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No / In order to maintain a coherent, unified percept of the external environment, the brain must continuously combine information encoded by our different sensory systems. Contemporary models suggest that multisensory integration produces a weighted average of sensory estimates, where the contribution of each system to the ultimate multisensory percept is governed by the relative reliability of the information it provides (maximum-likelihood estimation). In the present study, we investigate interactions between auditory and visual rate perception, where observers are required to make judgments in one modality while ignoring conflicting rate information presented in the other. We show a gradual transition between partial cue integration and complete cue segregation with increasing inter-modal discrepancy that is inconsistent with mandatory implementation of maximum-likelihood estimation. To explain these findings, we implement a simple Bayesian model of integration that is also able to predict observer performance with novel stimuli. The model assumes that the brain takes into account prior knowledge about the correspondence between auditory and visual rate signals, when determining the degree of integration to implement. This provides a strategy for balancing the benefits accrued by integrating sensory estimates arising from a common source, against the costs of conflating information relating to independent objects or events.

Discovering a word’s part of speech is an essential step in acquiring the grammar of a language. In this thesis we examine a variety of computational Bayesian models that use linguistic input available to children, in the form of transcribed child directed speech, to learn part of speech categories. Part of speech categories are characterised by contextual (distributional/syntactic) and word-internal (morphological) similarity. In this thesis, we assume language learners will be aware of these types of cues, and investigate exactly how they can make use of them. Firstly, we enrich the context of a standard model (the Bayesian Hidden Markov Model) by adding sentence type to the wider distributional context.We show that children are exposed to a much more diverse set of sentence types than evident in standard corpora used for NLP tasks, and previous work suggests that they are aware of the differences between sentence type as signalled by prosody and pragmatics. Sentence type affects local context distributions, and as such can be informative when relying on local context for categorisation. Adding sentence types to the model improves performance, depending on how it is integrated into our models. We discuss how to incorporate novel features into the model structure we use in a flexible manner, and present a second model type that learns to use sentence type as a distinguishing cue only when it is informative. Secondly, we add a model of morphological segmentation to the part of speech categorisation model, in order to model joint learning of syntactic categories and morphology. These two tasks are closely linked: categorising words into syntactic categories is aided by morphological information, and finding morphological patterns in words is aided by knowing the syntactic categories of those words. In our joint model, we find improved performance vis-a-vis single-task baselines, but the nature of the improvement depends on the morphological typology of the language being modelled. This is the first token-based joint model of unsupervised morphology and part of speech category learning of which we are aware.

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Technological advances have enabled profiling gene expression variability, both at the RNA and the protein level, with ever increasing throughput. In addition, miniaturisation has enabled quantifying gene expression from small volumes of the input material and most recently at the level of single cells. Increasingly these technologies also preserve context information, such as assaying tissues with high spatial resolution. A second example of contextual information is multi-omics protocols, for example to assay gene expression and DNA methylation from the same cells or samples. Although such contextual gene expression datasets are increasingly available for both popu- lation and single-cell variation studies, methods for their analysis are not established. In this thesis, we propose two modelling approaches for the analysis of gene expression variation in specific biological contexts. The first contribution of this thesis is a statistical method for analysing single cell expression data in a spatial context. Our method identifies the sources of gene expression variability by decomposing it into different components, each attributable to a different source. These sources include aspects of spatial variation such as cell-cell interactions. In applications to data across different technologies, we show that cell-cell interactions are indeed a major determinant of the expression level of specific genes with a relevant link to their function. The second contribution is a latent variable model for the unsupervised analysis of gene expression data, while accounting for structured prior knowledge on experimental context. The proposed method enables the joint analysis of gene expression data and other omics data profiled in the same samples, and the model can be used to account for the grouping structure of samples, e.g. samples from individuals with different clinical covariates or from distinct experimental batches. Our model constitutes a principled framework to compare the molecular identities of these distinct groups.

