Context tree selection: A unifying view

Context tree models have been introduced by Rissanen in [25] as a parsimonious generalization of Markov models. Since then, they have been widely used in applied probability and statistics. The present paper investigates non-asymptotic properties of two popular procedures of context tree estimation: Rissanen's algorithm Context and penalized maximum likelihood. First showing how they are related, we prove finite horizon bounds for the probability of over- and under-estimation. Concerning overestimation, no boundedness or loss-of-memory conditions are required: the proof relies on new deviation inequalities for empirical probabilities of independent interest. The under-estimation properties rely on classical hypotheses for processes of infinite memory. These results improve on and generalize the bounds obtained in Duarte et al. (2006) [12], Galves et al. (2008) [18], Galves and Leonardi (2008) [17], Leonardi (2010) [22], refining asymptotic results of Buhlmann and Wyner (1999) [4] and Csiszar and Talata (2006) [9]. (C) 2011 Elsevier B.V. All rights reserved.

A note on the likelihood and moments of the skew-normal distribution

In this paper an alternative approach to the one in Henze (1986) is proposed for deriving the odd moments of the skew-normal distribution considered in Azzalini (1985). The approach is based on a Pascal type triangle, which seems to greatly simplify moments computation. Moreover, it is shown that the likelihood equation for estimating the asymmetry parameter in such model is generated as orthogonal functions to the sample vector. As a consequence, conditions for a unique solution of the likelihood equation are established, which seem to hold in more general setting.

An integrated molecular map of yellow passion fruit based on simultaneous maximum-likelihood estimation of linkage and linkage phases

The development of genetic maps for auto-incompatible species, such as the yellow passion fruit (Passiflora edulis Sims f.flavicarpa Deg.) is restricted due to the unfeasibility of obtaining traditional mapping populations based on inbred lines. For this reason, yellow passion fruit linkage maps were generally constructed using a strategy known as two-way pseudo-testeross, based on monoparental dominant markers segregating in a 1:1 fashion. Due to the lack of information from these markers in one of the parents, two individual (parental) maps were obtained. However, integration of these maps is essential, and biparental markers can be used for such an operation. The objective of our study was to construct an integrated molecular map for a full-sib population of yellow passion fruit combining different loci configuration generated from amplified fragment length polymorphisms (AFLPs) and microsatellite markers and using a novel approach based on simultaneous maximum-likelihood estimation of linkage and linkage phases, specially designed for outcrossing species. Of the total number of loci, approximate to 76%, 21%, 0.7%, and 2.3% did segregate in 1:1, 3:1, 1:2:1, and 1:1:1:1 ratios, respectively. Ten linkage groups (LGs) were established with a logarithm of the odds (LOD) score >= 5.0 assuming a recombination fraction : <= 0.35. On average, 24 markers were assigned per LG, representing a total map length of 1687 cM, with a marker density of 6.9 cM. No markers were placed as accessories on the map as was done with previously constructed individual maps.

Likelihood-based estimation of the regression model with scrambled responses

A significant problem in the collection of responses to potentially sensitive questions, such as relating to illegal, immoral or embarrassing activities, is non-sampling error due to refusal to respond or false responses. Eichhorn & Hayre (1983) suggested the use of scrambled responses to reduce this form of bias. This paper considers a linear regression model in which the dependent variable is unobserved but for which the sum or product with a scrambling random variable of known distribution, is known. The performance of two likelihood-based estimators is investigated, namely of a Bayesian estimator achieved through a Markov chain Monte Carlo (MCMC) sampling scheme, and a classical maximum-likelihood estimator. These two estimators and an estimator suggested by Singh, Joarder & King (1996) are compared. Monte Carlo results show that the Bayesian estimator outperforms the classical estimators in almost all cases, and the relative performance of the Bayesian estimator improves as the responses become more scrambled.

Maximum Likelihood Estimation of Mixture Densities for Binned and Truncated Multivariate Data

Binning and truncation of data are common in data analysis and machine learning. This paper addresses the problem of fitting mixture densities to multivariate binned and truncated data. The EM approach proposed by McLachlan and Jones (Biometrics, 44: 2, 571-578, 1988) for the univariate case is generalized to multivariate measurements. The multivariate solution requires the evaluation of multidimensional integrals over each bin at each iteration of the EM procedure. Naive implementation of the procedure can lead to computationally inefficient results. To reduce the computational cost a number of straightforward numerical techniques are proposed. Results on simulated data indicate that the proposed methods can achieve significant computational gains with no loss in the accuracy of the final parameter estimates. Furthermore, experimental results suggest that with a sufficient number of bins and data points it is possible to estimate the true underlying density almost as well as if the data were not binned. The paper concludes with a brief description of an application of this approach to diagnosis of iron deficiency anemia, in the context of binned and truncated bivariate measurements of volume and hemoglobin concentration from an individual's red blood cells.

Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods

There has been a resurgence of interest in the mean trace length estimator of Pahl for window sampling of traces. The estimator has been dealt with by Mauldon and Zhang and Einstein in recent publications. The estimator is a very useful one in that it is non-parametric. However, despite some discussion regarding the statistical distribution of the estimator, none of the recent works or the original work by Pahl provide a rigorous basis for the determination a confidence interval for the estimator or a confidence region for the estimator and the corresponding estimator of trace spatial intensity in the sampling window. This paper shows, by consideration of a simplified version of the problem but without loss of generality, that the estimator is in fact the maximum likelihood estimator (MLE) and that it can be considered essentially unbiased. As the MLE, it possesses the least variance of all estimators and confidence intervals or regions should therefore be available through application of classical ML theory. It is shown that valid confidence intervals can in fact be determined. The results of the work and the calculations of the confidence intervals are illustrated by example. (C) 2003 Elsevier Science Ltd. All rights reserved.

Estratégias para aumentar a sensibilidade da farmacovigilância em Portugal

OBJETIVO: Avaliar os resultados de intervenção para melhoria da quantidade e relevância das notificações de reacções adversas a medicamentos. MÉTODOS: Foi implementado um estudo controlado aleatorizado, por agrupamentos em farmacêuticos a exercer actividade profissional na região norte de Portugal, em 2007. Após aleatorização, 364 indivíduos foram alocados ao grupo de intervenção (261 na intervenção telefónica e 103 nos workshops); o grupo de controlo foi constituído por 1.103 farmacêuticos. Na intervenção educativa foram abordados a problemática das reacções adversas a medicamentos, o impacto na saúde pública e a notificação espontânea. Quanto à relevância, as reações adversas foram classificadas em graves e inesperadas. A análise estatística foi efectuada com base no princípio intention-to-treat; aplicaram-se modelos lineares generalizados mistos, utilizando o método penalized quasi-likelihood. Os farmacêuticos estudados foram seguidos durante um período de 20 meses. RESULTADOS: A intervenção aumentou três vezes a taxa de notificação espontânea das reações adversas (RR = 3,22; IC 95%: 1,33; 7,80) relativamente ao grupo de controlo. Houve incremento da relevância das notificações com aumento das reações adversas graves em cerca de quatro vezes (RR = 3,87; IC 95%: 1,29;11,61) e inesperadas em cinco vezes (RR = 5,02; IC 95%: 1,33;18,93), relativamente ao grupo de controlo. CONCLUSÕES: As intervenções educativas aumentam significativamente, por até quatro meses, a quantidade e a relevância das notificações espontâneas de reacções adversas a medicamentos por parte dos farmacêuticos da região norte de Portugal.

Maximum likelihood detection for OFDM signals with strong nonlinear distortion effects

Dissertação para obtenção do Grau de Mestre em Engenharia Electrotécnica e de Computadores

Hierarchical modelling of timber reference properties using probabilistic methods: Maximum Likelihood Method, Bayesian Methods and Probability Networks

In recent decades, an increased interest has been evidenced in the research on multi-scale hierarchical modelling in the field of mechanics, and also in the field of wood products and timber engineering. One of the main motivations for hierar-chical modelling is to understand how properties, composition and structure at lower scale levels may influence and be used to predict the material properties on a macroscopic and structural engineering scale. This chapter presents the applicability of statistic and probabilistic methods, such as the Maximum Likelihood method and Bayesian methods, in the representation of timber’s mechanical properties and its inference accounting to prior information obtained in different importance scales. These methods allow to analyse distinct timber’s reference properties, such as density, bending stiffness and strength, and hierarchically consider information obtained through different non, semi or destructive tests. The basis and fundaments of the methods are described and also recommendations and limitations are discussed. The methods may be used in several contexts, however require an expert’s knowledge to assess the correct statistic fitting and define the correlation arrangement between properties.

On convergence of the maximum likelihood estimator in adaptive designs

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Dissertation, 2016

Likelihood inferences with interval-censored data

En l’anàlisi de la supervivència el problema de les dades censurades en un interval es tracta, usualment,via l’estimació per màxima versemblança. Amb l’objectiu d’utilitzar una expressió simplificada de la funció de versemblança, els mètodes estàndards suposen que les condicions que produeixen la censura no afecten el temps de fallada. En aquest article formalitzem les condicions que asseguren la validesa d’aquesta versemblança simplificada. Així, precisem diferents condicions de censura no informativa i definim una condició de suma constant anàloga a la derivada en el context de censura per la dreta. També demostrem que les inferències obtingudes amb la versemblançaa simplificada són correctes quan aquestes condicions són certes. Finalment, tractem la identificabilitat de la funció distribució del temps de fallada a partir de la informació observada i estudiem la possibilitat de contrastar el compliment de la condició de suma constant.

