An environmentally based growth model that uses finite difference calculus with maximum likelihood method: its application to the brackish water bivalve Corbicula japonica in Lake Abashiri, Japan

We present a growth analysis model that combines large amounts of environmental data with limited amounts of biological data and apply it to Corbicula japonica. The model uses the maximum-likelihood method with the Akaike information criterion, which provides an objective criterion for model selection. An adequate distribution for describing a single cohort is selected from available probability density functions, which are expressed by location and scale parameters. Daily relative increase rates of the location parameter are expressed by a multivariate logistic function with environmental factors for each day and categorical variables indicating animal ages as independent variables. Daily relative increase rates of the scale parameter are expressed by an equation describing the relationship with the daily relative increase rate of the location parameter. Corbicula japonica grows to a modal shell length of 0.7 mm during the first year in Lake Abashiri. Compared with the attain-able maximum size of about 30 mm, the growth of juveniles is extremely slow because their growth is less susceptible to environmental factors until the second winter. The extremely slow growth in Lake Abashiri could be a geographical genetic variation within C. japonica.

Phylogeny of freshwater parasitic copepods in the Ergasilidae (Copepoda : Poecilostomatoida) based on 18S and 28S rDNA sequences

The phylogenetic relationships among the Ergasilidae genera are poorly understood. In this study, 14 species from four genera in the Ergasilidae including Sinergasilus, Ergasilus, Pseudergasilus, and Paraergasilus were collected in China, and their phylogenetic relationships were examined using neighbor-joining, maximum parsimony, maximum likelihood, and Bayesian inference methods based on partial sequences of 18S and 28S ribosomal deoxyribonucleic acid, respectively. All the analyses suggest that the Sinergasilus and Paraergasilus are both monophyletic, but the Ergasilus is polyphyletic rather than monophyletic. Considering the relationships among the four genera, the phylogenetic analyses and subsequent hypothesis tests all suggest that Pseudergasilus clustered with some Ergasilus species may have a closer relationship with Sinergasilus rather than with Paraergasilus. It is proposed that the Sinergasilus and the Pseudergasilus species might have evolved from Ergasilus species.

Finding optimal alternatives based on efficient comparative preference inference

Choosing the right or the best option is often a demanding and challenging task for the user (e.g., a customer in an online retailer) when there are many available alternatives. In fact, the user rarely knows which offering will provide the highest value. To reduce the complexity of the choice process, automated recommender systems generate personalized recommendations. These recommendations take into account the preferences collected from the user in an explicit (e.g., letting users express their opinion about items) or implicit (e.g., studying some behavioral features) way. Such systems are widespread; research indicates that they increase the customers' satisfaction and lead to higher sales. Preference handling is one of the core issues in the design of every recommender system. This kind of system often aims at guiding users in a personalized way to interesting or useful options in a large space of possible options. Therefore, it is important for them to catch and model the user's preferences as accurately as possible. In this thesis, we develop a comparative preference-based user model to represent the user's preferences in conversational recommender systems. This type of user model allows the recommender system to capture several preference nuances from the user's feedback. We show that, when applied to conversational recommender systems, the comparative preference-based model is able to guide the user towards the best option while the system is interacting with her. We empirically test and validate the suitability and the practical computational aspects of the comparative preference-based user model and the related preference relations by comparing them to a sum of weights-based user model and the related preference relations. Product configuration, scheduling a meeting and the construction of autonomous agents are among several artificial intelligence tasks that involve a process of constrained optimization, that is, optimization of behavior or options subject to given constraints with regards to a set of preferences. When solving a constrained optimization problem, pruning techniques, such as the branch and bound technique, point at directing the search towards the best assignments, thus allowing the bounding functions to prune more branches in the search tree. Several constrained optimization problems may exhibit dominance relations. These dominance relations can be particularly useful in constrained optimization problems as they can instigate new ways (rules) of pruning non optimal solutions. Such pruning methods can achieve dramatic reductions in the search space while looking for optimal solutions. A number of constrained optimization problems can model the user's preferences using the comparative preferences. In this thesis, we develop a set of pruning rules used in the branch and bound technique to efficiently solve this kind of optimization problem. More specifically, we show how to generate newly defined pruning rules from a dominance algorithm that refers to a set of comparative preferences. These rules include pruning approaches (and combinations of them) which can drastically prune the search space. They mainly reduce the number of (expensive) pairwise comparisons performed during the search while guiding constrained optimization algorithms to find optimal solutions. Our experimental results show that the pruning rules that we have developed and their different combinations have varying impact on the performance of the branch and bound technique.

