Bayesian analysis of extreme events with threshold estimation

The aim of this paper is to analyze extremal events using Generalized Pareto Distributions (GPD), considering explicitly the uncertainty about the threshold. Current practice empirically determines this quantity and proceeds by estimating the GPD parameters based on data beyond it, discarding all the information available be10w the threshold. We introduce a mixture model that combines a parametric form for the center and a GPD for the tail of the distributions and uses all observations for inference about the unknown parameters from both distributions, the threshold inc1uded. Prior distribution for the parameters are indirectly obtained through experts quantiles elicitation. Posterior inference is available through Markov Chain Monte Carlo (MCMC) methods. Simulations are carried out in order to analyze the performance of our proposed mode1 under a wide range of scenarios. Those scenarios approximate realistic situations found in the literature. We also apply the proposed model to a real dataset, Nasdaq 100, an index of the financiai market that presents many extreme events. Important issues such as predictive analysis and model selection are considered along with possible modeling extensions.

We're Chained: an analysis of systemic risk in finance

This dissertation presents two papers on how to deal with simple systemic risk measures to assess portfolio risk characteristics. The first paper deals with the Granger-causation of systemic risk indicators based in correlation matrices in stock returns. Special focus is devoted to the Eigenvalue Entropy as some previous literature indicated strong re- sults, but not considering different macroeconomic scenarios; the Index Cohesion Force and the Absorption Ratio are also considered. Considering the S&P500, there is not ev- idence of Granger-causation from Eigenvalue Entropies and the Index Cohesion Force. The Absorption Ratio Granger-caused both the S&P500 and the VIX index, being the only simple measure that passed this test. The second paper develops this measure to capture the regimes underlying the American stock market. New indicators are built using filtering and random matrix theory. The returns of the S&P500 is modelled as a mixture of normal distributions. The activation of each normal distribution is governed by a Markov chain with the transition probabilities being a function of the indicators. The model shows that using a Herfindahl-Hirschman Index of the normalized eigenval- ues exhibits best fit to the returns from 1998-2013.

Evaluation of an average numerator relationship matrix model and a Bayesian hierarchical model for growth traits in Nellore cattle with uncertain paternity

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

Controle on-line por atributos para o número de não-conformidades no item inspecionado com base em uma sequência de inspeção

This paper proposes a procedure to control on-line processes for attributes, using an Shewhart control chart with two control limits (warning limit and control limit) and will be based on a sequence of inspection (h). The inspection procedure is based on Taguchi et al. (1989), in which to inspect the item, if the number of non-conformities is higher than an upper control limit, the process needs to be stopped and some adjustment is required; and, if the last inspection h, from all items inspected present a number of non-conformities between the control limit and warning limit. The items inspected will suffer destructive inspection, being discarded after inspection. Properties of an ergodic Markov chain are used to get the expression of average cost per item and the aim was the determination of four optimized parameters: the sampling interval of the inspections (m); the constant W to draw the warning limit (W); the constant C to draw the control limit (C), where W £ C, and the length of sequence of inspections (h). Numerical examples illustrate the proposed procedure

Stochastic stability for Markovian jump linear systems associated with a finite number of jump times

This paper deals with a stochastic stability concept for discrete-time Markovian jump linear systems. The random jump parameter is associated to changes between the system operation modes due to failures or repairs, which can be well described by an underlying finite-state Markov chain. In the model studied, a fixed number of failures or repairs is allowed, after which, the system is brought to a halt for maintenance or for replacement. The usual concepts of stochastic stability are related to pure infinite horizon problems, and are not appropriate in this scenario. A new stability concept is introduced, named stochastic tau-stability that is tailored to the present setting. Necessary and sufficient conditions to ensure the stochastic tau-stability are provided, and the almost sure stability concept associated with this class of processes is also addressed. The paper also develops equivalences among second order concepts that parallels the results for infinite horizon problems. (C) 2003 Elsevier B.V. All rights reserved.

Use of Poisson spatiotemporal regression models for the Brazilian Amazon Forest: malaria count data

INTRODUÇÃO: A malaria é uma doença endêmica na região da Amazônia Brasileira, e a detecção de possíveis fatores de risco pode ser de grande interesse às autoridades em saúde pública. O objetivo deste artigo é investigar a associação entre variáveis ambientais e os registros anuais de malária na região amazônica usando métodos bayesianos espaço-temporais. MÉTODOS: Utilizaram-se modelos de regressão espaço-temporais de Poisson para analisar os dados anuais de contagem de casos de malária entre os anos de 1999 a 2008, considerando a presença de alguns fatores como a taxa de desflorestamento. em uma abordagem bayesiana, as inferências foram obtidas por métodos Monte Carlo em cadeias de Markov (MCMC) que simularam amostras para a distribuição conjunta a posteriori de interesse. A discriminação de diferentes modelos também foi discutida. RESULTADOS: O modelo aqui proposto sugeriu que a taxa de desflorestamento, o número de habitants por km² e o índice de desenvolvimento humano (IDH) são importantes para a predição de casos de malária. CONCLUSÕES: É possível concluir que o desenvolvimento humano, o crescimento populacional, o desflorestamento e as alterações ecológicas associadas a estes fatores estão associados ao aumento do risco de malária. Pode-se ainda concluir que o uso de modelos de regressão de Poisson que capturam o efeito temporal e espacial em um enfoque bayesiano é uma boa estratégia para modelar dados de contagem de malária.