Likelihood-based approaches to modeling demand for medical care

We review recent likelihood-based approaches to modeling demand for medical care. A semi-nonparametric model along the lines of Cameron and Johansson's Poisson polynomial model, but using a negative binomial baseline model, is introduced. We apply these models, as well a semiparametric Poisson, hurdle semiparametric Poisson, and finite mixtures of negative binomial models to six measures of health care usage taken from the Medical Expenditure Panel survey. We conclude that most of the models lead to statistically similar results, both in terms of information criteria and conditional and unconditional prediction. This suggests that applied researchers may not need to be overly concerned with the choice of which of these models they use to analyze data on health care demand.

The use of the likelihood ratio for evaluative and investigative purposes in comparative forensic handwriting examination

This paper extends previous research and discussion on the use of multivariate continuous data, which are about to become more prevalent in forensic science. As an illustrative example, attention is drawn here on the area of comparative handwriting examinations. Multivariate continuous data can be obtained in this field by analysing the contour shape of loop characters through Fourier analysis. This methodology, based on existing research in this area, allows one describe in detail the morphology of character contours throughout a set of variables. This paper uses data collected from female and male writers to conduct a comparative analysis of likelihood ratio based evidence assessment procedures in both, evaluative and investigative proceedings. While the use of likelihood ratios in the former situation is now rather well established (typically, in order to discriminate between propositions of authorship of a given individual versus another, unknown individual), focus on the investigative setting still remains rather beyond considerations in practice. This paper seeks to highlight that investigative settings, too, can represent an area of application for which the likelihood ratio can offer a logical support. As an example, the inference of gender of the writer of an incriminated handwritten text is forwarded, analysed and discussed in this paper. The more general viewpoint according to which likelihood ratio analyses can be helpful for investigative proceedings is supported here through various simulations. These offer a characterisation of the robustness of the proposed likelihood ratio methodology.

The use of classification and regression trees to predict the likelihood of seasonal influenza.

Background Individual signs and symptoms are of limited value for the diagnosis of influenza. Objective To develop a decision tree for the diagnosis of influenza based on a classification and regression tree (CART) analysis. Methods Data from two previous similar cohort studies were assembled into a single dataset. The data were randomly divided into a development set (70%) and a validation set (30%). We used CART analysis to develop three models that maximize the number of patients who do not require diagnostic testing prior to treatment decisions. The validation set was used to evaluate overfitting of the model to the training set. Results Model 1 has seven terminal nodes based on temperature, the onset of symptoms and the presence of chills, cough and myalgia. Model 2 was a simpler tree with only two splits based on temperature and the presence of chills. Model 3 was developed with temperature as a dichotomous variable (≥38°C) and had only two splits based on the presence of fever and myalgia. The area under the receiver operating characteristic curves (AUROCC) for the development and validation sets, respectively, were 0.82 and 0.80 for Model 1, 0.75 and 0.76 for Model 2 and 0.76 and 0.77 for Model 3. Model 2 classified 67% of patients in the validation group into a high- or low-risk group compared with only 38% for Model 1 and 54% for Model 3. Conclusions A simple decision tree (Model 2) classified two-thirds of patients as low or high risk and had an AUROCC of 0.76. After further validation in an independent population, this CART model could support clinical decision making regarding influenza, with low-risk patients requiring no further evaluation for influenza and high-risk patients being candidates for empiric symptomatic or drug therapy.

Indirect likelihood inference

Given a sample from a fully specified parametric model, let Zn be a given finite-dimensional statistic - for example, an initial estimator or a set of sample moments. We propose to (re-)estimate the parameters of the model by maximizing the likelihood of Zn. We call this the maximum indirect likelihood (MIL) estimator. We also propose a computationally tractable Bayesian version of the estimator which we refer to as a Bayesian Indirect Likelihood (BIL) estimator. In most cases, the density of the statistic will be of unknown form, and we develop simulated versions of the MIL and BIL estimators. We show that the indirect likelihood estimators are consistent and asymptotically normally distributed, with the same asymptotic variance as that of the corresponding efficient two-step GMM estimator based on the same statistic. However, our likelihood-based estimators, by taking into account the full finite-sample distribution of the statistic, are higher order efficient relative to GMM-type estimators. Furthermore, in many cases they enjoy a bias reduction property similar to that of the indirect inference estimator. Monte Carlo results for a number of applications including dynamic and nonlinear panel data models, a structural auction model and two DSGE models show that the proposed estimators indeed have attractive finite sample properties.