arXiv subjects

Marko Laine

Publications and source records attributed to Marko Laine.

5 recordsLinked to original sources

arXiv2021

Hierarchical Bayesian propulsion power models for marine vessels

Assessing the magnitude of fuel consumption of marine traffic is a challenging task. The consumption can be reduced by the ways the vessels are operated, to achieve both improved cost efficiency and reduced CO2 emissions. Mathematical models for predicting ships' consumption are in a central role in both of these tasks. Nowadays, many ships are equipped with data collection systems, which enable data-based calibration of the consumption models. Typically this calibration procedure is carried out independently for each particular ship, using only data collected from the ship in question. In this paper, we demonstrate a hierarchical Bayesian modeling approach, where we fit a single model over many vessels, with the assumption that the parameters of vessels of same type and similar characteristics (e.g. vessel size) are likely close to each other. The benefits of such an approach are two-fold; 1) we can borrow information about parameters that are not well informed by the vessel-specific data using data from similar ships, and 2) we can use the final hierarchical model to predict the behavior of a vessel from which we don't have any data, based only on its characteristics. In this paper, we discuss the basic concept and present a first simple version of the model. We apply the Stan statistical modeling tool for the model fitting and use real data from 64 cruise ships collected via the widely used commercial Eniram platform. By using Bayesian statistical methods we obtain uncertainties for the model predictions, too. The prediction accuracy of the model is compared to an existing data-free modeling approach.

stat.AP↗

arXiv2019

Introduction to Dynamic Linear Models for Time Series Analysis

Dynamic linear models (DLM) offer a very generic framework to analyse time series data. Many classical time series models can be formulated as DLMs, including ARMA models and standard multiple linear regression models. The models can be seen as general regression models where the coefficients can vary in time. In addition, they allow for a state space representation and a formulation as hierarchical statistical models, which in turn is the key for efficient estimation by Kalman formulas and by Markov chain Monte Carlo (MCMC) methods. A dynamic linear model can handle non-stationary processes, missing values and non-uniform sampling as well as observations with varying accuracies. This chapter gives an introduction to DLM and shows how to build various useful models for analysing trends and other sources of variability in geodetic time series.

stat.ME↗

arXiv2018

Likelihood informed dimension reduction for inverse problems in remote sensing of atmospheric constituent profiles

We use likelihood informed dimension reduction (LIS) (T. Cui et al. 2014) for inverting vertical profile information of atmospheric methane from ground based Fourier transform infrared (FTIR) measurements at Sodankylä, Northern Finland. The measurements belong to the word wide TCCON network for greenhouse gas measurements and, in addition to providing accurate greenhouse gas measurements, they are important for validating satellite observations. LIS allows construction of an efficient Markov chain Monte Carlo sampling algorithm that explores only a reduced dimensional space but still produces a good approximation of the original full dimensional Bayesian posterior distribution. This in effect makes the statistical estimation problem independent of the discretization of the inverse problem. In addition, we compare LIS to a dimension reduction method based on prior covariance matrix truncation used earlier (S. Tukiainen et al. 2016).

stat.CO↗

arXiv2017

Bayesian Principal Component Regression model with spatial effects for forest inventory under small field sample size

Remote sensing observations are extensively used for analysis of environmental variables. These variables often exhibit spatial correlation, which has to be accounted for in the calibration models used in predictions, either by direct modelling of the dependencies or by allowing for spatially correlated stochastic effects. Another feature in many remote sensing instruments is that the derived predictor variables are highly correlated, which can lead to unnecessary model over-training and at worst, singularities in the estimates. Both of these affect the prediction accuracy, especially when the training set for model calibration is small. To overcome these modelling challenges, we present a general model calibration procedure for remotely sensed data and apply it to airborne laser scanning data for forest inventory. We use a linear regression model that accounts for multicollinearity in the predictors by principal components and Bayesian regularization. It has a spatial random effect component for the spatial correlations that are not explained by a simple linear model. An efficient Markov chain Monte Carlo sampling scheme is used to account for the uncertainty in all the model parameters. We tested the proposed model against several alternatives and it outperformed the other linear calibration models, especially when there were spatial effects, multicollinearity and the training set size was small.

stat.AP↗

arXiv2016

Shape recovery from sparse tomographic X-ray data

A two-dimensional tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A Non Uniform Rational Basis Splines (NURBS) curve is used as computational representation of the boundary. This approach conveniently provides the result in a format readily compatible with computer-aided design (CAD) software. However, the linear tomography task becomes a nonlinear inverse problem due to the NURBS-based parameterization. Therefore, Bayesian inversion with Markov chain Monte Carlo (MCMC) sampling is used for calculating an estimate of the NURBS control points. The reconstruction method is tested with both simulated data and measured X-ray projection data. The proposed method recovers the shape and the attenuation coefficient significantly better than the baseline algorithm (optimally thresholded total variation regularization), but at the cost of heavier computation.

math.NA↗