Changing in variance or volatility with time can be modeled as deterministic by using autoregressive conditional heteroscedastic (ARCH) type models, or as stochastic by using stochastic volatility (SV) models. This study compares these two kinds of models which are estimated on Turkish / USA exchange rate data. First, a GARCH(1,1) model is fitted to the data by using the package E-views and then a Bayesian estimation procedure is used for estimating an appropriate SV model with the help of Ox code. In order to compare these models, the LR test statistic calculated for non-nested hypotheses is obtained.

Gravitational waves are predicted by general relativity theory. Their existence could be confirmed by astronomical observations, but until today they have not yet been measured directly. A measurement would not only confirm general relativity, but also allow for interesting astronomical observations. Great effort is currently being expended to facilitate gravitational radiation measurement, most notably through earth-bound interferometers (such as LIGO and Virgo), and the planned space-based LISA interferometer. Earth-bound interferometers have recently taken up operation, so that a detection might be made at any time, while the space-borne LISA interferometer is scheduled to be launched within the next decade.Among the most promising signals for a detection are the waves emitted by the inspiral of a binary system of stars or black holes. The observable gravitational-wave signature of such an event is determined by properties of the inspiralling system, which may in turn be inferred from theobserved data. A Bayesian inference framework for the estimation of parameters of binary inspiral events as measured by ground- and space-based interferometers is described here. Furthermore, appropriate computational methods are developed that are necessary for its application in practice. Starting with a simplified model considering only 5 parameters and data from a single earth-bound interferometer, the model is subsequently refined by extending it to 9 parameters, measurements from several interferometers, and more accurate signal waveform approximations. A realistic joint prior density for the 9 parameters is set up. For the LISA application the model is generalised so that the noise spectrum is treated as unknown as well and can be inferred along with the signal parameters. Inference through the posterior distribution is facilitated by the implementation of Markov chain Monte Carlo (MCMC) methods. The posterior distribution exhibits many local modes, and there is only a small "attraction region" around the global mode(s), making it hard, if not impossible, for basic MCMC algorithms to find the relevant region in parameter space. This problem is solved by introducing a parallel tempering algorithm. Closer investigation of its internal functionality yields some insight into a proper setup of this algorithm, which in turn also enables the efficient implementation for the LISA problem with its vastly enlarged parameter space. Parallel programming was used to implement this computationally expensive MCMC algorithm, so that the code can be run efficiently on a computer cluster. In this thesis, a Bayesian approach to gravitational wave astronomy is shown to be feasible and promising.

Gravitational waves are predicted by general relativity theory. Their existence could be confirmed by astronomical observations, but until today they have not yet been measured directly. A measurement would not only confirm general relativity, but also allow for interesting astronomical observations. Great effort is currently being expended to facilitate gravitational radiation measurement, most notably through earth-bound interferometers (such as LIGO and Virgo), and the planned space-based LISA interferometer. Earth-bound interferometers have recently taken up operation, so that a detection might be made at any time, while the space-borne LISA interferometer is scheduled to be launched within the next decade.Among the most promising signals for a detection are the waves emitted by the inspiral of a binary system of stars or black holes. The observable gravitational-wave signature of such an event is determined by properties of the inspiralling system, which may in turn be inferred from theobserved data. A Bayesian inference framework for the estimation of parameters of binary inspiral events as measured by ground- and space-based interferometers is described here. Furthermore, appropriate computational methods are developed that are necessary for its application in practice. Starting with a simplified model considering only 5 parameters and data from a single earth-bound interferometer, the model is subsequently refined by extending it to 9 parameters, measurements from several interferometers, and more accurate signal waveform approximations. A realistic joint prior density for the 9 parameters is set up. For the LISA application the model is generalised so that the noise spectrum is treated as unknown as well and can be inferred along with the signal parameters. Inference through the posterior distribution is facilitated by the implementation of Markov chain Monte Carlo (MCMC) methods. The posterior distribution exhibits many local modes, and there is only a small "attraction region" around the global mode(s), making it hard, if not impossible, for basic MCMC algorithms to find the relevant region in parameter space. This problem is solved by introducing a parallel tempering algorithm. Closer investigation of its internal functionality yields some insight into a proper setup of this algorithm, which in turn also enables the efficient implementation for the LISA problem with its vastly enlarged parameter space. Parallel programming was used to implement this computationally expensive MCMC algorithm, so that the code can be run efficiently on a computer cluster. In this thesis, a Bayesian approach to gravitational wave astronomy is shown to be feasible and promising.

