Plan af Uleåborg utgifven 1839 af C. W. Gyldén

Oulun kartta

Plan af Wasa stad utgifven 1839 af C. W. Gyldén

Vaasan kartta. 1 kartta : vär. ; 41 x 55,3 cm, lehti 45 x 60 cm. - Mittakaava: [1:4000]. - Sisältää luettelon julkisista rakennuksista.

S. Maria Antiqua, S. Maria Rotonda, Moserato, Santa, S. Martino, Buchima, Dominica

Julkaisussa: Libro di Benedetto Bordone nel qual si ragiona de tutte l'isole del mondo

Jamaiqua, Spagnola, Chanchite, Curtana, Maria Tambal, Paria

Julkaisussa: Libro di Benedetto Bordone nel qual si ragiona de tutte l'isole del mondo

Adaptive Markov chain Monte Carlo and Bayesian filtering for state space models

This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.

Plan af Wiborg / utgifven 1839 af C. W. Gyldén.

[1:10000].