Sequential, Bayesian geostatistics:a principled method for large data sets

The principled statistical application of Gaussian random field models used in geostatistics has historically been limited to data sets of a small size. This limitation is imposed by the requirement to store and invert the covariance matrix of all the samples to obtain a predictive distribution at unsampled locations, or to use likelihood-based covariance estimation. Various ad hoc approaches to solve this problem have been adopted, such as selecting a neighborhood region and/or a small number of observations to use in the kriging process, but these have no sound theoretical basis and it is unclear what information is being lost. In this article, we present a Bayesian method for estimating the posterior mean and covariance structures of a Gaussian random field using a sequential estimation algorithm. By imposing sparsity in a well-defined framework, the algorithm retains a subset of “basis vectors” that best represent the “true” posterior Gaussian random field model in the relative entropy sense. This allows a principled treatment of Gaussian random field models on very large data sets. The method is particularly appropriate when the Gaussian random field model is regarded as a latent variable model, which may be nonlinearly related to the observations. We show the application of the sequential, sparse Bayesian estimation in Gaussian random field models and discuss its merits and drawbacks.

Estimating wave spectra from the motions of moored vessels: Experimental validation

The practicability of estimating directional wave spectra based on a vessel`s 1st order response has been recently addressed by several researchers. Different alternatives regarding statistical inference methods and possible drawbacks that could arise from their application have been extensively discussed, with an apparent preference for estimations based on Bayesian inference algorithms. Most of the results on this matter, however, rely exclusively on numerical simulations or at best on few and sparse full-scale measurements, comprising a questionable basis for validation purposes. This paper discusses several issues that have recently been debated regarding the advantages of Bayesian inference and different alternatives for its implementation. Among those are the definition of the best set of input motions, the number of parameters required for guaranteeing smoothness of the spectrum in frequency and direction and how to determine their optimum values. These subjects are addressed in the light of an extensive experimental campaign performed with a small-scale model of an FPSO platform (VLCC hull), which was conducted in an ocean basin in Brazil. Tests involved long and short crested seas with variable levels of directional spreading and also bimodal conditions. The calibration spectra measured in the tank by means of an array of wave probes configured the paradigm for estimations. Results showed that a wide range of sea conditions could be estimated with good precision, even those with somewhat low peak periods. Some possible drawbacks that have been pointed out in previous works concerning the viability of employing large vessels for such a task are then refuted. Also, it is shown that a second parameter for smoothing the spectrum in frequency may indeed increase the accuracy in some situations, although the criterion usually proposed for estimating the optimum values (ABIC) demands large computational effort and does not seem adequate for practical on-board systems, which require expeditious estimations. (C) 2009 Elsevier Ltd. All rights reserved.

Comparison of two population pharmacokinetic programs, NONMEM and P-PHARM, for tacrolimus

Objectives: To compare the population modelling programs NONMEM and P-PHARM during investigation of the pharmacokinetics of tacrolimus in paediatric liver-transplant recipients. Methods: Population pharmacokinetic analysis was performed using NONMEM and P-PHARM on retrospective data from 35 paediatric liver-transplant patients receiving tacrolimus therapy. The same data were presented to both programs. Maximum likelihood estimates were sought for apparent clearance (CL/F) and apparent volume of distribution (V/F). Covariates screened for influence on these parameters were weight, age, gender, post-operative day, days of tacrolimus therapy, transplant type, biliary reconstructive procedure, liver function tests, creatinine clearance, haematocrit, corticosteroid dose, and potential interacting drugs. Results: A satisfactory model was developed in both programs with a single categorical covariate - transplant type - providing stable parameter estimates and small, normally distributed (weighted) residuals. In NONMEM, the continuous covariates - age and liver function tests - improved modelling further. Mean parameter estimates were CL/F (whole liver) = 16.3 1/h, CL/F (cut-down liver) = 8.5 1/h and V/F = 565 1 in NONMEM, and CL/F = 8.3 1/h and V/F = 155 1 in P-PHARM. Individual Bayesian parameter estimates were CL/F (whole liver) = 17.9 +/- 8.8 1/h, CL/F (cutdown liver) = 11.6 +/- 18.8 1/h and V/F = 712 792 1 in NONMEM, and CL/F (whole liver) = 12.8 +/- 3.5 1/h, CL/F (cut-down liver) = 8.2 +/- 3.4 1/h and V/F = 221 1641 in P-PHARM. Marked interindividual kinetic variability (38-108%) and residual random error (approximately 3 ng/ml) were observed. P-PHARM was more user friendly and readily provided informative graphical presentation of results. NONMEM allowed a wider choice of errors for statistical modelling and coped better with complex covariate data sets. Conclusion: Results from parametric modelling programs can vary due to different algorithms employed to estimate parameters, alternative methods of covariate analysis and variations and limitations in the software itself.

