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Showing 1 to 2 of 2 (0.129 seconds)Spelling suggestions: "subject:"highest posterior density"" "subject:"lighest posterior density""
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Estimation of the Binomial parameter: in defence of Bayes (1763)Tuyl, Frank Adrianus Wilhelmus Maria January 2007 (has links)
Research Doctorate - Doctor of Philosophy (PhD) / Interval estimation of the Binomial parameter è, representing the true probability of a success, is a problem of long standing in statistical inference. The landmark work is by Bayes (1763) who applied the uniform prior to derive the Beta posterior that is the normalised Binomial likelihood function. It is not well known that Bayes favoured this ‘noninformative’ prior as a result of considering the observable random variable x as opposed to the unknown parameter è, which is an important difference. In this thesis we develop additional arguments in favour of the uniform prior for estimation of è. We start by describing the frequentist and Bayesian approaches to interval estimation. It is well known that for common continuous models, while different in interpretation, frequentist and Bayesian intervals are often identical, which is directly related to the existence of a pivotal quantity. The Binomial model, and its Poisson sister also, lack a pivotal quantity, despite having sufficient statistics. Lack of a pivotal quantity is the reason why there is no consensus on one particular estimation method, more so than its discreteness: frequentist (unconditional) coverage depends on è. Exact methods guarantee minimum coverage to be at least equal to nominal and approximate methods aim for mean coverage to be close to nominal. We agree with what seems like the majority of frequentists, that exact methods are too conservative in practice, and show additional undesirable properties. This includes more recent ‘short’ exact intervals. We argue that Bayesian intervals based on noninformative priors are preferable to the family of frequentist approximate intervals, some of which are wider than exact intervals for particular data values. A particular property of the interval based on the uniform prior is that its mean coverage is exactly equal to nominal. However, once committed to the Bayesian approach there is no denying that the current preferred choice, by ‘objective’ Bayesians, is the U-shaped Jeffreys prior which results from various methods aimed at finding noninformative priors. The most successful such method seems to be reference analysis which has led to sensible priors in previously unsolved problems, concerning multiparameter models that include ‘nuisance’ parameters. However, we argue that there is a class of models for which the Jeffreys/reference prior may be suboptimal and that in the case of the Binomial distribution the requirement of a uniform prior predictive distribution leads to a more reasonable ‘consensus’ prior.
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Quantitative Agricultural Policy Impact Analysis at Enhanced Farm & Regional ResolutionGocht, Alexander 18 June 2024 (has links)
In dieser Habilitationsschrift werden elf ausgewählte Zeitschriftenartikel vorgestellt. Alle Artikel zielen darauf ab, die Heterogenität der Betriebe des Agrarsektors durch eine bessere Auflösung der Angebotsmodelle zu berücksichtigen. Der erste Abschnitt konzentriert sich auf die Anwendungen mit dem partiellen Gleichgewichtsmodell CAPRI. Der Abschnitt deckt ein breites Spektrum politischer Fragen ab, zum Beispiel, Kopplung bzw. Konvergenz der Direktzahlungen, Ökologisierung, Verringerung der Treibhausgasemissionen und Kohlenstoffsequestrierung. Ich zeige, dass betriebsbezogene Angebotsmodelle eine detailliertere Analyse politischer Auswirkungen ermöglichen. Zudem erlauben diese Angebotsmodelle eine Verknüpfung mit Modellen höherer räumlicher Auflösung. Der zweite Abschnitt befasst sich mit methodischen Fragen zur Schätzung struktureller Veränderungen auf der Ebene der Betriebstypen in einem EU-weiten Ansatz. Der entwickelte Ansatz hilft, Faktoren, die den landwirtschaftlichen Strukturwandel beeinflussen, besser zu bestimmen und bietet die Möglichkeit einer umfassenden Analyse des landwirtschaftlichen Strukturwandels in der EU. Es wird gezeigt, dass die Ergebnisse zum Strukturwandel auch in der Modellierung berücksichtigt werden können. Dafür wurden Methoden entwickelt, die die Wahrung der Konsistenz der regionalen Ebene und die Berücksichtigung von betriebstypspezifischen Bilanzen, Indikatoren und Veränderungen in der Zahl der landwirtschaftlichen Betriebe gewähren. Der letzte Abschnitt befasst sich mit Methoden zur Rückschätzung von zensierten Daten. Ich untersuche verschiedene Datenaggregationsansätze, wie zum Beispiel, ein lokales gewichtetes Durchschnittsverfahren und ein bayesianisches Schätzverfahren, um Parameter für die zensierten Daten zu ermitteln, die der Realität so weit wie möglich entsprechen. / In this habilitation thesis, eleven selected journal articles were presented. All articles aimed to improve the resolution and thus reduce aggregation error to better account for farm heterogeneity in the agricultural sector models. The first section focused on model application with the partial equilibrium model CAPRI at the farm-type level. It covered many policy issues, such as coupling, convergence, greening, GHG mitigation, and carbon sequestration. I demonstrate that the farm-type supply models enable a detailed analysis of various policy impacts. It was demonstrated that the EU's supply models could improve model linkage with higher spatial resolution models, thus further closing the gap with spatial land-use models. The second section addressed significant methodological queries about estimating structural changes at the farm-type level in an EU-wide approach. A regional approach helps to identify better factors affecting agricultural structural change. The approach offers the opportunity for a comprehensive and previously unachievable analysis of agricultural structural change in the EU. Integrating the development into the CAPRI farm-type model poses challenges with the top-down approach. It requires maintaining consistency with the regional NUTS2 level and considering farm-type-specific balances, indicators, and changes in the number of farms from the structural change estimation. The last section addressed methods for back-estimating censored data. I explored different data aggregation approaches, such as a local weighted average method and a Bayesian estimation procedure, to establish parameters for the censored data that match reality as closely as possible.
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