hypothetical unmeasured confounding required to render the study's result inconclusive. We propose the Observed Covariate E-value to contextualize the sensitivity analysis' hypothetical E-value within the actual imp…
Although randomized experiments are widely regarded as the gold standard for estimating causal effects, missing data of the pretreatment covariates makes it challenging to estimate the subgroup causal effects. When the missing data mechanism of the covariates is nonignorable, the parameters of interest are generally not pointly identifiable, and we can only get bounds for the parameters of interest, which may be too wide for practical use. In some real cases, we have prior knowledge that some restrictions may be plausible. We show the identifiability of the causal effects and joint distributio…
Many contemporary large-scale applications involve building interpretable models linking a large set of potential covariates to a response in a nonlinear fashion, such as when the response is binary. Although this modeling problem has been extensively studied, it remains unclear how to effectively control the fraction of false discoveries even in high-dimensional logistic regression, not to mention general high-dimensional nonlinear models. To address such a practical problem, we propose a new framework of $model$-$X$ knockoffs, which reads from a different perspective the knockoff procedure (…