Padrões espaço-temporais da mortalidade por câncer de mama em mulheres no Estado do Espírito Santo - um estudo ecológico

O câncer de mama é a principal neoplasia maligna que acomete o sexo feminino no Brasil. O câncer de mama é hoje uma doença de extrema importância para a saúde pública nacional, motivando ampla discussão em torno das medidas que promova o seu diagnóstico precoce, a redução em sua morbidade e mortalidade. A presente pesquisa possui três objetivos, cujos resultados encontram-se organizados em artigos. O primeiro objetivo buscou analisar a completude dos dados do Sistema de Informação de Mortalidade sobre os óbitos por câncer de mama em mulheres no Espírito Santo, Sudeste e Brasil (1998 a 2007). Realizou-se um estudo descritivo analítico baseado em dados secundários, onde foi analisado o número absoluto e percentual de não preenchimento das variáveis nas declarações de óbitos. Adotou-se escore para avaliar os graus de não completude. Os resultados para as variáveis sexo e idade foram excelentes tanto para o Espírito Santo, Sudeste e Brasil. O preenchimento das variáveis raça/cor, grau de escolaridade e estado civil apresentam problemas no Espírito Santo. Enquanto no Sudeste e Brasil as variáveis raça/cor e escolaridade têm tendência decrescente para a não completude, no Espírito Santo a tendência se mantém estável. Para a variável estado civil, a não completude tem tendência crescente no Estado do Espírito Santo. O segundo objetivo foi analisar a evolução das taxas de mortalidade por câncer de mama, em mulheres no Espírito Santo no período de 1980 a 2007. Estudo de série temporal, cujos dados sobre óbitos foram obtidos do Sistema de Informação de Mortalidade e as estimativas populacionais segundo idade e anos-calendário, do Instituto Brasileiro Geografia e Estatística. Os coeficientes específicos 9 de mortalidade, segundo faixa etária, foram calculados anualmente. A análise de tendência foi realizada por meio da padronização das taxas de mortalidade pelo método direto, em que a população do senso IBGE-2000, foi considerada padrão. No período de estudo, ocorreram 2.736 óbitos por câncer de mama. O coeficiente de mortalidade neste período variou de 3,41 a 10,99 por 100.000 mulheres. Os resultados indicam que há tendência de mortalidade por câncer de mama ao longo da série (p=0,001 com crescimento de 75,42%). Todas as faixas etárias a partir de 30 anos apresentaram tendência de crescimento da mortalidade estatisticamente significante (p=0,001). Os percentuais de crescimento foram aumentando, segundo as idades mais avançadas, sendo 48,4% na faixa de 40 a 49 anos, chegando a 92,3%, na faixa de 80 anos e mais. O terceiro objetivo foi realizar a análise espacial dos óbitos em mulheres por câncer de mama no estado do Espírito Santo, nos anos de 2003 a 2007, com análise das correlações espaciais dessa mortalidade e componentes do município. O cenário foi o Estado do Espírito Santo, composto por 78 municípios. Para análise dos dados, utilizou-se a abordagem bayesiana (métodos EBest Global e EBest Local) para correção de taxas epidemiológicas. Calculou-se o índice I de Moran, para dependência espacial em nível global e a estatística Moran Local. As maiores taxas estão concentradas em 19 municípios pertencentes às Microrregiões: Metropolitana (Fundão, Vitória, Vila Velha, Viana, Cariacica e Guarapari), Metrópole Expandida Sul (Anchieta, Alfredo Chaves), Pólo Cachoeiro (Vargem Alta, Rio Novo do Sul, Mimoso do Sul, Cachoeiro de Itapemirim, Castelo, Jerônimo Monteiro, Bom Jesus do Norte, Apiacá e Muqui) e Caparaó (Alegre e São José do Calçado). Os resultados da Estimação Bayesiana (Índice de Moran) dos óbitos por câncer de mama em mulheres ocorridos no estado do Espírito Santo, segundo os dados brutos e 10 ajustados indicam a existência de correlação espacial significativa para o mapa Local (I = 0,573; p = 0,001) e Global (I = 0,118; p = 0,039). Os dados brutos não apresentam correlação espacial (I = 0,075; p = 0,142).