Gravitational waves are predicted by general relativity theory. Their existence could be confirmed by astronomical observations, but until today they have not yet been measured directly. A measurement would not only confirm general relativity, but also allow for interesting astronomical observations. Great effort is currently being expended to facilitate gravitational radiation measurement, most notably through earth-bound interferometers (such as LIGO and Virgo), and the planned space-based LISA interferometer. Earth-bound interferometers have recently taken up operation, so that a detection might be made at any time, while the space-borne LISA interferometer is scheduled to be launched within the next decade.Among the most promising signals for a detection are the waves emitted by the inspiral of a binary system of stars or black holes. The observable gravitational-wave signature of such an event is determined by properties of the inspiralling system, which may in turn be inferred from theobserved data. A Bayesian inference framework for the estimation of parameters of binary inspiral events as measured by ground- and space-based interferometers is described here. Furthermore, appropriate computational methods are developed that are necessary for its application in practice. Starting with a simplified model considering only 5 parameters and data from a single earth-bound interferometer, the model is subsequently refined by extending it to 9 parameters, measurements from several interferometers, and more accurate signal waveform approximations. A realistic joint prior density for the 9 parameters is set up. For the LISA application the model is generalised so that the noise spectrum is treated as unknown as well and can be inferred along with the signal parameters. Inference through the posterior distribution is facilitated by the implementation of Markov chain Monte Carlo (MCMC) methods. The posterior distribution exhibits many local modes, and there is only a small "attraction region" around the global mode(s), making it hard, if not impossible, for basic MCMC algorithms to find the relevant region in parameter space. This problem is solved by introducing a parallel tempering algorithm. Closer investigation of its internal functionality yields some insight into a proper setup of this algorithm, which in turn also enables the efficient implementation for the LISA problem with its vastly enlarged parameter space. Parallel programming was used to implement this computationally expensive MCMC algorithm, so that the code can be run efficiently on a computer cluster. In this thesis, a Bayesian approach to gravitational wave astronomy is shown to be feasible and promising.

This thesis is divided into two parts. In the first part we describe a new Monte Carlo algorithm for the consistent and unbiased estimation of multidimensional integrals and the efficient sampling from multidimensional densities. The algorithm is inspired by the classical splitting method and can be applied to general static simulation models. We provide examples from rare-event probability estimation, counting, optimization, and sampling, demonstrating that the proposed method can outperform existing Markov chain sampling methods in terms of convergence speed and accuracy. In the second part we present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we propose a new plug-in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods. We present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability.

Gravitational waves are predicted by general relativity theory. Their existence could be confirmed by astronomical observations, but until today they have not yet been measured directly. A measurement would not only confirm general relativity, but also allow for interesting astronomical observations. Great effort is currently being expended to facilitate gravitational radiation measurement, most notably through earth-bound interferometers (such as LIGO and Virgo), and the planned space-based LISA interferometer. Earth-bound interferometers have recently taken up operation, so that a detection might be made at any time, while the space-borne LISA interferometer is scheduled to be launched within the next decade.Among the most promising signals for a detection are the waves emitted by the inspiral of a binary system of stars or black holes. The observable gravitational-wave signature of such an event is determined by properties of the inspiralling system, which may in turn be inferred from theobserved data. A Bayesian inference framework for the estimation of parameters of binary inspiral events as measured by ground- and space-based interferometers is described here. Furthermore, appropriate computational methods are developed that are necessary for its application in practice. Starting with a simplified model considering only 5 parameters and data from a single earth-bound interferometer, the model is subsequently refined by extending it to 9 parameters, measurements from several interferometers, and more accurate signal waveform approximations. A realistic joint prior density for the 9 parameters is set up. For the LISA application the model is generalised so that the noise spectrum is treated as unknown as well and can be inferred along with the signal parameters. Inference through the posterior distribution is facilitated by the implementation of Markov chain Monte Carlo (MCMC) methods. The posterior distribution exhibits many local modes, and there is only a small "attraction region" around the global mode(s), making it hard, if not impossible, for basic MCMC algorithms to find the relevant region in parameter space. This problem is solved by introducing a parallel tempering algorithm. Closer investigation of its internal functionality yields some insight into a proper setup of this algorithm, which in turn also enables the efficient implementation for the LISA problem with its vastly enlarged parameter space. Parallel programming was used to implement this computationally expensive MCMC algorithm, so that the code can be run efficiently on a computer cluster. In this thesis, a Bayesian approach to gravitational wave astronomy is shown to be feasible and promising.

