Next-generation sequencing (NGS) has rapidly become the current standard in genetic related analysis. This switch from microarray to NGS required new statistical strategies to address the research questions inherent to the considered phenomena. First and foremost, NGS dataset usually consist of discrete observations characterized by overdispersion - that is, discrepancy between expected and observed variability - and an abundance of zeros, measured across a huge number of regions of the genome. With respect to chromatin immunoprecipitation sequencing (ChIP-Seq), a class of NGS data, it is of primary focus to discover the underlying (unobserved) pattern of `enrichment': more particularly, there is interest in the interactions between genes (or broader regions of the genome) and proteins, as they describe the mechanism of regulation under different conditions such as healthy or damaged tissue. Another interesting research question involves the clustering of these observations into groups that have practical relevance and interpretability, considering in particular that a single unit could potentially be allocated into more than one of these clusters, as it is reasonable to assume that its participation is not exclusive to one and only biological function and/or mechanism. Many of these complex processes, indeed, could also be described by sets of ordinary differential equations (ODE's), which are mathematical representations of the changes of a system through time, following a dynamic that is governed by some parameters we are interested in. In this thesis, we address the aforementioned tasks and research questions employing different statistical strategies, such as model-based clustering, graphical models, penalized smoothing and regression. We propose extensions of the existing approaches to better fit the problem at hand and we elaborate the methodology in a Bayesian environment, with the focus on incorporating the structural dependencies - both spatial and temporal - of the data at our disposal.

This thesis concerns the statistical analysis of open quantum systems subject to an external and non-stationary perturbation. In the first paper, a generalization of the explicit-duration hidden Markov models (EDHMM) which takes into account the presence of sparse data is presented. Introducing a kernel estimator in the estimation procedure increases the accuracy of the estimates, and thus allows one to obtain a more reliable information about the evolution of the unobservable system. A generalization of the Viterbi algorithm to EDHMM is developed. In the second paper, we develop a Markov Chain Monte Carlo (MCMC) procedure for estimating the EDHMM. We improve the flexibility of our formulation by adopting a Bayesian model selection procedure which allows one to avoid a direct specification of the number of states of the hidden chain. Motivated by the presence of sparsity, we make use of a non-parametric estimator to obtain more accurate estimates of the model parameters. The formulation presented turns out to be straightforward to implement, robust against the underflow problem and provides accurate estimates of the parameters. In the third paper, an extension of the Cramér-Rao inequality for quantum discrete parameter models is derived. The latter are models in which the parameter space is restricted to a finite set of points. In some estimation problems indeed, theory provides us with additional information that allow us to restrict the parameter space to a finite set of points. The extension presented sets the ultimate accuracy of an estimator, and determines a discrete counterpart of the quantum Fisher information. This is particularly useful in many experiments in which the parameters can assume only few different values: for example, the direction which the magnetic field points to. We also provide an illustration related to a quantum optics problem.

This thesis addresses the statistical modeling of turbulence, focusing on three main aspects: the critical transition from laminarity to turbulence, the effects of the so-called intermittency and the energy dynamics of a turbulent flow. The central part of the thesis consists of six papers, divided into two parts. In Part I we develop two new indices to quantify the proximity to critical transitions in stochastic dynamical systems, with particular attention to the transition from laminarity to turbulence in fluids (Paper A). The two indices are tested on two toy models and then applied to the detection of critical events in a magnetised fluid and in financial time series. We define a third index Y, which quantifies the effects of intermittency and does not require very long time series. This index turns out to be effective in recovering the structure of the turbulent flow (Papers B, C). In Paper D we show that Y is also sensitive to the turbulent behavior of financial markets, providing a possible early warning indicator of the proximity to critical events. In Part II we introduce a new local observable as the arrival times of tracer particles at a particular point in the fluid as a proxy of the turbulent velocity field. We model the universal self-organising structure of this observable in an effective and parsimonious way. In the second paper of Part II, we model the continuous-time dynamics of the energy budget of the turbulent field. We show that this observable can be characterised as the exponential of a stochastic integral on a Lévy basis, under the assumption that the energy transmission across time scales is a multiplicative cascade process.