An RBC model with a rich fiscal sector

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Economics from the NOVA – School of Business and Economics

Technology shocks and aggregate fluctuations in an estimated hybrid RBC model

This paper contributes to the on-going empirical debate regarding the role of the RBC model and in particular of technology shocks in explaining aggregate fluctuations. To this end we estimate the model’s posterior density using Markov-Chain Monte-Carlo (MCMC) methods. Within this framework we extend Ireland’s (2001, 2004) hybrid estimation approach to allow for a vector autoregressive moving average (VARMA) process to describe the movements and co-movements of the model’s errors not explained by the basic RBC model. The results of marginal likelihood ratio tests reveal that the more general model of the errors significantly improves the model’s fit relative to the VAR and AR alternatives. Moreover, despite setting the RBC model a more difficult task under the VARMA specification, our analysis, based on forecast error and spectral decompositions, suggests that the RBC model is still capable of explaining a significant fraction of the observed variation in macroeconomic aggregates in the post-war U.S. economy.

Productivity shocks and aggregate fluctuations in an estimated endogenous growth model with human capital

Employing an endogenous growth model with human capital, this paper explores how productivity shocks in the goods and human capital producing sectors contribute to explaining aggregate fluctuations in output, consumption, investment and hours. Given the importance of accounting for both the dynamics and the trends in the data not captured by the theoretical growth model, we introduce a vector error correction model (VECM) of the measurement errors and estimate the model’s posterior density function using Bayesian methods. To contextualize our findings with those in the literature, we also assess whether the endogenous growth model or the standard real business cycle model better explains the observed variation in these aggregates. In addressing these issues we contribute to both the methods of analysis and the ongoing debate regarding the effects of innovations to productivity on macroeconomic activity.

How Optimal is US Monetary Policy?

Most of the literature estimating DSGE models for monetary policy analysis assume that policy follows a simple rule. In this paper we allow policy to be described by various forms of optimal policy - commitment, discretion and quasi-commitment. We find that, even after allowing for Markov switching in shock variances, the inflation target and/or rule parameters, the data preferred description of policy is that the US Fed operates under discretion with a marked increase in conservatism after the 1970s. Parameter estimates are similar to those obtained under simple rules, except that the degree of habits is significantly lower and the prevalence of cost-push shocks greater. Moreover, we find that the greatest welfare gains from the ‘Great Moderation’ arose from the reduction in the variances in shocks hitting the economy, rather than increased inflation aversion. However, much of the high inflation of the 1970s could have been avoided had policy makers been able to commit, even without adopting stronger anti-inflation objectives. More recently the Fed appears to have temporarily relaxed policy following the 1987 stock market crash, and has lost, without regaining, its post-Volcker conservatism following the bursting of the dot-com bubble in 2000.

News Shocks and Business Cycles: Bridging the Gap from Different Methodologies

An important disconnect in the news driven view of the business cycle formalized by Beaudry and Portier (2004), is the lack of agreement between different—VAR and DSGE—methodologies over the empirical plausibility of this view. We argue that this disconnect can be largely resolved once we augment a standard DSGE model with a financial channel that provides amplification to news shocks. Both methodologies suggest news shocks to the future growth prospects of the economy to be significant drivers of U.S. business cycles in the post-Greenspan era (1990-2011), explaining as much as 50% of the forecast error variance in hours worked in cyclical frequencies

An Empirical Assessment of Optimal Monetary Policy Delegation in the Euro Area

We estimate a New Keynesian DSGE model for the Euro area under alternative descriptions of monetary policy (discretion, commitment or a simple rule) after allowing for Markov switching in policy maker preferences and shock volatilities. This reveals that there have been several changes in Euro area policy making, with a strengthening of the anti-inflation stance in the early years of the ERM, which was then lost around the time of German reunification and only recovered following the turnoil in the ERM in 1992. The ECB does not appear to have been as conservative as aggregate Euro-area policy was under Bundesbank leadership, and its response to the financial crisis has been muted. The estimates also suggest that the most appropriate description of policy is that of discretion, with no evidence of commitment in the Euro-area. As a result although both ‘good luck’ and ‘good policy’ played a role in the moderation of inflation and output volatility in the Euro-area, the welfare gains would have been substantially higher had policy makers been able to commit. We consider a range of delegation schemes as devices to improve upon the discretionary outcome, and conclude that price level targeting would have achieved welfare levels close to those attained under commitment, even after accounting for the existence of the Zero Lower Bound on nominal interest rates.

