Moment-Type Estimators for the Dirichlet and the Multivariate Gamma Distributions

This study presents new closed-form estimators for the Dirichlet and the Multivariate Gamma distribution families, whose maximum likelihood estimator cannot be explicitly derived. The methodology builds upon the score-adjusted estimators for the Beta and Gamma distributions, extending their applicability to the Dirichlet and Multivariate Gamma distributions. Expressions for the asymptotic variance-covariance matrices are provided, demonstrating the superior performance of score-adjusted estimators over the traditional moment ones. Leveraging well-established connections between Dirichlet and Multivariate Gamma distributions, a novel class of estimators for the latter is introduced, referred to as "Dirichlet-based moment-type estimators". The general asymptotic variance-covariance matrix form for this estimator class is derived. To facilitate the application of these innovative estimators, an R package called estimators is developed and made publicly available.Comment: 27 pages, 5 figure

Interaction of Laser Radiation with Plasmas and Nonadiabatic Motion of Particles in Magnetic Fields

Contains reports on two research projects.U. S. Atomic Energy Commission (Contract AT(30-1)-3285

A nonlinear mixed effects model to explain inter-individual variability in plant populations

15th Applied Stochastic Models and Data Analysis Conference (Accepted)International audienceIt is common knowledge that the genetic variability of plants, even of the same variety, can be very important and, if we add locally varying climatic effects, the development of two neighboring similar plants could be highly different. This is one of the reasons why population-based methods for modeling plant growth are of great interest. A highly promising individual-based plant growth model is the GreenLab model which was recently shown to have a good predictive capacity among competing models. In this study, we extend the GreenLab formulation to the population level. In order to model the deviations from some fixed but unknown important biophysical and genetic parameters we introduce into the GreenLab model appropriate random effects. Under some assumptions, the resulting model can be cast into the framework of nonlinear mixed effects models. A stochastic variant of an EM-type algorithm (Expectation-Maximization) is generally needed to perform MLE for this type of incomplete data models and the interest is focused on the design of an efficient algorithm. In this direction, we propose a suitable Monte-Carlo EM (MCEM) algorithm for our model, where at each EM-iteration, MCMC is used to draw from the hidden states given the observed data. Data consist in organ mass measurements and are treated sequentially as first proposed in Trevezas and Cournède (2013). The performance of the algorithm is illustrated on simulated data from the sugar beet plant. Some possible extensions and improvements are also discussed

Bayesian Estimation in Functional-Structural Plant Models with Stochastic Organogenesis

International audienceIn this article, Functional Structural Plant growth Models (FSPMs) with stochastic organogenesis are described in the framework of Jump Markov Models. A Bayesian approach is adopted to estimate uncertain ecophysiological parameters. In particular, two estimation procedures are detailed: the Rao-Blackwellized Particle Filter and the Convolution Particle Filter. These methods are then applied and compared throughout a particular FSPM: the GreenLab model with stochastic organogenesis

Simulation techniques for parameter estimation via a stochastic ECM algorithm with applications to plant growth modeling

preprintMathematical modeling of plant growth has gained increasing interest in recent years due to its potential applications. A general family of models of Carbon allocation formalized as dynamic systems serves as the basis for our study. They are known as functional-structural plant models (FSPMs, \cite{Sie00}). Modeling, parameterization and estimation are very challenging problems due to the complicated mechanisms involved in plant evolution. In \cite{Tre12} a specific type of a non-homogeneous hidden Markov model is proposed as an extension of the GreenLab FSPM (\cite{Ref03a}) to study a certain class of plants with known organogenesis. In such a model, the maximum likelihood estimator cannot be derived explicitly. A stochastic version of an ECM (expectation conditional maximization) algorithm was adopted, where the E-step was approximated by a sequential importance sampling with resampling method (SISR-ECM approach). In this paper, a Markov Chain Monte Carlo method is proposed for the approximation of the E-step (MCMC-ECM approach). The parameter estimates obtained with MCMC-ECM are compared with those obtained with SISR-ECM from simulated and real sugar beet data. Based on this real data set competing models are compared via model selection techniques. Moreover, a data-driven automated MCMC-ECM algorithm for finding the proper sample size in each ECM step and also the proper number of ECM steps is proposed. The MCMC approach seems to be more flexible for this particular application context and can be more easily generalized to the parameter estimation of other plant models for which observations are taken under destructive measurements

