Leitura do Dia - Bayesian heavy-tailed models and con‡flict resolution: a review

Bayesian heavy-tailed models and con‡flict resolution: a review

Anthony O’Hagan and Luis Pericchi

April 5, 2011

Abstract
We review a substantial literature, spanning 50 years, concerning the resolution of confl‡icts using Bayesian heavy-tailed models. Con‡icts arise when different sources of information about the model parameters (e.g. prior information, or the information in individual observations) sug-
gest quite different plausible regions for those parameters. Traditional Bayesian models based on normal distributions or other conjugate structures typically resolve con‡icts by centring the posterior at some compromise position, but this is not a realistic resolution when it means that
the posterior is then in con‡ict with the different information sources.
Bayesian modelling with heavy-tailed distributions has been shown to produce more reasonable con‡ict resolution, typically by favouring one source of information over the other. The less favoured source is ultimately wholly or partially rejected as the con‡ict becomes increasingly
extreme.
The literature reviewed here provides formal proofs of con‡ict resolution by asymptotic rejection of some information sources. Results are given for a variety of models, from the simplest case of a single observation relating to a single location parameter up to models with many
location parameters, location and scale parameters, or other kinds of parameters. However, these results do not begin to address models of the kind of complexity that are routinely used in practical Bayesian modelling. In addition to reviewing the available theory, we also identify clearly the gaps in the literature that need to be …filled in order for modellers to be able to develop applications with appropriate ‘built-in robustness’.

Keywords: rejection of information, partial rejection of information, built-in robustness, heavy-tailed modelling, theory of conffl‡ict resolution,
outliers

Uma boa noite de sono

Hoje, depois de muito tempo, terei uma boa noite de sono. Os dois últimos dias foram muito melhores que eu esperava. Ótimas notícias.

Novo Working Paper - Generalized Tests of Investment Fund Performance

Generalized Tests of Investment Fund Performance

Márcio Laurini

Rogério da Costa Monteiro

Antônio Zoratto Sanvicente

Abstract

The paper discusses the use of statistical methods in the comparison of investment fund performance indicators. The analysis is based on the robust statistics proposed by Ledoit and Wolf (2008), for the pairwise comparison of funds and two generalizations for sets of multiple investment funds. The multiple investment fund tests use the Wald and Distance Metric statistics, based on estimation by Generalized Method of Moments using HAC matrices. In order to correct power limitations in the GMM estimation in the case of a large number of moment conditions, the test distributions are obtained through block-bootstrap procedures. We applied the proposed procedures to daily return data for the largest 97 actively managed equity funds in the Brazilian market, covering the period from July 2006 to July 2008. The results indicate that there are no significant differences in the performances of the 97 funds in the sample, both in pairwise and joint comparisons, thus providing what is believed to be the first Brazilian market evidence for the so-called herding hypothesis.

Finalizando

Mais uma última revisada e fechamos a primeira versão completa do artigo sobre testes de desempenho de fundos. Era para ser uma nota, mas foi crescendo e virou um artigo completo. Uma adição relevante foi comparar os resultados com métodos de comparações múltiplas controlando para Familywise Error Rate e False Discovery Rate. Também foi interessante trabalhar mais diretamente com propriedades de testes de hipóteses, já que normalmente meu foco é mais em procedimentos de inferẽncia. Muitas e muitas leituras do clássico Testing Statistical Hypothesis, Lehmann and Romano para essa versão final.

Leitura do Dia - Markovian Gaussian models in spatial statistics

Think continuous: Markovian Gaussian models in spatial statistics

Daniel Simpson, Finn Lindgren & Hävard Rue

Department of Mathematical Sciences

Norwegian University of Science and Technology

N-7491 Trondheim, Norway

October 31, 2011

Abstract

Gaussian Markov random fields (GMRFs) are frequently used as computationally efficient

models in spatial statistics. Unfortunately, it has traditionally been difficult to link GMRFs with the more traditional Gaussian random field models as the Markov property is difficult to deploy in continuous space. Following the pioneering work of Lindgren et al. (2011), we expound on the link between Markovian Gaussian random fields and GMRFs. In particular, we discuss the theoretical and practical aspects of fast computation with continuously specified Markovian Gaussian random fields, as well as the clear advantages they offer in terms of clear, parsimonious and interpretable models of anisotropy and non-stationarity.