An Empirical Assessment of Optimal Monetary Policy Delegation in the Euro Area

We estimate a New Keynesian DSGE model for the Euro area under alternative descriptions of monetary policy (discretion, commitment or a simple rule) after allowing for Markov switching in policy maker preferences and shock volatilities. This reveals that there have been several changes in Euro area policy making, with a strengthening of the anti-inflation stance in the early years of the ERM, which was then lost around the time of German reunification and only recovered following the turnoil in the ERM in 1992. The ECB does not appear to have been as conservative as aggregate Euro-area policy was under Bundesbank leadership, and its response to the financial crisis has been muted. The estimates also suggest that the most appropriate description of policy is that of discretion, with no evidence of commitment in the Euro-area. As a result although both ‘good luck’ and ‘good policy’ played a role in the moderation of inflation and output volatility in the Euro-area, the welfare gains would have been substantially higher had policy makers been able to commit. We consider a range of delegation schemes as devices to improve upon the discretionary outcome, and conclude that price level targeting would have achieved welfare levels close to those attained under commitment, even after accounting for the existence of the Zero Lower Bound on nominal interest rates.

US Monetary and Fiscal Policies - Conflict or Cooperation?

Most of the literature estimating DSGE models for monetary policy analysis ignores fiscal policy and assumes that monetary policy follows a simple rule. In this paper we allow both fiscal and monetary policy to be described by rules and/or optimal policy which are subject to switches over time. We find that US monetary and fiscal policy have often been in conflict, and that it is relatively rare that we observe the benign policy combination of an conservative monetary policy paired with a debt stabilizing fiscal policy. In a series of counterfactuals, a conservative central bank following a time-consistent fiscal policy leader would come close to mimicking the cooperative Ramsey policy. However, if policy makers cannot credibly commit to such a regime, monetary accommodation of the prevailing fiscal regime may actually be welfare improving.

Performance persistence of equity funds in the Russian stock market

This thesis investigates performance persistence among the equity funds investing in Russia during 2003-2007. Fund performance is measured using several methods including the Jensen alpha, the Fama-French 3- factor alpha, the Sharpe ratio and two of its variations. Moreover, we apply the Bayesian shrinkage estimation in performance measurement and evaluate its usefulness compared with the OLS 3-factor alphas. The pattern of performance persistence is analyzed using the Spearman rank correlation test, cross-sectional regression analysis and stacked return time series. Empirical results indicate that the Bayesian shrinkage estimates may provide better and more accurate estimates of fund performance compared with the OLS 3-factor alphas. Secondly, based on the results it seems that the degree of performance persistence is strongly related to length of the observation period. For the full sample period the results show strong signs of performance reversal whereas for the subperiod analysis the results indicate performance persistence during the most recent years.

