Several previous works show that, in general, financial time series are characterized by periods ... more Several previous works show that, in general, financial time series are characterized by periods of large volatility followed by periods of relative quitness. In this paper we consider the product partition model (PPM) to identify changes in the volatility extending it to identify multiple change points in normal variances assuming known means. Yao's prior cohesions and a conjugate prior distribution for the variance-which in this case is a Inverted-Gamma distribution-are assumed. The ultimate goal is to provide a sensitivity analysis to the product estimates assuming different prior specifications for the parameter which indexes the Yao's cohesions and also for the variance. We analyze a Chilean stock market return series and conclude that the product estimates for the volatility of this series are strongly influenced by the prior specifications of both parameters.
The identification of multiple change points is a problem shared by many subject areas, including... more The identification of multiple change points is a problem shared by many subject areas, including disease and criminality mapping, medical diagnosis, industrial control, and finance. An algorithm based on the Product Partition Model (PPM) is developed to solve the multiple change point identification problem in Poisson data sequences. In order to address the PPM, a simple and easy way to implement Gibbs sampling scheme is derived. A sensitivity analysis is performed, for different prior specifications. The algorithm is then applied to the analysis of a real data sequence. The results show that the method is quite effective and provides useful inferences.
Brazilian Journal of Probability and Statistics, 2009
The usual finite population model-where information provided by a subset of units is used to redu... more The usual finite population model-where information provided by a subset of units is used to reduce uncertainty about functions of the complete population list of values-is explored from a predictivistic point of view. Under this approach, only operationally meaningful quantities (operational parameters) are considered and therefore no superpopulation parameters are involved. This paper addresses the estimation of both population total and maximum based on uniformity and/or exchangeability judgments on finite sequences of random variables. A central point of this paper is that there are contexts in which the superpopulation approach cannot be employed in inferential problems in finite populations. There are circumstances in which the prior distributions for the operational parameters cannot be obtained from any superpopulation model. Conditions for the extendibility to infinite populations are also established for some models, as this approach may ease the inferential problem.
... Applications and extensions of the PPM can be found in Barry and Hartigan (1993), Crowley (19... more ... Applications and extensions of the PPM can be found in Barry and Hartigan (1993), Crowley (1997), Quintana and Iglesias (2003), Loschi and Cruz (2005) and others (see more on Bayesian approach of multiple change points in Elliott and Shope, 2003). Page 2. ...
The APC framework for modeling and forecasting the education profile of Brazilian males and femal... more The APC framework for modeling and forecasting the education profile of Brazilian males and females is considered from both classical and Bayesian perspectives. For a classical analysis, I calculate maximum likelihood estimates of APC parameters. For the Bayesian analysis, I estimate posterior means and credible intervals. Both methods are simple and computationally efficient. Results show that both classical and Bayesian methods are able to provide very good forecasts in the short term. However, the Bayesian method performed best for in-sample and out-of-sample forecasts. On the other hand, in a Bayesian setting, uncertainty indeed becomes an issue for long-term forecasts because of the rapidly increasing width of the intervals as the length of the projection increases. A number of enhancements of the classical and Bayesian methods proposed here are suggested for a future research agenda. Foremost is an investigation into an integrated approach to account for uncertainty in the classical multinomial APC model and refined ways of eliciting prior information in the Bayesian framework.
In this paper, we consider the product partition model for the estimation of normal means and var... more In this paper, we consider the product partition model for the estimation of normal means and variances of a sequence of observations that experiences changes in these parameters at unknown times. The estimates of the parameters by using product partition model are the weighted average of the estimates based in blocks (groups) of observations by the posterior relevance of these blocks which depends on the prior cohesions. We implement the Barry and Hartigan's method to this change point problem and propose an easy-to-implement modiÿcation to their method. We use Yao's prior cohesions and investigate the in uence of di erent prior distributions to the parameter that indexes these cohesions in the product estimates. A comparison between the estimates obtained by using both these methods and those provided by using Yao's method is done considering di erent settings for its application. We apply the three methods presented in this paper to stock market data. The results seem to indicate that the method proposed is competitive and also that the prior speciÿcations in uence in the product estimates.
