The thesis considers two topics in the automation of cytogenetics and cytology: the automated allocation of human chromosomes to the twenty-four classes which humans possess; and the detection of abnormal cervical smear specimens. For chromosome allocation, the following work is presented and evaluated on a number of data sets derived from chromosome preparations of different quality:1. Three new procedures for modelling between-cell variation.2. Six ways of combining class information on variability in multivariate Normal discrimination.3. Covariance selection models for individual chromosome classes and an assumed common covariance structure for a number of classes.4. Some two-stage procedures for the calculation of discriminant scores in multivariate Normal discrimination.5. The application of some non-parametric and semi-parametric methods.6. The modelling of band-transition sequence probabilities. For the detection of abnormal cervical smear specimens, the use of a consensus probability of a specimen being abnormal, derived from a number of cytologists' assessments, is considered. The sequential use of multiple regression equations to try to predict the logit transformations of these consensus probabilities is described. Finally, the sequential use of features in multivariate discrimination is considered mainly for the case of two known multivariate Normal populations with equal covariance matrices.

Connectionism's main contribution to cognitive science will prove to be the renewed impetus it has imparted to learning. Learning can be integrated into the existing theoretical foundations of the subject, and the combination, statistical computational theories, provide a framework within which many connectionist mathematical mechanisms naturally fit. Examples from supervised and reinforcement learning demonstrate this. Statistical computational theories already exist for certainn associative matrix memories. This work is extended, allowing real valued synapses and arbitrarily biased inputs. It shows that a covariance learning rule optimises the signal/noise ratio, a measure of the potential quality of the memory, and quantifies the performance penalty incurred by other rules. In particular two that have been suggested as occuring naturally are shown to be asymptotically optimal in the limit of sparse coding. The mathematical model is justified in comparison with other treatments whose results differ. Reinforcement comparison is a way of hastening the learning of reinforcement learning systems in statistical environments. Previous theoretical analysis has not distinguished between different comparison terms, even though empirically, a covariance rule has been shown to be better than just a constant one. The workings of reinforcement comparison are investigated by a second order analysis of the expected statistical performance of learning, and an alternative rule is proposed and empirically justified. The existing proof that temporal difference prediction learning converges in the mean is extended from a special case involving adjacent time steps to the general case involving arbitary ones. The interaction between the statistical mechanism of temporal difference and the linear representation is particularly stark. The performance of the method given a linearly dependent representation is also analysed.

In this thesis we examine the question of model selection in systems which learn input-output mappings from a data set of examples. The models we consider are inspired by feed-forward architectures used within the artificial neural networks community. The approach taken here is to elucidate the properties of various <I>model selection </I>criteria by calculation of relevant quantities derived in a Bayesian framework. These calculations make the assumption that examples are generated from some underlying rule or <I>teacher</I> by randomly sampling the input space and are performed using techniques borrowed from statistical mechanics. Such an approach allows for the comparison of different approaches on the basis of the resultant ability of the system to <I>generalize</I> to novel examples. Broadly stated, the model selection problem is the following. Given only a limited set of examples, which model, or <I>student</I>, should one choose from a set of candidates in order to achieve the highest level of generalization? We consider four model selection criteria. A penalty based method utilising a quantity derived from Bayesian statistics termed the <I>evidence</I>, and two methods based on estimates of the generalization performance namely, the <I>test error</I> and the <I>cross validation error</I>. The fourth method, less widely used, is based on the <I>noise sensitivity </I>of he models. In a simple scenario we demonstrate that model selection based on the evidence is susceptible to misspecification of the student. Our analysis is conducted in the <I>thermodynamic limit</I> where the system size is taken to be arbitrarily large. In particular we examine the <I>evidence procedure</I> assignments of the <I>hyperparameters</I> which control the learning algorithm. We find that, where the student is not sufficiently powerful to fully model the teacher, despite being sub-optimal this procedure is remarkably robust towards such misspecifications. In a scenario in which the student is more than able to represent the teacher we find the evidence procedure is optimal.

