A 4-DOF SIMULINK model of a coastal patrol vessel for manoeuvring in waves

This paper presents a detailed simulation model of a Naval coastal patrol vessel. The vessel described is a 50m long, fast monohull coastal patrol vessel. The paper describes the complete model and its implementation in Matlab-Simulink. In order to promote the use of this model, the Simulink files are openly available through a website.

Clarification of the low-frequency modelling concept for marine craft

This article presents some remarks on models currently used in low speed manoeuvring and dynamic positioning problems. It discusses the relationship between the classical hydrodynamic equations for manoeuvring and seakeeping, and offers insight into the models used for simulation and control system design.

Estimation of cosmological parameters using adaptive importance sampling

We present a Bayesian sampling algorithm called adaptive importance sampling or population Monte Carlo (PMC), whose computational workload is easily parallelizable and thus has the potential to considerably reduce the wall-clock time required for sampling, along with providing other benefits. To assess the performance of the approach for cosmological problems, we use simulated and actual data consisting of CMB anisotropies, supernovae of type Ia, and weak cosmological lensing, and provide a comparison of results to those obtained using state-of-the-art Markov chain Monte Carlo (MCMC). For both types of data sets, we find comparable parameter estimates for PMC and MCMC, with the advantage of a significantly lower wall-clock time for PMC. In the case of WMAP5 data, for example, the wall-clock time scale reduces from days for MCMC to hours using PMC on a cluster of processors. Other benefits of the PMC approach, along with potential difficulties in using the approach, are analyzed and discussed.

Bayesian model comparison in cosmology with Population Monte Carlo

We use Bayesian model selection techniques to test extensions of the standard flat LambdaCDM paradigm. Dark-energy and curvature scenarios, and primordial perturbation models are considered. To that end, we calculate the Bayesian evidence in favour of each model using Population Monte Carlo (PMC), a new adaptive sampling technique which was recently applied in a cosmological context. The Bayesian evidence is immediately available from the PMC sample used for parameter estimation without further computational effort, and it comes with an associated error evaluation. Besides, it provides an unbiased estimator of the evidence after any fixed number of iterations and it is naturally parallelizable, in contrast with MCMC and nested sampling methods. By comparison with analytical predictions for simulated data, we show that our results obtained with PMC are reliable and robust. The variability in the evidence evaluation and the stability for various cases are estimated both from simulations and from data. For the cases we consider, the log-evidence is calculated with a precision of better than 0.08. Using a combined set of recent CMB, SNIa and BAO data, we find inconclusive evidence between flat LambdaCDM and simple dark-energy models. A curved Universe is moderately to strongly disfavoured with respect to a flat cosmology. Using physically well-motivated priors within the slow-roll approximation of inflation, we find a weak preference for a running spectral index. A Harrison-Zel'dovich spectrum is weakly disfavoured. With the current data, tensor modes are not detected; the large prior volume on the tensor-to-scalar ratio r results in moderate evidence in favour of r=0.

Dark-energy constraints and correlations with systematics from CFHTLS weak lensing, SNLS supernovae Ia and WMAP5

Aims We combine measurements of weak gravitational lensing from the CFHTLS-Wide survey, supernovae Ia from CFHT SNLS and CMB anisotropies from WMAP5 to obtain joint constraints on cosmological parameters, in particular, the dark-energy equation-of-state parameter w. We assess the influence of systematics in the data on the results and look for possible correlations with cosmological parameters. Methods We implemented an MCMC algorithm to sample the parameter space of a flat CDM model with a dark-energy component of constant w. Systematics in the data are parametrised and included in the analysis. We determine the influence of photometric calibration of SNIa data on cosmological results by calculating the response of the distance modulus to photometric zero-point variations. The weak lensing data set is tested for anomalous field-to-field variations and a systematic shape measurement bias for high-redshift galaxies. Results Ignoring photometric uncertainties for SNLS biases cosmological parameters by at most 20% of the statistical errors, using supernovae alone; the parameter uncertainties are underestimated by 10%. The weak-lensing field-to-field variance between 1 deg2-MegaCam pointings is 5-15% higher than predicted from N-body simulations. We find no bias in the lensing signal at high redshift, within the framework of a simple model, and marginalising over cosmological parameters. Assuming a systematic underestimation of the lensing signal, the normalisation increases by up to 8%. Combining all three probes we obtain -0.10 < 1 + w < 0.06 at 68% confidence ( -0.18 < 1 + w < 0.12 at 95%), including systematic errors. Our results are therefore consistent with the cosmological constant . Systematics in the data increase the error bars by up to 35%; the best-fit values change by less than 0.15.