Maximum likelihood estimation of higher-order integer-valued autoregressive processes

In this article, we extend the earlier work of Freeland and McCabe [Journal of time Series Analysis (2004) Vol. 25, pp. 701–722] and develop a general framework for maximum likelihood (ML) analysis of higher-order integer-valued autoregressive processes. Our exposition includes the case where the innovation sequence has a Poisson distribution and the thinning is binomial. A recursive representation of the transition probability of the model is proposed. Based on this transition probability, we derive expressions for the score function and the Fisher information matrix, which form the basis for ML estimation and inference. Similar to the results in Freeland and McCabe (2004), we show that the score function and the Fisher information matrix can be neatly represented as conditional expectations. Using the INAR(2) speci?cation with binomial thinning and Poisson innovations, we examine both the asymptotic e?ciency and ?nite sample properties of the ML estimator in relation to the widely used conditional least
squares (CLS) and Yule–Walker (YW) estimators. We conclude that, if the Poisson assumption can be justi?ed, there are substantial gains to be had from using ML especially when the thinning parameters are large.

Simulation-Based Finite and Large Sample Tests in Multivariate Regressions.

In the context of multivariate linear regression (MLR) models, it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection. In this paper, we propose a general method for constructing exact tests of possibly nonlinear hypotheses on the coefficients of MLR systems. For the case of uniform linear hypotheses, we present exact distributional invariance results concerning several standard test criteria. These include Wilks' likelihood ratio (LR) criterion as well as trace and maximum root criteria. The normality assumption is not necessary for most of the results to hold. Implications for inference are two-fold. First, invariance to nuisance parameters entails that the technique of Monte Carlo tests can be applied on all these statistics to obtain exact tests of uniform linear hypotheses. Second, the invariance property of the latter statistic is exploited to derive general nuisance-parameter-free bounds on the distribution of the LR statistic for arbitrary hypotheses. Even though it may be difficult to compute these bounds analytically, they can easily be simulated, hence yielding exact bounds Monte Carlo tests. Illustrative simulation experiments show that the bounds are sufficiently tight to provide conclusive results with a high probability. Our findings illustrate the value of the bounds as a tool to be used in conjunction with more traditional simulation-based test methods (e.g., the parametric bootstrap) which may be applied when the bounds are not conclusive.

Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments

It is well known that standard asymptotic theory is not valid or is extremely unreliable in models with identification problems or weak instruments [Dufour (1997, Econometrica), Staiger and Stock (1997, Econometrica), Wang and Zivot (1998, Econometrica), Stock and Wright (2000, Econometrica), Dufour and Jasiak (2001, International Economic Review)]. One possible way out consists here in using a variant of the Anderson-Rubin (1949, Ann. Math. Stat.) procedure. The latter, however, allows one to build exact tests and confidence sets only for the full vector of the coefficients of the endogenous explanatory variables in a structural equation, which in general does not allow for individual coefficients. This problem may in principle be overcome by using projection techniques [Dufour (1997, Econometrica), Dufour and Jasiak (2001, International Economic Review)]. AR-types are emphasized because they are robust to both weak instruments and instrument exclusion. However, these techniques can be implemented only by using costly numerical techniques. In this paper, we provide a complete analytic solution to the problem of building projection-based confidence sets from Anderson-Rubin-type confidence sets. The latter involves the geometric properties of “quadrics” and can be viewed as an extension of usual confidence intervals and ellipsoids. Only least squares techniques are required for building the confidence intervals. We also study by simulation how “conservative” projection-based confidence sets are. Finally, we illustrate the methods proposed by applying them to three different examples: the relationship between trade and growth in a cross-section of countries, returns to education, and a study of production functions in the U.S. economy.

A maximum likelihood framework for protein design

Affiliation: Claudia Kleinman, Nicolas Rodrigue & Hervé Philippe : Département de biochimie, Faculté de médecine, Université de Montréal

Estimators and Tests based on Likelihood-Depth with Application to Weibull Distribution, Gaussian and Gumbel Copula