PRODUKTIVITAS GETAH PINUS (Pinus merkusii) PADA VARIASI DIAMETER DAN JUMLAH KOAKAN DI KAMPUS PSDKU USK GAYO LUES

Pohon Pinus merkusii Jungh. et de Vriese merupakan jenis pinus yang tumbuh asli di wilayah Indonesia. Pinus merkusii termasuk dalam kategori pohon fast growing species yang secara alami tersebar di Pulau Sumatera (Aceh, Tapanuli dan Kerinci). Pohon ini memiliki beragam manfaat seperti getah yang dapat diolah menjadi gondorukem dan terpentin. Produksi getah pinus memiliki tingkatan dan metode penyadapan yang berbeda yang berpengaruh terhadap kuantitas getah pinus yang dihasilkan. Penelitian bertujuan untuk mengetahui produksi getah pinus dan pengaruh dari diameter pohon dengan menggunakan metode koakan. Penelitian telah dilakukan pada bulan Mei-Juli 2022 di sekitar kampus PSDKU Gayo Lues. Sampel diambil pada tiga kelas diameter pinus yaitu kelas diameter 1 (26-30 cm) sebanyak 3 koakan, kelas diameter 2 (31-35 cm) sebanyak 4 koakan, dan kelas diameter 3 (36-40 cm) sebanyak 5 koakan. Setiap kelas diulang 3 kali sehingga jumlah sampel perlakuan didapatkan 18 sampel secara acak lengkap (RAL). Data penelitian dianalisis menggunakan aplikasi software SPSS 16.0 dan untuk mengetahui perbedaan produksi getah pinus pada masing-masing kelas diameter akan dianalisis menggunakan uji one-way (ANOVA). Apabila hasil pengujian signifikansi < 0,05 maka dilakukan uji lanjut dengan uji Duncan. Hasil penelitian menunjukkan bahwa diameter pohon pinus sangat berpengaruh nyata terhadap produksi getah pinus, produksi getah pinus yang dihasilkan paling besar ada pada kelas diameter 3 dengan diameter batang 36-40 cm dengan ratarata produksi getah pinus 853.67 gr/kelas. Hal ini menunjukkan bahwa semakin besar diameter batang pinus maka produksi getah yang dihasilkan akan semakin banyak. Kata kunci: Diameter, Getah, Koakan, Pinus merkusii, RA

Uma fracção da barricada : Neno Vasco e os grupos anarquistas no Brasil e em Portugal

As reflexões desenvolvidas neste trabalho visam a aprofundar algumas questões de capital importância para o entendimento da formação de grupos de relação, de composição imigrante, no Brasil. Tratando-se, em especial, de imigrantes ideologicamente vinculados ao pensamento radical anarquista, tais questões assumem contornos específicos, diretamente relacionados à singularidade da proposta do grupo relacional e das várias procedências, regiões européias, de seus membros. Assim, o esforço hermenêutico que se inicia pretende definir e esquadrinhar os elementos que permitiram a formação de relações sociais estáveis entre os imigrantes radicais e seus interlocutores, de igual aspiração ideológica, no Brasil e em outras partes da Europa

Filtrage par noyaux de convolution itératif

International audienceL'estimation paramétrique des modèles dynamiques en biologie est souvent rendue complexe par les fortes interactions entre processus et les non-linéarités qui en découlent, ainsi que par la difficulté de l'observation du système par expérimentation. C'est en particulier le cas des modèles de croissance de plantes. Dans cet article nous étudions l'application de la méthode de filtrage particulaire par convolution, développée pour permettre d'estimer les paramètres et les états cachés simultanément pour des systèmes non-linéaires. Nous proposons une variation de cette méthode mettant en jeu des itérations multiples du filtre particulaire par convolution, en tenant compte des informations obtenues lors de l'itération précédente afin d'améliorer l'estimation des paramètres. Une version conditionnelle de l'approche est également proposée dans le cas d'un système dynamique bruité, en réalisant l'estimation paramètres-états en supposant les paramètres du modèle de bruits connus, puis en estimant ces derniers grâce aux états cachés estimés, et en relançant l'algorithme avec ces nouveaux paramètres. La méthode a été implémentée pour un modèle de croissance de betterave avec observations rares, et les résultats apparaissent meilleurs que la méthode de filtrage par convolution sans itération, même réalisée avec un nombre bien plus important de particules. La méthode est par ailleurs générique, robuste et facilement adaptable