Die Mutter wird mich fragen Lied für eine Sopranstimme mit Begleitung des Pianoforte : componirt von Fr. Pacius - [Pärmen]

Helsingfors : L. Beuermann [1840]

[Lass mich wandern durch das grün]

Soitinnus: lauluääni (tenori), piano.

Historian itsetutkistelu

Pääkirjoitus

"Minulle on eläminen Kristus" : uskonto ja yhteiskunnallinen äitiys Emma Mäkisen hyväntekeväisyystyössä

Zusammenfassung: "Für mich ist das Leben Christus" : Religion und soziale Mutterschaft in der Fürsorgetätigkeit Emma Mäkinens (1849-1915)

Adaptive MCMC methods with applications in environmental and geophysical models

This work presents new, efficient Markov chain Monte Carlo (MCMC) simulation methods for statistical analysis in various modelling applications. When using MCMC methods, the model is simulated repeatedly to explore the probability distribution describing the uncertainties in model parameters and predictions. In adaptive MCMC methods based on the Metropolis-Hastings algorithm, the proposal distribution needed by the algorithm learns from the target distribution as the simulation proceeds. Adaptive MCMC methods have been subject of intensive research lately, as they open a way for essentially easier use of the methodology. The lack of user-friendly computer programs has been a main obstacle for wider acceptance of the methods. This work provides two new adaptive MCMC methods: DRAM and AARJ. The DRAM method has been built especially to work in high dimensional and non-linear problems. The AARJ method is an extension to DRAM for model selection problems, where the mathematical formulation of the model is uncertain and we want simultaneously to fit several different models to the same observations. The methods were developed while keeping in mind the needs of modelling applications typical in environmental sciences. The development work has been pursued while working with several application projects. The applications presented in this work are: a winter time oxygen concentration model for Lake Tuusulanjärvi and adaptive control of the aerator; a nutrition model for Lake Pyhäjärvi and lake management planning; validation of the algorithms of the GOMOS ozone remote sensing instrument on board the Envisat satellite of European Space Agency and the study of the effects of aerosol model selection on the GOMOS algorithm.

Bayesian Estimation of Noise

In mathematical modeling the estimation of the model parameters is one of the most common problems. The goal is to seek parameters that fit to the measurements as well as possible. There is always error in the measurements which implies uncertainty to the model estimates. In Bayesian statistics all the unknown quantities are presented as probability distributions. If there is knowledge about parameters beforehand, it can be formulated as a prior distribution. The Bays’ rule combines the prior and the measurements to posterior distribution. Mathematical models are typically nonlinear, to produce statistics for them requires efficient sampling algorithms. In this thesis both Metropolis-Hastings (MH), Adaptive Metropolis (AM) algorithms and Gibbs sampling are introduced. In the thesis different ways to present prior distributions are introduced. The main issue is in the measurement error estimation and how to obtain prior knowledge for variance or covariance. Variance and covariance sampling is combined with the algorithms above. The examples of the hyperprior models are applied to estimation of model parameters and error in an outlier case.

Disputatio pro articulo V. Libri concordiae

Arkit: A-B4.

De laudatione funebri

Dedicatio: Laurentius Tammelin, Jacobus Garwolius, Michael Polviander, Martinus Polviander, Gustavus Rothovius, Justus Schultz Joh. fil., Johannes H. Wittfooth.

Quies coeli

Invocatio: HEPREAA.

Disputatio pro articulo II. Libri concordiae

Arkit: A-C4 D2.

Om medel til saltpettersjuderiernes förbättring och upkomst i riket

Invocatio: M.G.H.

Triga reqvisitorum eruditionis comparandae

Invocatio: I.N.S.S.T.

Animadversiones in commentationem nobilissimi von Crell

Dedicatio: Mich. Montin.