Thiago Rezende dos Santos

A Non‐Gaussian Family of State‐Space Models with Exact Marginal Likelihood

The Gaussian assumption generally employed in many state‐space models is usually not satisfied for real time series. Thus, in this work, a broad family of non‐Gaussian models is defined by integrating and expanding previous work in the literature. The expansion is obtained at two levels: at the observational level, it allows for many distributions not previously considered, and at the latent state level, it involves an expanded specification for the system evolution. The class retains analytical availability of the marginal likelihood function, uncommon outside Gaussianity. This expansion considerably increases the applicability of the models and solves many previously existing problems such as long‐term prediction, missing values and irregular temporal spacing. Inference about the state components can be performed because of the introduction of a new and exact smoothing procedure, in addition to filtered distributions. Inference for the hyperparameters is presented from the classical and Bayesian perspectives. The results seem to indicate competitive results of the models when compared with other non‐Gaussian state‐space models available. The methodology is applied to Gaussian and non‐Gaussian dynamic linear models with time‐varying means and variances and provides a computationally simple solution to inference in these models. The methodology is illustrated in a number of examples.

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.

Clinical Response to Donepezil in Mild and Moderate Dementia: Relationship to Drug Plasma Concentration and CYP2D6 and APOE Genetic Polymorphisms

The clinical response to donepezil in patients with mild and moderate dementia was investigated in relation to the drug plasma concentration and APOE and CYP2D6 polymorphisms. In a prospective naturalistic observational study, 42 patients with Alzheimers disease (AD) and AD with cerebrovascular disease who took donepezil (10 mg) for 12 months were evaluated. Their DNA was genotyped, and the donepezil plasma concentrations were measured after 3, 6, and 12 months. Good responders scored ≥-1 on the Mini-Mental State Examination at 12 months in comparison to the baseline score. The study results indicated the good response pattern was influenced by the concentration of donepezil, but not by APOE and CYP2D6 polymorphisms.

A 15-Year Time-series Study of Tooth Extraction in Brazil

AbstractTooth loss is considered to be a public health problem. Time-series studies that assess the influence of social conditions and access to health services on tooth loss are scarce.This study aimed to examine the time-series of permanent tooth extraction in Brazil between 1998 and 2012 and to compare these series in municipalities with different Human Development Index (HDI) scores and with different access to distinct primary and secondary care.The time-series study was performed between 1998 and 2012, using data from the Brazilian National Health Information System. Time-series study was performed between 1998 and 2012. Two annual rates of tooth extraction were calculated and evaluated separately according to 3 parameters: the HDI, the presence of a Dental Specialty Center, and coverage by Oral Health Teams. The time-series was analyzed using a linear regression model.An overall decrease in the tooth-loss tendencies during this period was observed, particularly in the tooth-extraction rate during primary care procedures. In the municipalities with an HDI that was lower than the median, the average tooth-loss rates were higher than in the municipalities with a higher HDI. The municipalities with lower rates of Oral Health Team coverage also showed lower extraction rates than the municipalities with higher coverage rates.In general, Brazil has shown a decrease in the trend to extract permanent teeth during these 15 years. Increased human development and access to dental services have influenced tooth-extraction rates.

A Closer Look at Degradation Models: Classical and Bayesian Approaches

Traditionally, reliability assessment of devices has been based on (accelerated) life tests. However, for highly reliable products, little information about reliability is provided by life tests in which few or no failures are typically observed. Since most failures arise from a degradation mechanism at work for which there are characteristics that degrade over time, one alternative is to monitor the device for a period of time and assess its reliability from the changes in performance (degradation) observed during that period. The goal of this chapter is to illustrate how degradation data can be modeled and analyzed by using “classical” and Bayesian approaches. Four methods of data analysis based on classical inference are presented. Next we show how Bayesian methods can also be used to provide a natural approach to analyzing degradation data. The approaches are applied to a real data set regarding train wheels degradation.

Reliability Analysis via Non-Gaussian State-Space Models

This paper proposes new reliability models whose likelihood consists of decomposition of data information in stages or times, thus leading to latent state parameters. Alternative versions of some well-known models such as piecewise exponential, proportional hazards, and software reliability models are shown to be included in our unifying framework. In general, latent parameters of many reliability models are high dimensional, and their inference requires approximating methods such as Markov chain Monte Carlo (MCMC) or Laplace. Latent states in our models are related across stages through a non-Gaussian state-space framework. This feature makes the models mathematically tractable and allows for the exact computation of the marginal likelihood function, despite the non-Gaussianity of the state. Our non-Gaussian evolution models circumvent the need for approximations, which are required in similar likelihood-based approaches. In addition, they allow for reduction of the dimension of the problem. Real-life examples illustrate the approach and indicate advantages over other existing models.

Confidence intervals based on the deviance statistic for the hyperparameters in state space models

ABSTRACT The main objective of this work is to evaluate the performance of confidence intervals, built using the deviance statistic, for the hyperparameters of state space models. The first procedure is a marginal approximation to confidence regions, based on the likelihood test, and the second one is based on the signed root deviance profile. Those methods are computationally efficient and are not affected by problems such as intervals with limits outside the parameter space, which can be the case when the focus is on the variances of the errors. The procedures are compared to the usual approaches existing in the literature, which includes the method based on the asymptotic distribution of the maximum likelihood estimator, as well as bootstrap confidence intervals. The comparison is performed via a Monte Carlo study, in order to establish empirically the advantages and disadvantages of each method. The results show that the methods based on the deviance statistic possess a better coverage rate than the asymptotic and bootstrap procedures.

A modified approximate method for analysis of degradation data

Estimation of the lifetime distribution of industrial components and systems yields very important information for manufacturers and consumers. However, obtaining reliability data is time consuming and costly. In this context, degradation tests are a useful alternative approach to lifetime and accelerated life tests in reliability studies. The approximate method is one of the most used techniques for degradation data analysis. It is very simple to understand and easy to implement numerically in any statistical software package. This paper uses time series techniques in order to propose a modified approximate method (MAM). The MAM improves the standard one in two aspects: (1) it uses previous observations in the degradation path as a Markov process for future prediction and (2) it is not necessary to specify a parametric form for the degradation path. Characteristics of interest such as mean or median time to failure and percentiles, among others, are obtained by using the modified method. A simulation study is performed in order to show the improved properties of the modified method over the standard one. Both methods are also used to estimate the failure time distribution of the fatigue-crack-growth data set.

Inference for the Hyperparameters of Structural Models Under Classical and Bayesian Perspectives: A Comparison Study

Structural models—or dynamic linear models as they are known in the Bayesian literature—have been widely used to model and predict time series using a decomposition in non observable components. Due to the direct interpretation of the parameters, structural models are a powerful and simple methodology to analyze time series in several areas, such as economy, climatology, environmental sciences, among others. The parameters of such models can be estimated either using maximum likelihood or Bayesian procedures, generally implemented using conjugate priors, and there are plenty of works in the literature employing both methods. But are there situations where one of these approaches should be preferred? In this work, instead of conjugate priors for the hyperparameters, the Jeffreys prior is used in the Bayesian approach, along with the uniform prior, and the results are compared to the maximum likelihood method, in an extensive Monte Carlo study. Interval estimation is also evaluated and, to this purpose, bootstrap confidence intervals are introduced in the context of structural models and their performance is compared to the asymptotic and credibility intervals. A real time series of a Brazilian electric company is used as illustration.