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Neste trabalho utilizamos um modelo espaço-temporal proposto em Rojas (2004) para medir a interação social da criminalidade na região metropolitana de São Paulo. Realizamos simulações de Monte Carlo para testar a capacidade de estimação do modelo em diferentes cenários. Observamos que a estimação melhora com o aumento de observações ao longo do tempo. Já os resultados empíricos indicam que a região metropolitana de São Paulo é um hot spot no estado, pois é encontrado um maior grau de interação social no índice de homicídio em relação aos índices de roubo e furto. / In this paper we employ a spatio-temporal model proposed in Rojas (2004) to evaluate the social interaction in crime in São Paulo metropolitan area. We carry out Monte Carlo simulations to test the model estimation capability in different scenarios. We notice that the estimation gets better as the number of observations in time raises. The results point out that São Paulo metropolitan area is a hot spot in the state since we found out a greater social interaction for the homicide index, compared to robbery and thievery.

Made available in DSpace on 2010-04-20T20:58:17Z (GMT). No. of bitstreams: 5 Juliana_Inhazs.pdf.jpg: 19103 bytes, checksum: 3eae73777efe179efa4f61323cb6007a (MD5) Juliana_Inhazs.pdf.txt: 56465 bytes, checksum: 6aa6f5ecdab4f2116adba5b71f4a111d (MD5) license.txt: 4810 bytes, checksum: be830a7f281cc1281c4d014095a9ff87 (MD5) Juliana_Inhazs.pdf: 234479 bytes, checksum: 982e4b9180d265432c016715b7246a7c (MD5) 1_63070100005.pdf: 267678 bytes, checksum: 6e117ca7ccce2de984bce0f4cc915746 (MD5) Previous issue date: 2009-08-18T00:00:00Z / The term structure interest rate determination is one of the main subjects of the financial assets management. Considering the great importance of the financial assets for the economic policies conduction it is basic to understand structure is determined. The main purpose of this study is to estimate the term structure of Brazilian interest rates together with short term interest rate. The term structure will be modeled based on a model with an affine structure. The estimation was made considering the inclusion of three latent factors and two macroeconomic variables, through the Bayesian technique of the Monte Carlo Markov Chain (MCMC). / A determinação da taxa de juros estrutura a termo é um dos temas principais da gestão de ativos financeiros. Considerando a grande importância dos ativos financeiros para a condução das políticas econômicas, é fundamental para compreender a estrutura que é determinado. O principal objetivo deste estudo é estimar a estrutura a termo das taxas de juros brasileiras, juntamente com taxa de juros de curto prazo. A estrutura a termo será modelado com base em um modelo com uma estrutura afim. A estimativa foi feita considerando a inclusão de três fatores latentes e duas variáveis ​​macroeconômicas, através da técnica Bayesiana da Cadeia de Monte Carlo Markov (MCMC).

Neste trabalho utilizamos um modelo espaço-temporal proposto em Rojas (2004) para medir a interação social da criminalidade na região metropolitana de São Paulo. Realizamos simulações de Monte Carlo para testar a capacidade de estimação do modelo em diferentes cenários. Observamos que a estimação melhora com o aumento de observações ao longo do tempo. Já os resultados empíricos indicam que a região metropolitana de São Paulo é um hot spot no estado, pois é encontrado um maior grau de interação social no índice de homicídio em relação aos índices de roubo e furto. / In this paper we employ a spatio-temporal model proposed in Rojas (2004) to evaluate the social interaction in crime in São Paulo metropolitan area. We carry out Monte Carlo simulations to test the model estimation capability in different scenarios. We notice that the estimation gets better as the number of observations in time raises. The results point out that São Paulo metropolitan area is a hot spot in the state since we found out a greater social interaction for the homicide index, compared to robbery and thievery.