Bayesian fisheries stock assessment: integrating and updating knowledge

In this thesis the use of the Bayesian approach to statistical inference in fisheries stock assessment is studied. The work was conducted in collaboration of the Finnish Game and Fisheries Research Institute by using the problem of monitoring and prediction of the juvenile salmon population in the River Tornionjoki as an example application. The River Tornionjoki is the largest salmon river flowing into the Baltic Sea. This thesis tackles the issues of model formulation and model checking as well as computational problems related to Bayesian modelling in the context of fisheries stock assessment. Each article of the thesis provides a novel method either for extracting information from data obtained via a particular type of sampling system or for integrating the information about the fish stock from multiple sources in terms of a population dynamics model. Mark-recapture and removal sampling schemes and a random catch sampling method are covered for the estimation of the population size. In addition, a method for estimating the stock composition of a salmon catch based on DNA samples is also presented. For most of the articles, Markov chain Monte Carlo (MCMC) simulation has been used as a tool to approximate the posterior distribution. Problems arising from the sampling method are also briefly discussed and potential solutions for these problems are proposed. Special emphasis in the discussion is given to the philosophical foundation of the Bayesian approach in the context of fisheries stock assessment. It is argued that the role of subjective prior knowledge needed in practically all parts of a Bayesian model should be recognized and consequently fully utilised in the process of model formulation.

Bayesian Inference for Retrospective Population Genetics Models Using Markov Chain Monte Carlo Methods

Genetics, the science of heredity and variation in living organisms, has a central role in medicine, in breeding crops and livestock, and in studying fundamental topics of biological sciences such as evolution and cell functioning. Currently the field of genetics is under a rapid development because of the recent advances in technologies by which molecular data can be obtained from living organisms. In order that most information from such data can be extracted, the analyses need to be carried out using statistical models that are tailored to take account of the particular genetic processes. In this thesis we formulate and analyze Bayesian models for genetic marker data of contemporary individuals. The major focus is on the modeling of the unobserved recent ancestry of the sampled individuals (say, for tens of generations or so), which is carried out by using explicit probabilistic reconstructions of the pedigree structures accompanied by the gene flows at the marker loci. For such a recent history, the recombination process is the major genetic force that shapes the genomes of the individuals, and it is included in the model by assuming that the recombination fractions between the adjacent markers are known. The posterior distribution of the unobserved history of the individuals is studied conditionally on the observed marker data by using a Markov chain Monte Carlo algorithm (MCMC). The example analyses consider estimation of the population structure, relatedness structure (both at the level of whole genomes as well as at each marker separately), and haplotype configurations. For situations where the pedigree structure is partially known, an algorithm to create an initial state for the MCMC algorithm is given. Furthermore, the thesis includes an extension of the model for the recent genetic history to situations where also a quantitative phenotype has been measured from the contemporary individuals. In that case the goal is to identify positions on the genome that affect the observed phenotypic values. This task is carried out within the Bayesian framework, where the number and the relative effects of the quantitative trait loci are treated as random variables whose posterior distribution is studied conditionally on the observed genetic and phenotypic data. In addition, the thesis contains an extension of a widely-used haplotyping method, the PHASE algorithm, to settings where genetic material from several individuals has been pooled together, and the allele frequencies of each pool are determined in a single genotyping.