This thesis provides the first template for estimating relative sea level curves and their associated uncertainties. More specifically, the thesis estimates the changing state of sea level in the Humber estuary, UK, over the course of the Holocene. These estimates are obtained through Bayesian methods involving Gaussian processes. Part of the task involves collating data sources from both archaeologists and geologists which have been collected during frequent study of the region. A portion of the thesis is devoted to studying the nature of the data, and the adjustment of the archaeological information so it can be used in a format suitable for estimating former sea level. The Gaussian processes are used to model sea-level change via a correlation function which assumes that data points close together in time and space should be at a similar elevation. This assumption is relaxed by incorporating non-stationary correlation functions and aspects of anisotropy. A sequence of models are fitted using Markov chain Monte Carlo. The resultant curves do not pre-suppose a functional form, and give a comprehensive framework for accounting for their uncertainty. A further complication is introduced as the temporal explanatory variables are stochastic: they arise as radiocarbon dates which require statistical calibration. The resulting posterior date densities are irregular and multi-modal. The spatio-temporal Gaussian process 2 model takes account of such irregularities via Monte Carlo simulation. The resultant sea-level curves are scrutinised at a number of locations around the Humber over a selection of time periods. It is hoped that they can provide insight into other areas of sea-level research, and into a broader palaeoclimate framework.

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For a company to stay profitable and be competitive, the customer satisfaction must be very high. This means that the company must provide the right item at the right place at the right time, or the customer may bring its business to the competitor. But these factors bring uncertainty for the company in the supply chain of when, what and how much of the item to produce and distribute. For reducing this uncertainty and for making better plans for future demand, some sort of forecasting method must be provided. A forecast can however be statistically based and also completed with a judgmental knowledge if the statistics are not sufficient. This thesis has been done in cooperation with the Sales and Operations (S&amp;OP) department at Sandvik Mining Rock Tools in Sandviken, where a statistical forecast is currently used in combination with manual changes from sales. The forecasts are used as base for planning inventory levels and making production plans and are created by looking at the history of sales. This is done in order to meet market expectations and continuously be in sync with market fluctuations. The purpose with this thesis has been to study the item- customer combination demand and the statistical forecasting process that is currently used at the S&amp;OP department. One problem when creating forecast is how to forecast irregular demand accurately. This thesis has therefore been examining the history of sales too see in what extent irregular demand exists and how it can be treated. The result is a basic tool for mapping customers' demand behavior, where the behavior is decomposed into average monthly demand and volatility. Another result is that history of sales can get decomposed into Volatility, Volume, Value, Number of sales and Sales interval for better analysis. These variables can also be considered whenever analyzing and forecasting irregular demand. A third result is a classification of time series working as a guideline if demand should be statistically or judgmentally forecasted or being event based. The study analyzed 36 months history of sales for 56 850 time series of item- customer specific demand. The findings were that customers should have at least one year of continuous sales before the demand can be entirely statistically forecasted. The limits for demand to even be forecasted, the history of sales should at least occur every third month in average and contain at least six sales. Then the demand is defined as irregular and the forecast method is set to judgmental forecasting, which can be forecasted using statistical methods with manual adjustments. The results showed that the class of irregular demand represents approximately 70 percent in the aspect of revenue and therefore requires attention. / För att ett företag ska kunna vara lönsamt och konkurrenskraftigt måste kundnöjdheten vara mycket hög. Detta betyder att ett företag måste kunna förse rätt produkt i rätt tid på rätt plats, annars kommer kunden troligtvis att vända sig till konkurrenten. Men dessa faktorer kommer med osäkerhet för företaget i försörjningskedjan i när, vad och hur mycket av produkten de ska producera och distribuera. För att minska osäkerheten och för att planera bättre för framtida efterfrågan, måste någon typ av prognos upprättas. En prognos kan vara baserad på statistiska metoder men också kompletterad med subjektiv marknadsinformation om statistiken inte är tillräcklig. Studien som denna rapport beskriver är gjord i samarbete med Sales och Operations- avdelning (S&amp;OP) på Sandvik Mining Rock Tools i Sandviken. Där används statistiska prognoser i kombination med manuella förändringar av säljare samt regionala planerare som bas för planering av lagernivåer och produktion. Detta gör man för att möta marknadens efterfråga och för att kontinuerligt vara uppdaterad med marknadens variationer. Syftet med detta arbete har varit att studera kunders efterfrågan av produkt- kund kombination och den metod som används vid statistiska prognoser hos S&amp;OP- avdelningen. Ett problem som finns när man vill skapa prognoser är hur man ska prognostisera oregelbunden försäljning korrekt. Detta arbete har därför analyserat historisk försäljning för att se i vilken utsträckning oregelbunden efterfrågan finns och hur den kan hanteras. Resultatet är ett enkelt verktyg för att kunna kartlägga kunders köpbeteende. Ett till resultat är att historisk försäljning kan bli uppdelat i Volatilitet, Volym, Värde, Antalet köptillfällen och Tidsintervallet mellan köptillfällena. Dessa variabler kan även tas till hänsyn när man analyserar och prognostiserar oregelbunden försäljning. Ett tredje resultat är en klassificering av tidsserier som kan fungera som riktmärken om efterfrågan ska vara statistisk eller manuellt prognostiserade eller inte bör ha en prognos över huvud taget. Denna studie analyserade 36 månaders historik för 56 850 tidsserier av försäljning per produkt- kund kombination. Resultaten var att en kund bör ha åtminstone ett år av kontinuerlig efterfrågan innan man kan ha en prognos med statistiska modeller. Gränsen för att ens ha en prognos är att efterfrågan bör återkomma var tredje månad i genomsnitt och ha en historik av åtminstone sex försäljningstillfällen. Då klassificeras efterfrågan som oregelbunden och prognosen kan vara baserad på statistiska metoder men med manuella ändringar. I resultatet framkom det att oregelbunden efterfrågan representerar cirka 70 procent i avseende på intäkter och kräver således mycket uppmärksamhet.