In this paper we analyze the fraction of non-disjunction in Meiosis I assuming reference (non-inf... more In this paper we analyze the fraction of non-disjunction in Meiosis I assuming reference (non-informative) priors. We consider Jeffreys's approach to built a non-informative prior (Jeffreys's prior) for the fraction of non-disjunction in Meiosis I. We prove that Jeffreys's prior is a proper distribution. We perform Monte Carlo studies in order to compare Bayes estimates obtained assuming Jeffreys's and uniform priors. We consider full Bayesian significance test (FBST) and Bayes factor (BF) for testing precise hypothesis on the fraction of non-disjunction in Meiosis I. The ultimate goal of this paper is to compare these two test procedures through simulation studies using both prior specifications. An application to Down Syndrome data is also presented.
This paper discusses the Three Prisoners paradox in the light of three different procedures for t... more This paper discusses the Three Prisoners paradox in the light of three different procedures for the updating of probabilities - Bayesian conditioning, superconditioning and Jeffrey's rule - as well as assuming the unpredictability of receipt of information by prisoner A. The formulation of the paradox in this temporal setting brings new insight to the problem and, on the other hand, the paradox is a good way to explain the different updating probability procedures and the difference between conditional probabilities and posterior distributions.
Este é o primeiro de dois artigos complementares que versam sobre um método para a estimação dos ... more Este é o primeiro de dois artigos complementares que versam sobre um método para a estimação dos quantis de enchentes extremas, a partir de uma abordagem Bayesiana, com a possibilidade de inclusão de informações históricas e paleohidrológicas e emprego de distribuições de probabilidades com cauda superior finita. Este artigo aborda o desenvolvimento teórico do método proposto, enquanto o segundo artigo apresenta três aplicações a bacias com diferentes conjuntos de dados disponíveis. Depois de contextualizar o problema de estimação de enchentes extremas, introduz-se aqui a viabilidade de agregação da Cheia Máxima Provável, ou simplesmente PMF (de Probable Maximum Flood), à análise de frequência de variáveis hidrológicas, mediante emprego do paradigma Bayesiano para inferência estatística e de distribuições de probabilidade limitadas superiormente. O limite superior da distribuição em questão está sujeito a incertezas, as quais podem ser sumariadas a partir de distribuições a priori eliciadas, em alguns casos estudados, a partir de um grande banco de estimativas de PMF, conforme aqui demonstrado. Na sequência, o sumário a priori das incertezas pode ser atualizado pela inclusão de informações exatas, obtidas dos registros sistemáticos, e censuradas, de fontes não sistemáticas históricas ou paleohidrológicas, por meio de uma função de verossimilhança suficientemente genérica. A possibilidade do emprego desse grande conjunto de informações em uma estrutura de inferência Bayesiana abre perspectivas para a obtenção de estimativas mais confiáveis de quantis de enchentes extremas. Palavras Chave: cheia máxima provável, análise Bayesiana, enchentes extremas, eventos hidrológicos raros.
Some recent research on fluvial processes suggests the idea that some hydrological variables, suc... more Some recent research on fluvial processes suggests the idea that some hydrological variables, such as flood flows, are upper-bounded. However, most probability distributions that are currently employed in flood frequency analysis are unbounded to the right. This paper describes an exploratory study on the joint use of an upper-bounded probability distribution and non-systematic flood information, within a Bayesian framework. Accordingly,
Page 1. A Bayesian Approach to Spatial Clustering Renato Assunção; Alexandra M. Schmidt; Rosângel... more Page 1. A Bayesian Approach to Spatial Clustering Renato Assunção; Alexandra M. Schmidt; Rosângela Loschi; Joãão Monteiro Departamento de Estatística UFMG, Instituto de Matematica UFRJ. 1 Introduction Consider ...
The multiple change point identification problem may be encountered in many subject areas, includ... more The multiple change point identification problem may be encountered in many subject areas, including disease mapping, medical diagnosis, industrial control, and finance. One appealing way of tackling the problem is through the product partition model (PPM), a Bayesian approach. Nowadays, practical applications of Bayesian methods have attracted attention perhaps because of the generalized use of powerful and inexpensive personal computers. A Gibbs sampling scheme, simple and easy to implement, is used to obtain the estimates. We apply the algorithm to the analysis of two important stock market data in Brazil. The results show that the method is efficient and effective in analyzing change point problems.