Methods to improve gene signal: Application to cDNA microarrays

Microarrays are high throughput biological assays that allow the screening of thousands of genes for their expression. The main idea behind microarrays is to compute for each gene a unique signal that is directly proportional to the quantity of mRNA that was hybridized on the chip. A large number of steps and errors associated with each step make the generated expression signal noisy. As a result, microarray data need to be carefully pre-processed before their analysis can be assumed to lead to reliable and biologically relevant conclusions. This thesis focuses on developing methods for improving gene signal and further utilizing this improved signal for higher level analysis. To achieve this, first, approaches for designing microarray experiments using various optimality criteria, considering both biological and technical replicates, are described. A carefully designed experiment leads to signal with low noise, as the effect of unwanted variations is minimized and the precision of the estimates of the parameters of interest are maximized. Second, a system for improving the gene signal by using three scans at varying scanner sensitivities is developed. A novel Bayesian latent intensity model is then applied on these three sets of expression values, corresponding to the three scans, to estimate the suitably calibrated true signal of genes. Third, a novel image segmentation approach that segregates the fluorescent signal from the undesired noise is developed using an additional dye, SYBR green RNA II. This technique helped in identifying signal only with respect to the hybridized DNA, and signal corresponding to dust, scratch, spilling of dye, and other noises, are avoided. Fourth, an integrated statistical model is developed, where signal correction, systematic array effects, dye effects, and differential expression, are modelled jointly as opposed to a sequential application of several methods of analysis. The methods described in here have been tested only for cDNA microarrays, but can also, with some modifications, be applied to other high-throughput technologies. Keywords: High-throughput technology, microarray, cDNA, multiple scans, Bayesian hierarchical models, image analysis, experimental design, MCMC, WinBUGS.

Primordial Isocurvature Perturbation in Light of CMB and LSS Data

The increased accuracy in the cosmological observations, especially in the measurements of the comic microwave background, allow us to study the primordial perturbations in grater detail. In this thesis, we allow the possibility for a correlated isocurvature perturbations alongside the usual adiabatic perturbations. Thus far the simplest six parameter \Lambda CDM model has been able to accommodate all the observational data rather well. However, we find that the 3-year WMAP data and the 2006 Boomerang data favour a nonzero nonadiabatic contribution to the CMB angular power sprctrum. This is primordial isocurvature perturbation that is positively correlated with the primordial curvature perturbation. Compared with the adiabatic \Lambda CMD model we have four additional parameters describing the increased complexity if the primordial perturbations. Our best-fit model has a 4% nonadiabatic contribution to the CMB temperature variance and the fit is improved by \Delta\chi^2 = 9.7. We can attribute this preference for isocurvature to a feature in the peak structure of the angular power spectrum, namely, the widths of the second and third acoustic peak. Along the way, we have improved our analysis methods by identifying some issues with the parametrisation of the primordial perturbation spectra and suggesting ways to handle these. Due to the improvements, the convergence of our Markov chains is improved. The change of parametrisation has an effect on the MCMC analysis because of the change in priors. We have checked our results against this and find only marginal differences between our parametrisation.

Bayesian parameter identification in dynamic state space models using modified measurement equations

When Markov chain Monte Carlo (MCMC) samplers are used in problems of system parameter identification, one would face computational difficulties in dealing with large amount of measurement data and (or) low levels of measurement noise. Such exigencies are likely to occur in problems of parameter identification in dynamical systems when amount of vibratory measurement data and number of parameters to be identified could be large. In such cases, the posterior probability density function of the system parameters tends to have regions of narrow supports and a finite length MCMC chain is unlikely to cover pertinent regions. The present study proposes strategies based on modification of measurement equations and subsequent corrections, to alleviate this difficulty. This involves artificial enhancement of measurement noise, assimilation of transformed packets of measurements, and a global iteration strategy to improve the choice of prior models. Illustrative examples cover laboratory studies on a time variant dynamical system and a bending-torsion coupled, geometrically non-linear building frame under earthquake support motions. (C) 2015 Elsevier Ltd. All rights reserved.