11th Brazilian Bayesian Statistics Meeting

Nessa semana está acontecendo o 11th Brazilian Bayesian Statistics Meeting. Estou realmente me lamentando por não ter ido este ano. Espero me organizar melhor ano que vem para não ficar tão entupido de trabalho como esse começo de ano.

Yossarian Lives

"Catch-22 states that agents enforcing Catch-22 need not prove that Catch-22 actually contains whatever provision the accused violator is accused of violating."

Novo Working Paper - A Hybrid Data Cloning Maximum Likelihood Estimator for Stochastic Volatility Models

A Hybrid Data Cloning Maximum Likelihood Estimator for Stochastic Volatility Models

Márcio Laurini

(IBMEC Business School)

Abstract

In this paper we analyze a maximum likelihood estimator using data cloning for stochastic volatility models. This estimator is constructed using a hybrid methodology based on Integrated Nested Laplace Approximations to calculate analytically the auxiliary Bayesian estimators with great accuracy and computational efficiency, without requiring the use of simulation methods as Markov Chain Monte Carlo. We analyze the performance of this estimator compared to methods based in Monte Carlo simulations (Simulated Maximum Likelihood, MCMC Maximum Likelihood) and approximate maximum likelihood estimators using Laplace Approximations. The results indicate that this data cloning methodology achieves superior results over methods based on MCMC, and comparable to results obtained by the Simulated Maximum Likelihood estimator.

É a primeira versão do artigo de HDC-MLE para a estimação de modelos SV. É o desenvolvimento de uma idéia que apresentei durante o mini-curso de modelos de volatilidade que apresentei na Escola de Séries Temporais no ano passado.

Novo Working Paper - Dynamic Functional Data Analysis with Nonparametric State Space Models

Dynamic Functional Data Analysis with Nonparametric State Space Models

Márcio Laurini

(IBMEC Business School)

Abstract

In this article we introduce a new methodology for modeling curves with a dynamic structure, using a non-parametric approach formulated as a state space model. The non-parametric approach is based on the use of penalized splines, represented as a dynamic mixed model. This formulation can capture the dynamic evolution of curves using a limited number of latent factors, allowing a accurate fit with a limited number of parameters. We also present a new method to determine the optimal smoothing parameter through an adaptive procedure using a formulation analogous to a model of stochastic volatility. This methodology allows unifying different methodologies applied to data with a functional structure in finance. We present the advantages and limitations of this methodology through a simulation study and also comparing its predictive performance with other parametric and non-parametric methods used in financial applications using data from term structure of interest rates.

É a segunda versão deste artigo, focando as aplicações em estrutura a termo de taxas de juros. Na primeira versão haviam outras aplicações em finanças, mas estava um pouco longo.

Revisão finalizada

Revisão finalizada. Como já escrevi, normalmente revisar artigos não é algo muito agradável. No caso a revisão foi facilitada porque muito dos pedidos dos pareceristas já estavam quase prontos. Eu já havia testado muitas das especificações alternativas para a primeira versão do artigo, e a parte mais complicada foi organizar estes resultados. Outro fator positivo foi que no tempo entre a primeira versão do artigo e essa revisão foram publicados alguns artigos que ajudaram a explicar alguns dos resultados que eu tive, com resultados analíticos sobre viés de discretização e algumas propriedades que não eram conhecidas do estimador de Inferência Indireta.

Moebius

Adeus Moebius. Dono de um estilo único. Lembro especialmente da sua versão do Surfista Prateado.

90%

Quase finalizando a revisão do artigo de fractional brownian motion. Depois de muitas horas de sono perdido e muitas e muitas horas em simulações e novas análises, o texto está tomando a forma final.

Abraham De Moivre

Xi'an's Og fez uma revisão bastante favorável da biografia de Abraham De Moivre, escrita por David Bellhouse. Já coloquei na minha lista de compras.

On the Road, Again

Caindo na estrada. Aproveitando o feriado aqui no Rio, vou a São Paulo hoje trabalhar em alguns projetos de pesquisa. Dois estão bem adiantados, mas o terceiro ainda engatinhando. Pena que com essa correria da revisão não vou poder ficar no final de semana e devo voltar na sexta mesmo. Seria bom curtir SP de novo.