This thesis comprises 51 papers and a book. It is divided into three sections: on statistical methodology, statistical applications and image analysis. Papers in the first section present new methodology on regression with serially correlated errors, computer-intensive inference and clustering methodology on regression with serially correlated errors, computer-intensive inference and clustering criteria. The second section comprises papers on a range of innovative applications of statistical methods. Papers are grouped by application into: combine harvesting, forage conservation, the modelling of climate, estimating and characterising soil properties, specifying and using the distribution of potato sizes and analysing ion channel data. The final section consists of a book and papers on image analysis. Methodology and applications in medical imaging, microscopy and electrophoresis are covered.

Thesis (PhD (Statistics and Actuarial Science))--University of Stellenbosch, 2007. / The smoothing of time series plays a very important role in various practical applications. Estimating the signal and removing the noise is the main goal of smoothing. Traditionally linear smoothers were used, but nonlinear smoothers became more popular through the years. From the family of nonlinear smoothers, the class of median smoothers, based on order statistics, is the most popular. A new class of nonlinear smoothers, called LULU smoothers, was developed by using the minimum and maximum selectors. These smoothers have very attractive mathematical properties. In this thesis their statistical properties are investigated and compared to that of the class of median smoothers. Smoothing, together with related concepts, are discussed in general. Thereafter, the class of median smoothers, from the literature is discussed. The class of LULU smoothers is defined, their properties are explained and new contributions are made. The compound LULU smoother is introduced and its property of variation decomposition is discussed. The probability distributions of some LULUsmoothers with independent data are derived. LULU smoothers and median smoothers are compared according to the properties of monotonicity, idempotency, co-idempotency, stability, edge preservation, output distributions and variation decomposition. A comparison is made of their respective abilities for signal recovery by means of simulations. The success of the smoothers in recovering the signal is measured by the integrated mean square error and the regression coefficient calculated from the least squares regression of the smoothed sequence on the signal. Finally, LULU smoothers are practically applied.

This thesis considers graphical models that are represented by families of probability distributions having sets of conditional independence constraints specified by an influence diagram. Chapter 1 introduces the notion of a directed acyclic graph, a particular type of independence graph, which is used to define the influence diagram. Examples of such structures are given, and of how they are used in building a graphical model. Models may contain discrete or continuous variables, or both. Local computational schemes using exact probabilistic methods on these models are then reviewed. Chapter 2 presents a review of the use of graphical models in legal reasoning literature. The use of likelihood ratios to propagate probabilities through an influence diagram is investigated in this chapter, and a method for calculating LRs in graphical models is presented. The notion of recovering the structure of a graphical model from observed data is studied in Chapter 3. An established method on discrete data is described, and extended to include continuous variables. Kernel methods are introduced and applied to the probability estimation needed in these methods. Chapters 4 and 5 describe the use of stochastic simulation on mixed graphical association models. Simulation methods, in particular the Gibbs sampler, can be used on a wider range of models than exact probabilistic methods. Also estimates of marginal density functions of continuous variables can be obtained by using kernel estimates on the simulated values; exact methods generally only provide the marginal means and variances of continuous variables.

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