Essays on oil price fluctuations and macroeconomic activity

Dans cette thèse, je me suis intéressé aux effets des fluctuations du prix de pétrole sur l'activité macroéconomique selon la cause sous-jacente ces fluctuations. Les modèles économiques utilisés dans cette thèse sont principalement les modèles d'équilibre général dynamique stochastique (de l'anglais Dynamic Stochastic General Equilibrium, DSGE) et les modèles Vecteurs Autorégressifs, VAR. Plusieurs études ont examiné les effets des fluctuations du prix de pétrole sur les principaux variables macroéconomiques, mais très peu d'entre elles ont fait spécifiquement le lien entre les effets des fluctuations du prix du pétrole et la l'origine de ces fluctuations. Pourtant, il est largement admis dans les études plus récentes que les augmentations du prix du pétrole peuvent avoir des effets très différents en fonction de la cause sous-jacente de cette augmentation. Ma thèse, structurée en trois chapitres, porte une attention particulière aux sources de fluctuations du prix de pétrole et leurs impacts sur l'activité macroéconomique en général, et en particulier sur l'économie du Canada. Le premier chapitre examine comment les chocs d'offre de pétrole, de demande agrégée, et de demande de précaution de pétrole affectent l'économie du Canada, dans un Modèle d'équilibre Général Dynamique Stochastique estimé. L'estimation est réalisée par la méthode Bayésienne, en utilisant des données trimestrielles canadiennes sur la période 1983Q1 à 2010Q4. Les résultats montrent que les effets dynamiques des fluctuations du prix du pétrole sur les principaux agrégats macro-économiques canadiens varient en fonction de leurs sources. En particulier, une augmentation de 10% du prix réel du pétrole causée par des chocs positifs sur la demande globale étrangère a un effet positif significatif de l'ordre de 0,4% sur le PIB réel du Canada au moment de l'impact et l'effet reste positif sur tous les horizons. En revanche, une augmentation du prix réel du pétrole causée par des chocs négatifs sur l'offre de pétrole ou par des chocs positifs de la demande de pétrole de précaution a un effet négligeable sur le PIB réel du Canada au moment de l'impact, mais provoque une baisse légèrement significative après l'impact. En outre, parmi les chocs pétroliers identifiés, les chocs sur la demande globale étrangère ont été relativement plus important pour expliquer la fluctuation des principaux agrégats macroéconomiques du Canada au cours de la période d'estimation. Le deuxième chapitre utilise un modèle Structurel VAR en Panel pour examiner les liens entre les chocs de demande et d'offre de pétrole et les ajustements de la demande de travail et des salaires dans les industries manufacturières au Canada. Le modèle est estimé sur des données annuelles désagrégées au niveau industriel sur la période de 1975 à 2008. Les principaux résultats suggèrent qu'un choc positif de demande globale a un effet positif sur la demande de travail et les salaires, à court terme et à long terme. Un choc négatif sur l'offre de pétrole a un effet négatif relativement faible au moment de l'impact, mais l'effet devient positif après la première année. En revanche, un choc positif sur la demande précaution de pétrole a un impact négatif à tous les horizons. Les estimations industrie-par-industrie confirment les précédents résultats en panel. En outre, le papier examine comment les effets des différents chocs pétroliers sur la demande travail et les salaires varient en fonction du degré d'exposition commerciale et de l'intensité en énergie dans la production. Il ressort que les industries fortement exposées au commerce international et les industries fortement intensives en énergie sont plus vulnérables aux fluctuations du prix du pétrole causées par des chocs d'offre de pétrole ou des chocs de demande globale. Le dernier chapitre examine les implications en terme de bien-être social de l'introduction des inventaires en pétrole sur le marché mondial à l'aide d'un modèle DSGE de trois pays dont deux pays importateurs de pétrole et un pays exportateur de pétrole. Les gains de bien-être sont mesurés par la variation compensatoire de la consommation sous deux règles de politique monétaire. Les principaux résultats montrent que l'introduction des inventaires en pétrole a des effets négatifs sur le bien-être des consommateurs dans chacun des deux pays importateurs de pétrole, alors qu'il a des effets positifs sur le bien-être des consommateurs dans le pays exportateur de pétrole, quelle que soit la règle de politique monétaire. Par ailleurs, l'inclusion de la dépréciation du taux de change dans les règles de politique monétaire permet de réduire les coûts sociaux pour les pays importateurs de pétrole. Enfin, l'ampleur des effets de bien-être dépend du niveau d'inventaire en pétrole à l'état stationnaire et est principalement expliquée par les chocs sur les inventaires en pétrole.

Bayes quadratic unbiased estimator of spatial covariance parameters

This work presents Bayes invariant quadratic unbiased estimator, for short BAIQUE. Bayesian approach is used here to estimate the covariance functions of the regionalized variables which appear in the spatial covariance structure in mixed linear model. Firstly a brief review of spatial process, variance covariance components structure and Bayesian inference is given, since this project deals with these concepts. Then the linear equations model corresponding to BAIQUE in the general case is formulated. That Bayes estimator of variance components with too many unknown parameters is complicated to be solved analytically. Hence, in order to facilitate the handling with this system, BAIQUE of spatial covariance model with two parameters is considered. Bayesian estimation arises as a solution of a linear equations system which requires the linearity of the covariance functions in the parameters. Here the availability of prior information on the parameters is assumed. This information includes apriori distribution functions which enable to find the first and the second moments matrix. The Bayesian estimation suggested here depends only on the second moment of the prior distribution. The estimation appears as a quadratic form y'Ay , where y is the vector of filtered data observations. This quadratic estimator is used to estimate the linear function of unknown variance components. The matrix A of BAIQUE plays an important role. If such a symmetrical matrix exists, then Bayes risk becomes minimal and the unbiasedness conditions are fulfilled. Therefore, the symmetry of this matrix is elaborated in this work. Through dealing with the infinite series of matrices, a representation of the matrix A is obtained which shows the symmetry of A. In this context, the largest singular value of the decomposed matrix of the infinite series is considered to deal with the convergence condition and also it is connected with Gerschgorin Discs and Poincare theorem. Then the BAIQUE model for some experimental designs is computed and compared. The comparison deals with different aspects, such as the influence of the position of the design points in a fixed interval. The designs that are considered are those with their points distributed in the interval [0, 1]. These experimental structures are compared with respect to the Bayes risk and norms of the matrices corresponding to distances, covariance structures and matrices which have to satisfy the convergence condition. Also different types of the regression functions and distance measurements are handled. The influence of scaling on the design points is studied, moreover, the influence of the covariance structure on the best design is investigated and different covariance structures are considered. Finally, BAIQUE is applied for real data. The corresponding outcomes are compared with the results of other methods for the same data. Thereby, the special BAIQUE, which estimates the general variance of the data, achieves a very close result to the classical empirical variance.