Bayesian inference for generalized additive mixed models based on Markov random field priors

Most regression problems in practice require flexible semiparametric forms of the predictor for modelling the dependence of responses on covariates. Moreover, it is often necessary to add random effects accounting for overdispersion caused by unobserved heterogeneity or for correlation in longitudinal or spatial data. We present a unified approach for Bayesian inference via Markov chain Monte Carlo simulation in generalized additive and semiparametric mixed models. Different types of covariates, such as the usual covariates with fixed effects, metrical covariates with non-linear effects, unstructured random effects, trend and seasonal components in longitudinal data and spatial covariates, are all treated within the same general framework by assigning appropriate Markov random field priors with different forms and degrees of smoothness. We applied the approach in several case-studies and consulting cases, showing that the methods are also computationally feasible in problems with many covariates and large data sets. In this paper, we choose two typical applications.     

Leaning into Browser Extensions

abstract

An array of browser extensions has been developed to help researchers locate full-text content, whether that full text is available in an institutional repository, on a publishers site, or in an open access journal. Examples of such browser extensions include Unpaywall, Kopernio, EZproxy tools, and Lean Library. This Balance Point column focuses on the growth of browser extensions, the need they are filling, and their adoption by libraries. Particular attention is paid to the Lean Library browser extension and the services offered by Lean Library. Drawing on the literature and interviews with librarians in the field, the advantages and disadvantages of browser extensions are addressed, as well as security concerns.     

Confidence Intervals for the Hyperparameters in Structural Models

This article deals with the bootstrap as an alternative method to construct confidence intervals for the hyperparameters of structural models. The bootstrap procedure considered is the classical nonparametric bootstrap in the residuals of the fitted model using a well-known approach. The performance of this procedure is empirically obtained through Monte Carlo simulations implemented in Ox. Asymptotic and percentile bootstrap confidence intervals for the hyperparameters are built and compared by means of the coverage percentages. The results are similar but the bootstrap procedure is better for small sample sizes. The methods are applied to a real time series and confidence intervals are built for the hyperparameters.     

On the asymptotic properties of parameter estimates in a regression model with non-normally distributed errors

As pointed out in a recent paper by Amirkhalkhali and Rao (1986) (henceforth referred to as A&R), the usual assumption of normality for the error terms of a regression model isoften untenable. However, when this assumption is dropped, it may be difficult to characterize parameter estimates for the model. For example, A&R (p. 189) state that “if the regression errors are non-normal, we are not even sure of their [e.g., the generalized least squares parameter estimates1] asymptotic properties.” A partial answer, however, is given by Spall and Wall (1984), which presents an asymptotic distribution theory for Kalman filter estimates for cases where the random terms of the state space model are not necessarily Gaussian. Certain of these asymptotic distribution results are also discussed in Spall (1985) in the context of model validation (diagnostic checking)     

Some Results on Modeling Biological Sequences and Web Navigation with a Semi Markov Chain

In the article, the entrance probabilities and the probability distribution of the number of transitions to a state are studied to provide some answers to questions related to state occupancies for the semi Markov model. Biological sequences and Web navigation are two cases that initially seem to be different but to a certain extent they do have similarities. Two main aspects of word occurrences in biological sequences are: (a) where do they occur and (b) how many times do they occur. In Web navigation the similar questions are (a) when a node is visited and (b) how many times a node is visited. So, the theoretical results of this study are applied to model these two cases and derive distributions of word location or node occurrence and frequency of occurrences. Rewards/costs are included in the Web navigation model and analytic forms for the means, variances, and moments of total interval rewards/costs are provided.     

Inference for a Linear Functional of Cumulative Hazard Function Via Empirical Likelihood

This article discusses sampling plans, that is, the allocation of sampling units, for computing tolerance limits in a balanced one--way random-effects model. The expected width of the tolerance interval is derived and used as the basis for comparing different sampling plans. A well-known cost function and examples are used to facilitate the discussion.     

Convergence of Discount Time Series Dynamic Linear Models

This article studies the limiting behavior of multiple discount time series dynamic linear models (TSDLMs). It is shown that, under mild conditions, all discount TSDLMs converge to the constant (time-invariant) TSDLM. In particular, the limiting posterior precision matrix of the superposition of multiple discount TSDLMs is explored. For non seasonal models, the elements of the limiting posterior precision of the states are given in a recurrence relationship, while for seasonal models the solution of a linear system provides the elements of the respective limiting precision matrix. The proposed methodology uses canonical Jordan forms and it is illustrated with a detailed example of simulated data featuring both trend and seasonal time series.     

Estimation Bias in Complete-Case Analysis in Crossover Studies with Missing Data

Crossover designs are used often in clinical trials. It is not uncommon that subjects discontinue before completing all treatment periods in a crossover study. Despite availability of statistical methodologies utilizing all available data and software for obtaining valid inferences under the assumption of missing at random (MAR), naïve approaches, such as the complete case (CC) analysis, which is only valid with a strong assumption of missing completely at random are still widely used in practice. In this article, we obtain the analytical form of the estimation bias of treatment effects with CC for linear mixed models. We use simulation studies to examine the inflation of Type I error and efficiency loss in the inferences with CC under MAR. Invalidity and inefficiency of two other commonly used approaches for defining analyzed data in the presence of missing data, including data from at least two periods in three period crossover and available cases for a specific comparison of interest, are also demonstrated through simulation studies.     

Reml and best linear unbiased prediction in state space models

This article takes a hierarchical model approach to the estimation of state space models with diffuse initial conditions. An initial state is said to be diffuse when it cannot be assigned a proper prior distribution. In state space models this occurs either when fixed effects are present or when modelling nonstationarity in the state transition equation. Whereas much of the literature views diffuse states as an initialization problem, we follow the approach of Sallas and Harville (1981,1988) and incorporate diffuse initial conditions via noninformative prior distributions into hierarchical linear models. We apply existing results to derive the restricted loglike-lihood and appropriate modifications to the standard Kalman filter and smoother. Our approach results in a better understanding of De Jong's (1991) contributions. This article also shows how to adjust the standard Kalman filter, the fixed inter- val smoother and the state space model forecasting recursions, together with their mean square errors, for he presence of diffuse components. Using a hierarchical model approach it is shown that the estimates obtained are Best Linear Unbiased Predictors (BLUP).     

禁忌语的“言有所指”刍议

语言学家奥斯汀在他的言语行为理论中把施为句分成三种：以言指事、以言行事和以言成事。我们借用奥斯汀的以言指事之称，认为语言中的禁忌语也是“言有所指”，指代的是客观世界中人们所避讳的事物和理念，因此被禁忌。禁忌语的“言有所指”大致可以分为人称代词指称语类、专有名词指称语类、普通名词指称语类三个类别。人们之所以禁忌这些言语，是混淆了“能指”和“所指”之间的关系。