The usual finite population model—where information provided by a subset of units is used to redu... more The usual finite population model—where information provided by a subset of units is used to reduce uncertainty about functions of the complete population list of values—is explored from a predictivistic point of view. Under this approach, only operationally meaningful quantities (operational parameters) are considered and therefore no superpopulation parameters are involved. This paper addresses the estimation of both population total
Several previous works show that, in general, financial time series are characterized by periods ... more Several previous works show that, in general, financial time series are characterized by periods of large volatility followed by periods of relative quitness. In this paper we consider the product partition model (PPM) to identify changes in the volatility extending it to identify multiple change points in normal variances assuming known means. Yao's prior cohesions and a conjugate prior distribution for the variance-which in this case is a Inverted-Gamma distribution-are assumed. The ultimate goal is to provide a sensitivity analysis to the product estimates assuming different prior specifications for the parameter which indexes the Yao's cohesions and also for the variance. We analyze a Chilean stock market return series and conclude that the product estimates for the volatility of this series are strongly influenced by the prior specifications of both parameters.
The identification of multiple change points is a problem shared by many subject areas, including... more The identification of multiple change points is a problem shared by many subject areas, including disease and criminality mapping, medical diagnosis, industrial control, and finance. An algorithm based on the Product Partition Model (PPM) is developed to solve the multiple change point identification problem in Poisson data sequences. In order to address the PPM, a simple and easy way to implement Gibbs sampling scheme is derived. A sensitivity analysis is performed, for different prior specifications. The algorithm is then applied to the analysis of a real data sequence. The results show that the method is quite effective and provides useful inferences.
Brazilian Journal of Probability and Statistics, 2009
The usual finite population model-where information provided by a subset of units is used to redu... more The usual finite population model-where information provided by a subset of units is used to reduce uncertainty about functions of the complete population list of values-is explored from a predictivistic point of view. Under this approach, only operationally meaningful quantities (operational parameters) are considered and therefore no superpopulation parameters are involved. This paper addresses the estimation of both population total and maximum based on uniformity and/or exchangeability judgments on finite sequences of random variables. A central point of this paper is that there are contexts in which the superpopulation approach cannot be employed in inferential problems in finite populations. There are circumstances in which the prior distributions for the operational parameters cannot be obtained from any superpopulation model. Conditions for the extendibility to infinite populations are also established for some models, as this approach may ease the inferential problem.
... Applications and extensions of the PPM can be found in Barry and Hartigan (1993), Crowley (19... more ... Applications and extensions of the PPM can be found in Barry and Hartigan (1993), Crowley (1997), Quintana and Iglesias (2003), Loschi and Cruz (2005) and others (see more on Bayesian approach of multiple change points in Elliott and Shope, 2003). Page 2. ...
The APC framework for modeling and forecasting the education profile of Brazilian males and femal... more The APC framework for modeling and forecasting the education profile of Brazilian males and females is considered from both classical and Bayesian perspectives. For a classical analysis, I calculate maximum likelihood estimates of APC parameters. For the Bayesian analysis, I estimate posterior means and credible intervals. Both methods are simple and computationally efficient. Results show that both classical and Bayesian methods are able to provide very good forecasts in the short term. However, the Bayesian method performed best for in-sample and out-of-sample forecasts. On the other hand, in a Bayesian setting, uncertainty indeed becomes an issue for long-term forecasts because of the rapidly increasing width of the intervals as the length of the projection increases. A number of enhancements of the classical and Bayesian methods proposed here are suggested for a future research agenda. Foremost is an investigation into an integrated approach to account for uncertainty in the classical multinomial APC model and refined ways of eliciting prior information in the Bayesian framework.
In this paper, we consider the product partition model for the estimation of normal means and var... more In this paper, we consider the product partition model for the estimation of normal means and variances of a sequence of observations that experiences changes in these parameters at unknown times. The estimates of the parameters by using product partition model are the weighted average of the estimates based in blocks (groups) of observations by the posterior relevance of these blocks which depends on the prior cohesions. We implement the Barry and Hartigan's method to this change point problem and propose an easy-to-implement modiÿcation to their method. We use Yao's prior cohesions and investigate the in uence of di erent prior distributions to the parameter that indexes these cohesions in the product estimates. A comparison between the estimates obtained by using both these methods and those provided by using Yao's method is done considering di erent settings for its application. We apply the three methods presented in this paper to stock market data. The results seem to indicate that the method proposed is competitive and also that the prior speciÿcations in uence in the product estimates.
