Bayesian estimation and selection of nonlinear vector error correction models: The case of the sugar-ethanol-oil nexus in Brazil

Nonlinear adjustment toward long-run price equilibrium relationships in the sugar-ethanol-oil nexus in Brazil is examined. We develop generalized bivariate error correction models that allow for cointegration between sugar, ethanol, and oil prices, where dynamic adjustments are potentially nonlinear functions of the disequilibrium errors. A range of models are estimated using Bayesian Monte Carlo Markov Chain algorithms and compared using Bayesian model selection methods. The results suggest that the long-run drivers of Brazilian sugar prices are oil prices and that there are nonlinearities in the adjustment processes of sugar and ethanol prices to oil price but linear adjustment between ethanol and sugar prices.

Gráficos de controle de EWMA e de X-barra para monitoramento de processos autocorrelacionados

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

O uso da estatística de qui-quadrado no controle de processos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The Variable Sample Size (X)over-bar Chart with Estimated Parameters

The VSS X chart, dedicated to the detection of small to moderate mean shifts in the process, has been investigated by several researchers under the assumption of known process parameters. In practice, the process parameters are rarely known and are usually estimated from an in-control Phase I data set. In this paper, we evaluate the (run length) performances of the VSS chart when the process parameters are estimated, we compare them in the case where the process parameters are assumed known and we propose specific optimal control chart parameters taking the number of Phase I samples into account.

A new sampling strategy to reduce the effect of autocorrelation on a control chart

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Double-objective economic statistical design of the VP T-2 control chart: Wald's identity approach

Research has shown that applying the T-2 control chart by using a variable parameters (VP) scheme yields rapid detection of out-of-control states. In this paper, the problem of economic statistical design of the VP T-2 control chart is considered as a double-objective minimization problem with the statistical objective being the adjusted average time to signal and the economic objective being expected cost per hour. We then find the Pareto-optimal designs in which the two objectives are met simultaneously by using a multi-objective genetic algorithm. Through an illustrative example, we show that relatively large benefits can be achieved by applying the VP scheme when compared with usual schemes, and in addition, the multi-objective approach provides the user with designs that are flexible and adaptive.

The steady-state behavior of the synthetic and side-sensitive synthetic double sampling (X)over-bar charts

The steady-state average run length is used to measure the performance of the recently proposed synthetic double sampling (X) over bar chart (synthetic DS chart). The overall performance of the DS X chart in signaling process mean shifts of different magnitudes does not improve when it is integrated with the conforming run length chart, except when the integrated charts are designed to offer very high protection against false alarms, and the use of large samples is prohibitive. The synthetic chart signals when a second point falls beyond the control limits, no matter whether one of them falls above the centerline and the other falls below it; with the side-sensitive feature, the synthetic chart does not signal when they fall on opposite sides of the centerline. We also investigated the steady-state average run length of the side-sensitive synthetic DS X chart. With the side-sensitive feature, the overall performance of the synthetic DS X chart improves, but not enough to outperform the non-synthetic DS X chart. Copyright (C) 2014 John Wiley &Sons, Ltd.

Epidemiology of malaria in the municipality of Cruzeiro do Sul, State of Acre, Brazil, in 2010: uses of a control chart at the local level

INTRODUCTION: This study describes the uses of a control chart in the malaria surveillance at the local level, signaling whether there is a need to intensify or adapt control measures. METHODS: The districts of Cruzeiro do Sul (n=14), State of Acre, Brazil, were classified into three groups: I) those with an incidence lower than expected; II) those with an incidence within the expected range; and III) those with an epidemic. RESULTS: Thirteen of the fourteen districts had outbreaks of malaria at some point in 2010, and six districts showed persistent malaria epidemic throughout the year. CONCLUSIONS: The control chart may help the malaria control at the local level.

Bayesian estimation of speciation and extinction from incomplete fossil occurrence data.

The temporal dynamics of species diversity are shaped by variations in the rates of speciation and extinction, and there is a long history of inferring these rates using first and last appearances of taxa in the fossil record. Understanding diversity dynamics critically depends on unbiased estimates of the unobserved times of speciation and extinction for all lineages, but the inference of these parameters is challenging due to the complex nature of the available data. Here, we present a new probabilistic framework to jointly estimate species-specific times of speciation and extinction and the rates of the underlying birth-death process based on the fossil record. The rates are allowed to vary through time independently of each other, and the probability of preservation and sampling is explicitly incorporated in the model to estimate the true lifespan of each lineage. We implement a Bayesian algorithm to assess the presence of rate shifts by exploring alternative diversification models. Tests on a range of simulated data sets reveal the accuracy and robustness of our approach against violations of the underlying assumptions and various degrees of data incompleteness. Finally, we demonstrate the application of our method with the diversification of the mammal family Rhinocerotidae and reveal a complex history of repeated and independent temporal shifts of both speciation and extinction rates, leading to the expansion and subsequent decline of the group. The estimated parameters of the birth-death process implemented here are directly comparable with those obtained from dated molecular phylogenies. Thus, our model represents a step towards integrating phylogenetic and fossil information to infer macroevolutionary processes.

Bayesian estimation of diameter distribution during harvesting

Abstract

Bayesian Estimation of Noise

In mathematical modeling the estimation of the model parameters is one of the most common problems. The goal is to seek parameters that fit to the measurements as well as possible. There is always error in the measurements which implies uncertainty to the model estimates. In Bayesian statistics all the unknown quantities are presented as probability distributions. If there is knowledge about parameters beforehand, it can be formulated as a prior distribution. The Bays’ rule combines the prior and the measurements to posterior distribution. Mathematical models are typically nonlinear, to produce statistics for them requires efficient sampling algorithms. In this thesis both Metropolis-Hastings (MH), Adaptive Metropolis (AM) algorithms and Gibbs sampling are introduced. In the thesis different ways to present prior distributions are introduced. The main issue is in the measurement error estimation and how to obtain prior knowledge for variance or covariance. Variance and covariance sampling is combined with the algorithms above. The examples of the hyperprior models are applied to estimation of model parameters and error in an outlier case.