In dieser Arbeit werden mithilfe der Likelihood-Tiefen, eingeführt von Mizera und Müller (2004), (ausreißer-)robuste Schätzfunktionen und Tests für den unbekannten Parameter einer stetigen Dichtefunktion entwickelt. Die entwickelten Verfahren werden dann auf drei verschiedene Verteilungen angewandt. Für eindimensionale Parameter wird die Likelihood-Tiefe eines Parameters im Datensatz als das Minimum aus dem Anteil der Daten, für die die Ableitung der Loglikelihood-Funktion nach dem Parameter nicht negativ ist, und dem Anteil der Daten, für die diese Ableitung nicht positiv ist, berechnet. Damit hat der Parameter die größte Tiefe, für den beide Anzahlen gleich groß sind. Dieser wird zunächst als Schätzer gewählt, da die Likelihood-Tiefe ein Maß dafür sein soll, wie gut ein Parameter zum Datensatz passt. Asymptotisch hat der Parameter die größte Tiefe, für den die Wahrscheinlichkeit, dass für eine Beobachtung die Ableitung der Loglikelihood-Funktion nach dem Parameter nicht negativ ist, gleich einhalb ist. Wenn dies für den zu Grunde liegenden Parameter nicht der Fall ist, ist der Schätzer basierend auf der Likelihood-Tiefe verfälscht. In dieser Arbeit wird gezeigt, wie diese Verfälschung korrigiert werden kann sodass die korrigierten Schätzer konsistente Schätzungen bilden. Zur Entwicklung von Tests für den Parameter, wird die von Müller (2005) entwickelte Simplex Likelihood-Tiefe, die eine U-Statistik ist, benutzt. Es zeigt sich, dass für dieselben Verteilungen, für die die Likelihood-Tiefe verfälschte Schätzer liefert, die Simplex Likelihood-Tiefe eine unverfälschte U-Statistik ist. Damit ist insbesondere die asymptotische Verteilung bekannt und es lassen sich Tests für verschiedene Hypothesen formulieren. Die Verschiebung in der Tiefe führt aber für einige Hypothesen zu einer schlechten Güte des zugehörigen Tests. Es werden daher korrigierte Tests eingeführt und Voraussetzungen angegeben, unter denen diese dann konsistent sind. Die Arbeit besteht aus zwei Teilen. Im ersten Teil der Arbeit wird die allgemeine Theorie über die Schätzfunktionen und Tests dargestellt und zudem deren jeweiligen Konsistenz gezeigt. Im zweiten Teil wird die Theorie auf drei verschiedene Verteilungen angewandt: Die Weibull-Verteilung, die Gauß- und die Gumbel-Copula. Damit wird gezeigt, wie die Verfahren des ersten Teils genutzt werden können, um (robuste) konsistente Schätzfunktionen und Tests für den unbekannten Parameter der Verteilung herzuleiten. Insgesamt zeigt sich, dass für die drei Verteilungen mithilfe der Likelihood-Tiefen robuste Schätzfunktionen und Tests gefunden werden können. In unverfälschten Daten sind vorhandene Standardmethoden zum Teil überlegen, jedoch zeigt sich der Vorteil der neuen Methoden in kontaminierten Daten und Daten mit Ausreißern.

A Statistical Image-Based Shape Model for Visual Hull Reconstruction and 3D Structure Inference

We present a statistical image-based shape + structure model for Bayesian visual hull reconstruction and 3D structure inference. The 3D shape of a class of objects is represented by sets of contours from silhouette views simultaneously observed from multiple calibrated cameras. Bayesian reconstructions of new shapes are then estimated using a prior density constructed with a mixture model and probabilistic principal components analysis. We show how the use of a class-specific prior in a visual hull reconstruction can reduce the effect of segmentation errors from the silhouette extraction process. The proposed method is applied to a data set of pedestrian images, and improvements in the approximate 3D models under various noise conditions are shown. We further augment the shape model to incorporate structural features of interest; unknown structural parameters for a novel set of contours are then inferred via the Bayesian reconstruction process. Model matching and parameter inference are done entirely in the image domain and require no explicit 3D construction. Our shape model enables accurate estimation of structure despite segmentation errors or missing views in the input silhouettes, and works even with only a single input view. Using a data set of thousands of pedestrian images generated from a synthetic model, we can accurately infer the 3D locations of 19 joints on the body based on observed silhouette contours from real images.

A likelihood ratio appropach to family-based association studies with covariates

We introduce a procedure for association based analysis of nuclear families that allows for dichotomous and more general measurements of phenotype and inclusion of covariate information. Standard generalized linear models are used to relate phenotype and its predictors. Our test procedure, based on the likelihood ratio, unifies the estimation of all parameters through the likelihood itself and yields maximum likelihood estimates of the genetic relative risk and interaction parameters. Our method has advantages in modelling the covariate and gene-covariate interaction terms over recently proposed conditional score tests that include covariate information via a two-stage modelling approach. We apply our method in a study of human systemic lupus erythematosus and the C-reactive protein that includes sex as a covariate.