Search results for " Methodology"
showing 10 items of 575 documents
A penalized approach to the bivariate logistic regression model for the association between ordinal responses
2014
Bivariate ordered logistic models (BOLMs) are appealing to jointly model the marginal distribution of two ordered responses and their association, given a set of covariates. When the number of categories of the responses increases, the number of global odds ratios (or their re-parametrizations) to be estimated also increases and estimating the association structure becomes crucial for this type of data. In fact, such data could be too "rich" to be fully modelled with an ordinary BOLM while, sometimes, the well-known Dale's model could be too parsimonious to provide a good fit. In addition, when the cross-tabulation of the responses contains some zeros, for a number of model configurations, …
Optimal design of observational studies: overview and synthesis
2016
We review typical design problems encountered in the planning of observational studies and propose a unifying framework that allows us to use the same concepts and notation for different problems. In the framework, the design is defined as a probability measure in the space of observational processes that determine whether the value of a variable is observed for a specific unit at the given time. The optimal design is then defined, according to Bayesian decision theory, to be the one that maximizes the expected utility related to the design. We present examples on the use of the framework and discuss methods for deriving optimal or approximately optimal designs.
Large-Sample Properties of Blind Estimation of the Linear Discriminant Using Projection Pursuit
2021
We study the estimation of the linear discriminant with projection pursuit, a method that is blind in the sense that it does not use the class labels in the estimation. Our viewpoint is asymptotic and, as our main contribution, we derive central limit theorems for estimators based on three different projection indices, skewness, kurtosis and their convex combination. The results show that in each case the limiting covariance matrix is proportional to that of linear discriminant analysis (LDA), an unblind estimator of the discriminant. An extensive comparative study between the asymptotic variances reveals that projection pursuit is able to achieve efficiency equal to LDA when the groups are…
Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes
2023
A local version of spatio-temporal log-Gaussian Cox processes is proposed by using Local Indicators of Spatio-Temporal Association (LISTA) functions plugged into the minimum contrast procedure, to obtain space as well as time-varying parameters. The new procedure resorts to the joint minimum contrast fitting method to estimate the set of second-order parameters. This approach has the advantage of being suitable in both separable and non-separable parametric specifications of the correlation function of the underlying Gaussian Random Field. Simulation studies to assess the performance of the proposed fitting procedure are presented, and an application to seismic spatio-temporal point pattern…
Bayesian joint models for longitudinal and survival data
2020
This paper takes a quick look at Bayesian joint models (BJM) for longitudinal and survival data. A general formulation for BJM is examined in terms of the sampling distribution of the longitudinal and survival processes, the conditional distribution of the random effects and the prior distribution. Next a basic BJM defined in terms of a mixed linear model and a Cox survival regression models is discussed and some extensions and other Bayesian topics are briefly outlined.
Conditional particle filters with bridge backward sampling
2022
Conditional particle filters (CPFs) with backward/ancestor sampling are powerful methods for sampling from the posterior distribution of the latent states of a dynamic model such as a hidden Markov model. However, the performance of these methods deteriorates with models involving weakly informative observations and/or slowly mixing dynamics. Both of these complications arise when sampling finely time-discretised continuous-time path integral models, but can occur with hidden Markov models too. Multinomial resampling, which is commonly employed with CPFs, resamples excessively for weakly informative observations and thereby introduces extra variance. Furthermore, slowly mixing dynamics rend…
Bayesian subcohort selection for longitudinal covariate measurements in follow-up studies
2016
We consider planning longitudinal covariate measurements in follow-up studies where covariates are time-varying. We assume that the entire cohort cannot be selected for longitudinal measurements due to financial limitations and study how a subset of the cohort should be selected optimally in order to obtain precise estimates of covariate effects in a survival model. In our approach, the study will be designed sequentially utilizing the data collected in previous measurements of the individuals as prior information. We propose using a Bayesian optimality criterion in the subcohort selections, which is compared with simple random sampling using simulated and real follow-up data. This study ex…
Generalization of Jeffreys' divergence based priors for Bayesian hypothesis testing
2008
In this paper we introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence based (DB) priors. DB priors have simple forms and desirable properties, like information (finite sample) consistency; often, they are similar to other existing proposals like the intrinsic priors; moreover, in normal linear models scenarios, they exactly reproduce Jeffreys-Zellner-Siow priors. Most importantly, in challenging scenarios such as irregular models and mixture models, the DB priors are well defined and very reasonable, while alternative proposals are not. We derive approximations to the D…
Calibration and partial calibration on principal components when the number of auxiliary variables is large
2014
In survey sampling, calibration is a very popular tool used to make total estimators consistent with known totals of auxiliary variables and to reduce variance. When the number of auxiliary variables is large, calibration on all the variables may lead to estimators of totals whose mean squared error (MSE) is larger than the MSE of the Horvitz-Thompson estimator even if this simple estimator does not take account of the available auxiliary information. We study in this paper a new technique based on dimension reduction through principal components that can be useful in this large dimension context. Calibration is performed on the first principal components, which can be viewed as the synthet…
Minimum contrast for the first-order intensity estimation of spatial and spatio-temporal point processes
2023
In this paper, we exploit a result in point process theory, knowing the expected value of the $K$-function weighted by the true first-order intensity function. This theoretical result can serve as an estimation method for obtaining the parameters estimates of a specific model, assumed for the data. The motivation is to generally avoid dealing with the complex likelihoods of some complex point processes models and their maximization. This can be more evident when considering the local second-order characteristics, since the proposed method can estimate the vector of the local parameters, one for each point of the analysed point pattern. We illustrate the method through simulation studies for…