In this paper we analyze the fraction of non-disjunction in Meiosis I assuming reference (non-inf... more In this paper we analyze the fraction of non-disjunction in Meiosis I assuming reference (non-informative) priors. We consider Jeffreys's approach to built a non-informative prior (Jeffreys's prior) for the fraction of non-disjunction in Meiosis I. We prove that Jeffreys's prior is a proper distribution. We perform Monte Carlo studies in order to compare Bayes estimates obtained assuming Jeffreys's and uniform priors. We consider full Bayesian significance test (FBST) and Bayes factor (BF) for testing precise hypothesis on the fraction of non-disjunction in Meiosis I. The ultimate goal of this paper is to compare these two test procedures through simulation studies using both prior specifications. An application to Down Syndrome data is also presented.
This paper discusses the Three Prisoners paradox in the light of three different procedures for t... more This paper discusses the Three Prisoners paradox in the light of three different procedures for the updating of probabilities - Bayesian conditioning, superconditioning and Jeffrey's rule - as well as assuming the unpredictability of receipt of information by prisoner A. The formulation of the paradox in this temporal setting brings new insight to the problem and, on the other hand, the paradox is a good way to explain the different updating probability procedures and the difference between conditional probabilities and posterior distributions.
Este é o primeiro de dois artigos complementares que versam sobre um método para a estimação dos ... more Este é o primeiro de dois artigos complementares que versam sobre um método para a estimação dos quantis de enchentes extremas, a partir de uma abordagem Bayesiana, com a possibilidade de inclusão de informações históricas e paleohidrológicas e emprego de distribuições de probabilidades com cauda superior finita. Este artigo aborda o desenvolvimento teórico do método proposto, enquanto o segundo artigo apresenta três aplicações a bacias com diferentes conjuntos de dados disponíveis. Depois de contextualizar o problema de estimação de enchentes extremas, introduz-se aqui a viabilidade de agregação da Cheia Máxima Provável, ou simplesmente PMF (de Probable Maximum Flood), à análise de frequência de variáveis hidrológicas, mediante emprego do paradigma Bayesiano para inferência estatística e de distribuições de probabilidade limitadas superiormente. O limite superior da distribuição em questão está sujeito a incertezas, as quais podem ser sumariadas a partir de distribuições a priori eliciadas, em alguns casos estudados, a partir de um grande banco de estimativas de PMF, conforme aqui demonstrado. Na sequência, o sumário a priori das incertezas pode ser atualizado pela inclusão de informações exatas, obtidas dos registros sistemáticos, e censuradas, de fontes não sistemáticas históricas ou paleohidrológicas, por meio de uma função de verossimilhança suficientemente genérica. A possibilidade do emprego desse grande conjunto de informações em uma estrutura de inferência Bayesiana abre perspectivas para a obtenção de estimativas mais confiáveis de quantis de enchentes extremas. Palavras Chave: cheia máxima provável, análise Bayesiana, enchentes extremas, eventos hidrológicos raros.
Some recent research on fluvial processes suggests the idea that some hydrological variables, suc... more Some recent research on fluvial processes suggests the idea that some hydrological variables, such as flood flows, are upper-bounded. However, most probability distributions that are currently employed in flood frequency analysis are unbounded to the right. This paper describes an exploratory study on the joint use of an upper-bounded probability distribution and non-systematic flood information, within a Bayesian framework. Accordingly,
Page 1. A Bayesian Approach to Spatial Clustering Renato Assunção; Alexandra M. Schmidt; Rosângel... more Page 1. A Bayesian Approach to Spatial Clustering Renato Assunção; Alexandra M. Schmidt; Rosângela Loschi; Joãão Monteiro Departamento de Estatística UFMG, Instituto de Matematica UFRJ. 1 Introduction Consider ...
The multiple change point identification problem may be encountered in many subject areas, includ... more The multiple change point identification problem may be encountered in many subject areas, including disease mapping, medical diagnosis, industrial control, and finance. One appealing way of tackling the problem is through the product partition model (PPM), a Bayesian approach. Nowadays, practical applications of Bayesian methods have attracted attention perhaps because of the generalized use of powerful and inexpensive personal computers. A Gibbs sampling scheme, simple and easy to implement, is used to obtain the estimates. We apply the algorithm to the analysis of two important stock market data in Brazil. The results show that the method is efficient and effective in analyzing change point problems.
The usual finite population model—where information provided by a subset of units is used to redu... more The usual finite population model—where information provided by a subset of units is used to reduce uncertainty about functions of the complete population list of values—is explored from a predictivistic point of view. Under this approach, only operationally meaningful quantities (operational parameters) are considered and therefore no superpopulation parameters are involved. This paper addresses the estimation of both population total
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Papers by R. Loschi