Model and parameter uncertainty in IDF relationships under climate change

Quantifying distributional behavior of extreme events is crucial in hydrologic designs. Intensity Duration Frequency (IDF) relationships are used extensively in engineering especially in urban hydrology, to obtain return level of extreme rainfall event for a specified return period and duration. Major sources of uncertainty in the IDF relationships are due to insufficient quantity and quality of data leading to parameter uncertainty due to the distribution fitted to the data and uncertainty as a result of using multiple GCMs. It is important to study these uncertainties and propagate them to future for accurate assessment of return levels for future. The objective of this study is to quantify the uncertainties arising from parameters of the distribution fitted to data and the multiple GCM models using Bayesian approach. Posterior distribution of parameters is obtained from Bayes rule and the parameters are transformed to obtain return levels for a specified return period. Markov Chain Monte Carlo (MCMC) method using Metropolis Hastings algorithm is used to obtain the posterior distribution of parameters. Twenty six CMIP5 GCMs along with four RCP scenarios are considered for studying the effects of climate change and to obtain projected IDF relationships for the case study of Bangalore city in India. GCM uncertainty due to the use of multiple GCMs is treated using Reliability Ensemble Averaging (REA) technique along with the parameter uncertainty. Scale invariance theory is employed for obtaining short duration return levels from daily data. It is observed that the uncertainty in short duration rainfall return levels is high when compared to the longer durations. Further it is observed that parameter uncertainty is large compared to the model uncertainty. (C) 2015 Elsevier Ltd. All rights reserved.

Nonparametric Bayesian Density Modeling with Gaussian Processes

We present the Gaussian process density sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a distribution defined by a density that is a transformation of a function drawn from a Gaussian process prior. Our formulation allows us to infer an unknown density from data using Markov chain Monte Carlo, which gives samples from the posterior distribution over density functions and from the predictive distribution on data space. We describe two such MCMC methods. Both methods also allow inference of the hyperparameters of the Gaussian process.

Models and algorithms for detection and tracking of coordinated groups

In this paper, we describe models and algorithms for detection and tracking of group and individual targets. We develop two novel group dynamical models, within a continuous time setting, that aim to mimic behavioural properties of groups. We also describe two possible ways of modeling interactions between closely using Markov Random Field (MRF) and repulsive forces. These can be combined together with a group structure transition model to create realistic evolving group models. We use a Markov Chain Monte Carlo (MCMC)-Particles Algorithm to perform sequential inference. Computer simulations demonstrate the ability of the algorithm to detect and track targets within groups, as well as infer the correct group structure over time. ©2008 IEEE.

Reversible jump sampler for autoregressive time series

We use reversible jump Markov chain Monte Carlo (MCMC) methods to address the problem of model order uncertainty in autoregressive (AR) time series within a Bayesian framework. Efficient model jumping is achieved by proposing model space moves from the full conditional density for the AR parameters, which is obtained analytically. This is compared with an alternative method, for which the moves are cheaper to compute, in which proposals are made only for new parameters in each move. Results are presented for both synthetic and audio time series.

Fixed-lag blind equalization and sequence estimation in digital communications systems using sequential importance sampling

We present methods for fixed-lag smoothing using Sequential Importance sampling (SIS) on a discrete non-linear, non-Gaussian state space system with unknown parameters. Our particular application is in the field of digital communication systems. Each input data point is taken from a finite set of symbols. We represent transmission media as a fixed filter with a finite impulse response (FIR), hence a discrete state-space system is formed. Conventional Markov chain Monte Carlo (MCMC) techniques such as the Gibbs sampler are unsuitable for this task because they can only perform processing on a batch of data. Data arrives sequentially, so it would seem sensible to process it in this way. In addition, many communication systems are interactive, so there is a maximum level of latency that can be tolerated before a symbol is decoded. We will demonstrate this method by simulation and compare its performance to existing techniques.