Modelling via normalisation for parametric and nonparametric inference

Bayesian nonparametric modelling has recently attracted a lot of attention, mainly due to the advancement of various simulation techniques, and especially Monte Carlo Markov Chain (MCMC) methods. In this thesis I propose some Bayesian nonparametric models for grouped data, which make use of dependent random probability measures. These probability measures are constructed by normalising infinitely divisible probability measures and exhibit nice theoretical properties. Implementation of these models is also easy, using mainly MCMC methods. An additional step in these algorithms is also proposed, in order to improve mixing. The proposed models are applied on both simulated and real-life data and the posterior inference for the parameters of interest are investigated, as well as the effect of the corresponding simulation algorithms. A new, n-dimensional distribution on the unit simplex, that contains many known distributions as special cases, is also proposed. The univariate version of this distribution is used as the underlying distribution for modelling binomial probabilities. Using simulated and real data, it is shown that this proposed model is particularly successful in modelling overdispersed count data

Modelling via normalisation for parametric and nonparametric inference

Bayesian nonparametric modelling has recently attracted a lot of attention, mainly due to the advancement of various simulation techniques, and especially Monte Carlo Markov Chain (MCMC) methods. In this thesis I propose some Bayesian nonparametric models for grouped data, which make use of dependent random probability measures. These probability measures are constructed by normalising infinitely divisible probability measures and exhibit nice theoretical properties. Implementation of these models is also easy, using mainly MCMC methods. An additional step in these algorithms is also proposed, in order to improve mixing. The proposed models are applied on both simulated and real-life data and the posterior inference for the parameters of interest are investigated, as well as the effect of the corresponding simulation algorithms. A new, n-dimensional distribution on the unit simplex, that contains many known distributions as special cases, is also proposed. The univariate version of this distribution is used as the underlying distribution for modelling binomial probabilities. Using simulated and real data, it is shown that this proposed model is particularly successful in modelling overdispersed count data.EThOS - Electronic Theses Online ServiceEngineering and Physical Sciences Research Council (Great Britain) (EPSRC)University of Warwick. Centre for Research in Statistical Methodology (CRiSM)Cyprus. Hypourgeio Oikonomikōn [Cyprus. Ministry of Finance] (C.MoF)GBUnited Kingdo

On Bayesian nonparametric modelling of two correlated distributions

In this paper, we consider the problem of modelling a pair of related distributions using Bayesian nonparametric methods. A representation of the distributions as weighted sums of distributions is derived through normalisation. This allows us to define several classes of nonparametric priors. The properties of these distributions are explored and efficient Markov chain Monte Carlo methods are developed. The methodology is illustrated on simulated data and an example concerning hospital efficiency measurement

Comparing distributions using dependent normalized random measure mixtures

A methodology for the simultaneous Bayesian nonparametric modelling of several distributions is developed. Our approach uses normalized random measures with independent increments and builds dependence through the superposition of shared processes. The properties of the prior are described and the modelling possibilities of this framework are explored in some detail. Efficient slice sampling methods are developed for inference. Various posterior summaries are introduced which allow better understanding of the differences between distributions. The methods are illustrated on simulated data and examples from survival analysis and stochastic frontier analysis

Modelling overdispersion with the normalized tempered stable distribution

This paper discusses a multivariate distribution which generalizes the Dirichlet distribution and demonstrates its usefulness for modelling overdispersion in count data. The distribution is constructed by normalizing a vector of independent Tempered Stable random variables. General formulae for all moments and cross-moments of the distribution are derived and they are found to have similar forms to those for the Dirichlet distribution. The univariate version of the distribution can be used as a mixing distribution for the success probability of a Binomial distribution to define an alternative to the well-studied Beta-Binomial distribution. Examples of fitting this model to simulated and real data are presented

How variability and effort determine coordination at large forces

Motor control is a challenging task for the central nervous system, since it involves redundant degrees of freedom, nonlinear dynamics of actuators and limbs, as well as noise. When an action is carried out, which factors does your nervous system consider to determine the appropriate set of muscle forces between redundant degrees-of-freedom? Important factors determining motor output likely encompass effort and the resulting motor noise. However, the tasks used in many previous motor control studies could not identify these two factors uniquely, as signal-dependent noise monotonically increases as a function of the effort. To address this, a recent paper introduced a force control paradigm involving one finger in each hand that can disambiguate these two factors. It showed that the central nervous system considers both force noise and amplitude, with a larger weight on the absolute force and lower weights on both noise and normalized force. While these results are valid for the relatively low force range considered in that paper, the magnitude of the force shared between the fingers for large forces is not known. This paper investigates this question experimentally, and develops an appropriate Markov chain Monte Carlo method in order to estimate the weightings given to these factors. Our results demonstrate that the force sharing strongly depends on the force level required, so that for higher force levels the normalized force is considered as much as the absolute force, whereas the role of noise minimization becomes negligible

Modeling overdispersion with the normalized tempered stable distribution

A multivariate distribution which generalizes the Dirichlet distribution is introduced and its use for modeling overdispersion in count data is discussed. The distribution is constructed by normalizing a vector of independent tempered stable random variables. General formulae for all moments and cross-moments of the distribution are derived and they are found to have similar forms to those for the Dirichlet distribution. The univariate version of the distribution can be used as a mixing distribution for the success probability of a binomial distribution to define an alternative to the well-studied beta-binomial distribution. Examples of fitting this model to simulated and real data are presented

Mean and standard deviation over all participants for the coefficient of variation measured in our experiments and in [10]. All measurements are in Newtons (N).

<p>Mean and standard deviation over all participants for the coefficient of variation measured in our experiments and in [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0149512#pone.0149512.ref010" target="_blank">10</a>]. All measurements are in Newtons (N).</p

Experimental setup: participants pressed with a finger (index or little) of both left and right hands on isometric force transducers.

<p>The subjects were required to match the goal force level (a horizontal line in the central bar) as accurately as possible with the summation of each finger’s force level (summation of the force levels is given by the LEDs in the central bar and the individuals’ force levels of the left and right hand are given by the left and right bars, respectively).</p