Algoritmos genéticos canônico e elitista: uma abordagem comparativa

Universidade Federal do Rio Grande do Norte

Economic-statistical design of the (X)over-bar chart used to control a wandering process mean using genetic algorithm

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A teoria da ruína aplicada em um modelo de empresa financeira com risco de crédito

In this work we study a new risk model for a firm which is sensitive to its credit quality, proposed by Yang(2003): Are obtained recursive equations for finite time ruin probability and distribution of ruin time and Volterra type integral equation systems for ultimate ruin probability, severity of ruin and distribution of surplus before and after ruin

Controle on-line para o número de não-conformidades em um ítem inspecionado

The on-line processes control for attributes consists of inspecting a single item at every m produced ones. If the examined item is conforming, the production continues; otherwise, the process stops for adjustment. However, in many practical situations, the interest consist of monitoring the number of non-conformities among the examined items. In this case, if the number of non-conformities is higher than an upper control limit, the process needs to be stopped and some adjustment is required. The contribution of this paper is to propose a control system for the number of nonconforming of the inspected item. Employing properties of an ergodic Markov chain, an expression for the expected cost per item of the control system was obtained and it will be minimized by two parameters: the sampling interval and the upper limit control of the non-conformities of the examined item. Numerical examples illustrate the proposed procedure

Ajuste preventivo versus ajuste corretivo no controle on-line de processo do número de não-conformidades num item inspecionado

In production lines, the entire process is bound to unexpected happenings which may cost losing the production quality. Thus, it means losses to the manufacturer. Identify such causes and remove them is the task of the processing management. The on-line control system consists of periodic inspection of every month produced item. Once any of those items is quali ed as not t, it is admitted that a change in the fraction of the items occurred, and then the process is stopped for adjustments. This work is an extension of Quinino & Ho (2010) and has as objective main to make the monitoramento in a process through the control on-line of quality for the number of non-conformities about the inspected item. The strategy of decision to verify if the process is under control, is directly associated to the limits of the graphic control of non-conformities of the process. A policy of preventive adjustments is incorporated in order to enlarge the conforming fraction of the process. With the help of the R software, a sensibility analysis of the proposed model is done showing in which situations it is most interesting to execute the preventive adjustment

A Markovian model market-Akerlof's lemons and the asymmetry of information

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Bayesian binary regression model: an application to in-hospital death after AMI prediction

Um modelo bayesiano de regressão binária é desenvolvido para predizer óbito hospitalar em pacientes acometidos por infarto agudo do miocárdio. Métodos de Monte Carlo via Cadeias de Markov (MCMC) são usados para fazer inferência e validação. Uma estratégia para construção de modelos, baseada no uso do fator de Bayes, é proposta e aspectos de validação são extensivamente discutidos neste artigo, incluindo a distribuição a posteriori para o índice de concordância e análise de resíduos. A determinação de fatores de risco, baseados em variáveis disponíveis na chegada do paciente ao hospital, é muito importante para a tomada de decisão sobre o curso do tratamento. O modelo identificado se revela fortemente confiável e acurado, com uma taxa de classificação correta de 88% e um índice de concordância de 83%.

Comparison between the complete Bayesian method and empirical Bayesian method for ARCH models using Brazilian financial time series

In this work we compared the estimates of the parameters of ARCH models using a complete Bayesian method and an empirical Bayesian method in which we adopted a non-informative prior distribution and informative prior distribution, respectively. We also considered a reparameterization of those models in order to map the space of the parameters into real space. This procedure permits choosing prior normal distributions for the transformed parameters. The posterior summaries were obtained using Monte Carlo Markov chain methods (MCMC). The methodology was evaluated by considering the Telebras series from the Brazilian financial market. The results show that the two methods are able to adjust ARCH models with different numbers of parameters. The empirical Bayesian method provided a more parsimonious model to the data and better adjustment than the complete Bayesian method.

Monitoring a wandering mean with an np chart

Este artigo considera um gráfico np x proposto por Wu et al. (2009) para controle de média de processo como uma alternativa ao uso do gráfico de. O que distingue do gráfico de controle np x é o fato das unidades amostrais serem classificadas como unidades de primeiro ou de segunda classe de acordo com seus limites discriminantes. O gráfico tradicional np é um caso particular do gráfico np x quando os limites discriminantes coincidem com os limites de especificação e unidade de primeira (segunda) classe é um item conforme (não conforme). Estendendo o trabalho de Reynolds Junior, Arnold e Baik (1996), consideramos que a média de processo oscila mesmo na ausência de alguma causa especial. As propriedades de Cadeia de Markov foram adotadas para avaliar o desempenho do gráfico np x no monitoramento de média de processos que oscila. de modo geral, o gráfico np x requer amostras duas vezes maior para superar desempenho do gráfico (enquanto que o gráfico tradicional np necessita tamanho de amostras cinco ou seis vezes maior).