Analysis of a circular code model

A circular code has been identified in the protein (coding) genes of both eukaryotes and prokaryotes by using a statistical method called Trinucleotide Frequency method (TF method) [Arquès & Michel, (1996) J.Theor. Biol. 182, 45-58]. Recently, a probabilistic model based on the nucleotide frequencies with a hypothesis of absence of correlation between successive bases on a DNA strand, has been proposed by Koch & Lehmann [(1997) J.Theor. Biol. 189, 171-174] for constructing some particular circular codes. Their interesting method which we call here Nucleotide Frequency method (NF method), reveals several limits for constructing the circular code observed with protein genes

Inference in non stationary asymmetric garch models

This paper considers the statistical inference of the class of asymmetric power-transformed GARCH(1,1) models in presence of possible explosiveness. We study the explosive behavior of volatility when the strict stationarity condition is not met. This allows us to establish the asymptotic normality of the quasi-maximum likelihood estimator (QMLE) of the parameter, including the power but without the intercept, when strict stationarity does not hold. Two important issues can be tested in this framework: asymmetry and stationarity. The tests exploit the existence of a universal estimator of the asymptotic covariance matrix of the QMLE. By establishing the local asymptotic normality (LAN) property in this nonstationary framework, we can also study optimality issues

Portmanteau goodness-of-fit test for asymmetric power GARCH models

The asymptotic distribution of a vector of autocorrelations of squared residuals is derived for a wide class of asymmetric GARCH models. Portmanteau adequacy tests are deduced. %gathered These results are obtained under moment assumptions on the iid process, but fat tails are allowed for the observed process, which is particularly relevant for series of financial returns. A Monte Carlo experiment and an illustration to financial series are also presented.ARCH models; Leverage effect; Portmanteau test; Goodness-of-fit test; Diagnostic checking

On computational tools for Bayesian data analysis

While Robert and Rousseau (2010) addressed the foundational aspects of Bayesian analysis, the current chapter details its practical aspects through a review of the computational methods available for approximating Bayesian procedures. Recent innovations like Monte Carlo Markov chain, sequential Monte Carlo methods and more recently Approximate Bayesian Computation techniques have considerably increased the potential for Bayesian applications and they have also opened new avenues for Bayesian inference, first and foremost Bayesian model choice.Comment: This is a chapter for the book "Bayesian Methods and Expert Elicitation" edited by Klaus Bocker, 23 pages, 9 figure

Importance sampling methods for Bayesian discrimination between embedded models

This paper surveys some well-established approaches on the approximation of Bayes factors used in Bayesian model choice, mostly as covered in Chen et al. (2000). Our focus here is on methods that are based on importance sampling strategies rather than variable dimension techniques like reversible jump MCMC, including: crude Monte Carlo, maximum likelihood based importance sampling, bridge and harmonic mean sampling, as well as Chib's method based on the exploitation of a functional equality. We demonstrate in this survey how these different methods can be efficiently implemented for testing the significance of a predictive variable in a probit model. Finally, we compare their performances on a real dataset

Bayesian Core: The Complete Solution Manual

This solution manual contains the unabridged and original solutions to all the exercises proposed in Bayesian Core, along with R programs when necessary.Comment: 118+vii pages, 21 figures, 152 solution

From Global to Local Fluctuation Theorems

The Gallavotti-Cohen fluctuation theorem suggests a general symmetry in the fluctuations of the entropy production, a basic concept in the theory of irreversible processes, based on results in the theory of strongly chaotic maps. We study this symmetry for some standard models of nonequilibrium steady states. We give a general strategy to derive a 'local' fluctuation theorem exploiting the Gibbsian features of the stationary space-time distribution. This is applied to spin flip processes and to the asymmetric exclusion process.Comment: minor changes, to appear in the Moscow Mathematical Journa

QML estimation of a class of multivariate GARCH models without moment conditions on the observed process

We establish the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator of the parameters of a class of multivariate GARCH processes. The conditions are mild and coincide with the minimal ones in the univariate case. In particular, contrary to the current literature on the estimation of multivariate GARCH models, no moment assumption is made on the observed process. Instead, we require strict stationarity, for which a necessary and sufficient condition is established.Asymptotic Normality; Conditional Heteroskedasticity; Consistency; Constant Conditional Correlation; Multivariate GARCH; Quasi Maximum Likelihood Estimation; Strict Stationarity Condition