Detailed soil map?

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On probability-based inference under data missing by design

Whether a statistician wants to complement a probability model for observed data with a prior distribution and carry out fully probabilistic inference, or base the inference only on the likelihood function, may be a fundamental question in theory, but in practice it may well be of less importance if the likelihood contains much more information than the prior. Maximum likelihood inference can be justified as a Gaussian approximation at the posterior mode, using flat priors. However, in situations where parametric assumptions in standard statistical models would be too rigid, more flexible model formulation, combined with fully probabilistic inference, can be achieved using hierarchical Bayesian parametrization. This work includes five articles, all of which apply probability modeling under various problems involving incomplete observation. Three of the papers apply maximum likelihood estimation and two of them hierarchical Bayesian modeling. Because maximum likelihood may be presented as a special case of Bayesian inference, but not the other way round, in the introductory part of this work we present a framework for probability-based inference using only Bayesian concepts. We also re-derive some results presented in the original articles using the toolbox equipped herein, to show that they are also justifiable under this more general framework. Here the assumption of exchangeability and de Finetti's representation theorem are applied repeatedly for justifying the use of standard parametric probability models with conditionally independent likelihood contributions. It is argued that this same reasoning can be applied also under sampling from a finite population. The main emphasis here is in probability-based inference under incomplete observation due to study design. This is illustrated using a generic two-phase cohort sampling design as an example. The alternative approaches presented for analysis of such a design are full likelihood, which utilizes all observed information, and conditional likelihood, which is restricted to a completely observed set, conditioning on the rule that generated that set. Conditional likelihood inference is also applied for a joint analysis of prevalence and incidence data, a situation subject to both left censoring and left truncation. Other topics covered are model uncertainty and causal inference using posterior predictive distributions. We formulate a non-parametric monotonic regression model for one or more covariates and a Bayesian estimation procedure, and apply the model in the context of optimal sequential treatment regimes, demonstrating that inference based on posterior predictive distributions is feasible also in this case.

Growth of Jewish land setllements in Crimea 1924-1929

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Negative photocopy of the map of Crimea with marked settlements

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Karta Dzhankoǐskogo i Evpatoriǐskogo uezdov Krymskoǐ Avtonomnoǐ Respubliki s pokozaniem svobodnogo Gosfonda i chasti ego vydeli︠a︡emoǐ dli︠a︡ ustroǐstva trudi︠a︡shchikhsi︠a︡ evreev

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Map detailing growth of settlement tracts by year 1925-1929

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Settlements in Crimea

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Map of Crimea with major cities

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Vykopirovka s proektnogo plana na zemotvod Dzheleshaĭ sultanat

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Vykopirovka uchastkov Komzeta na Bakalʻskoǐ zemleustroitelʻnoǐ dache Evpatoriǐskogo raǐona

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Cover for plans regarding the Naǐbrot, Busul-Montanaǐ, Urchuk, Abuslar i Friling tracts of land in the Fraǐdorf region

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Vykopirovka iz obshschego plana Bii︠u︡k-Onlarskoǐ dachi razverstanii︠a︡ na uchastok Komzet'a Nº 70/31

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Vykopirovka s plana Fraǐdorfskogo raǐona, Kafiiskoǐ dachi razverstanii︠a︡, uchastkov Komzeta za Nº Nº 71z, 71v, 74, 12c, 75, 21 i Kaǐmachinskiǐ fond

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Vykopirovka s proėktnogo plana na zemelʻnyĭ otvod 22go pereselenskogo uchastka

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Vykopirovka s proėktnogo plana na zemotvod 20go Evreĭskogo pereselenskogo uchastku

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