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Determining the total concentration of elements in soils seldom provides sufficient insight into trace metal bioavailability. However, measurement of ‘isotopically exchangeable’ metal can provide a better evaluation of metal reactivity and potential toxicity. Traditionally this requires the use of problematic radio-isotopes (e.g. 109Cd (γ)). Fortunately, increasing access to Inductively Coupled Plasma Mass Spectrometry (ICP-MS) in recent years has led to greater use of enriched stable isotopes of trace metals. The lability of heavy metals has been determined through a variety of approaches, including single and sequential extraction or predicted by geochemical models. In the present work, multi-element stable isotopes methods were developed for simultaneously determination of the labile pool of Fe, Zn, Cd and Pb using isotopic exchange principles. This included experimental and instrumental development for an accurate and precise determination of labile metal pool in soils. This approach was then validated by quantifying Zn, Cd and Pb in contaminated soils (Derbyshire; n = 8 and Weardale catchment; n = 246) and comparing the outcome results with common traditional extraction procedures. The variation of metal lability with soil characteristics was used to predict metal lability from the simple soil measurements using a multiple regression approach. In addition, E-values of Fe, Zn, Cd and Pb was used as input to WHAM(VI) (Windermere Humic-Aqueous Model) to predict metal solubility, emphasising in the role of Fe under reducing conditions in this regard. The results showed that isotopic dilution is a robust mechanistic method for assessing the ‘reactive’ pool of multiple trace metals over a wide range of soil characteristics. The results showed a very wide range of metal reactivities (almost 1%-100%) for Zn, Cd and Pb that were consistent over a range of spike concentrations. Sub-micron forms of non labile metal are perhaps most likely to occur in suspension either strongly bonded to humic/fulvic acids or occluded within CaCO3 particles. It appears that E values have no consistent correspondence to any chemical extraction procedure. Nevertheless, the use of 0.43 M HNO3 to extract labile metal in organic soils at pH < 6 appears justifiable - especially where humus is likely to be the principal adsorption surface. It is also important to acknowledge that extractions are not necessarily intended to estimate the entire reactive fraction. Thus, DTPA has been successfully applied as an empirical prediction of plant uptake but its extraction capacity is particularly limited in calcareous systems where it substantially underestimates the isotopically exchangeable metal pool. Speciation calculations showed that prediction of metal solubility was much better when the isotopically reactive metal pools were used as input to WHAM(VI). The soil samples that fitted best had pH values less than 4.0 and high organic matter contents reflecting the strength of the humic binding component of WHAM(VI) particularly in the case of Zn. The changes in metal solubility and lability under reducing conditions were mainly affected by pH. Moreover, the measurement of Fe2+ in the solution phase was considerably lower than that of the isotopically labile Fe2+ which calls into question the dependence on soluble Fe2+ to predict reductive dissolution of Fe-oxides. In addition, under reducing conditions the variables input of Fe to WHAM(VI) showed greatest effects on predicting metal solubility. It was found that Zn and Cd were affected only by Fe2+ competition for adsorption sites while predicted Pb solubility was more affected by loss of oxides than competition processes. The fractionation results, output from WHAM(VI), showed that a significant proportion of Pb was associated with Mn-oxides. Therefore, the calculation of loss of the adsorption site of Mn-oxides depending on Mn2+ measured in the solution phase did not improve the predicted Pb solubility where the model underestimate the adsorbed labile Mn as inference from Fe results.

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This thesis is an attempt to estimate the regional and national economic consequences of a wholesale move to sustainable agricultural systems in the UK. The study reviews definitions of agricultural sustainability, and draws a distinction between sustainable and organic farming systems. Farm-level definitions of sustainability are developed for all the main farm types encountered in the UK, and key indicators with targets are developed to assess and monitor any move towards sustainability. Linear Programming models are constructed, for 23 representative UK farm types under conventional and sustainable farming scenarios, to estimate the farm-level impacts of the adoption of sustainable farming at some point in the future. The farm-level models are aggregated to regional and national levels to estimate the likely changes in UK agricultural production of a more widespread adoption of sustainable farming practices. The wider economic effects of these changes at the regional and national levels are then examined by the use of output, income and employment multipliers. The study found that the biggest financial losses were predicted to be on intensive livestock farms, and in the more productive agricultural regions in the East and the South. Losses in net farm income were greatest on pig and poultry farms on which incomes fell to 33% of the conventional incomes, specialist dairy incomes fell to 47%, and on mainly dairy farms they fell to 58%. Average incomes on cropping and large LFA farms fell only slightly to 97% of the conventional scenario, whilst incomes on small LFA farms rose slightly to 102% an on mixed lowland farms they increased to 119% of the conventional scenario. The aggregated results project a fall in total net farm income for the UK to 85% of that under conventional farming. However, the total net farm income for Scotland would rise, whilst the biggest losses would be projected for Wales and Northern Ireland. Agricultural output was projected to fall by £2.42 billion, leading to an indirect fall of £1.58 billion in the farm supply industries, and a further induced fall of £1.68 billion in household spending, totalling a net loss of output of £5.66 billion. There would be a negative direct effect on household incomes however of £167 million, with indirect losses of £84 million and induced losses of £565 million. Direct employment in agriculture was also projected to fall by 28,830 FTEs, which would lead to an indirect loss of 31,740 FTEs in industries supplying farming, and induced losses of 30,292 FTEs in the wider economy leading to an overall loss of 90,862 FTEs. Gains in direct agricultural employment were however projected for the South East of England, and the West of Scotland. The North West of Scotland being the only region, where there would be a net overall increase in employment. Nationally sustainable agriculture would lead to a significant fall in the total income from farming, yet there would be substantial variations around the country, and between farm sectors. Indirect effects on the farm supply industries, and induced effects on households spending would lead to substantial losses, which would need to be offset against the environmental gains. The implications of these results for agricultural policy are discussed.

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