Developing computational algorithms that capture the complex structure of natural language is an open problem. In particular, learning the abstract properties of language only from usage data remains a challenge. In this dissertation, we present a probabilistic usage-based model of verb argument structure acquisition that can successfully learn abstract knowledge of language from instances of verb usage, and use this knowledge in various language tasks. The model demonstrates the feasibility of a usage-based account of language learning, and provides concrete explanation for the observed patterns in child language acquisition. We propose a novel representation for the general constructions of language as probabilistic associations between syntactic and semantic features of a verb usage; these associations generalize over the syntactic patterns and the fine-grained semantics of both the verb and its arguments. The probabilistic nature of argument structure constructions in the model enables it to capture both statistical effects in language learning, and adaptability in language use. The acquisition of constructions is modeled as detecting similar usages and grouping them together. We use a probabilistic measure of similarity between verb usages, and a Bayesian framework for clustering them. Language use, on the other hand, is modeled as a prediction problem: each language task is viewed as finding the best value for a missing feature in a usage, based on the available features in that same usage and the acquired knowledge of language so far. In formulating prediction, we use the same Bayesian framework as used for learning, a formulation which takes into account both the general knowledge of language (i.e., constructions) and the specific behaviour of each verb. We show through computational simulation that the behaviour of the model mirrors that of young children in some relevant aspects. The model goes through the same learning stages as children do: the conservative use of the more frequent usages for each individual verb at the beginning, followed by a phase when general patterns are grasped and applied overtly, which leads to occasional overgeneralization errors. Such errors cease to be made over time as the model processes more input. We also investigate the learnability of verb semantic roles, a critical aspect of linking the syntax and semantics of verbs. In contrary to many existing linguistic theories and computational models which assume that semantic roles are innate and fixed, we show that general conceptions of semantic roles can be learned from the semantic properties of the verb arguments in the input usages. We represent each role as a semantic profile for an argument position in a general construction, where a profile is a probability distribution over a set of semantic properties that verb arguments can take. We extend this view to model the learning and use of verb selectional preferences, a phenomenon usually viewed as separate from verb semantic roles. Our experimental results show that the model learns intuitive profiles for both semantic roles and selectional preferences. Moreover, the learned profiles are shown to be useful in various language tasks as observed in reported experimental data on human subjects, such as resolving ambiguity in language comprehension and simulating human plausibility judgements.

Developing computational algorithms that capture the complex structure of natural language is an open problem. In particular, learning the abstract properties of language only from usage data remains a challenge. In this dissertation, we present a probabilistic usage-based model of verb argument structure acquisition that can successfully learn abstract knowledge of language from instances of verb usage, and use this knowledge in various language tasks. The model demonstrates the feasibility of a usage-based account of language learning, and provides concrete explanation for the observed patterns in child language acquisition. We propose a novel representation for the general constructions of language as probabilistic associations between syntactic and semantic features of a verb usage; these associations generalize over the syntactic patterns and the fine-grained semantics of both the verb and its arguments. The probabilistic nature of argument structure constructions in the model enables it to capture both statistical effects in language learning, and adaptability in language use. The acquisition of constructions is modeled as detecting similar usages and grouping them together. We use a probabilistic measure of similarity between verb usages, and a Bayesian framework for clustering them. Language use, on the other hand, is modeled as a prediction problem: each language task is viewed as finding the best value for a missing feature in a usage, based on the available features in that same usage and the acquired knowledge of language so far. In formulating prediction, we use the same Bayesian framework as used for learning, a formulation which takes into account both the general knowledge of language (i.e., constructions) and the specific behaviour of each verb. We show through computational simulation that the behaviour of the model mirrors that of young children in some relevant aspects. The model goes through the same learning stages as children do: the conservative use of the more frequent usages for each individual verb at the beginning, followed by a phase when general patterns are grasped and applied overtly, which leads to occasional overgeneralization errors. Such errors cease to be made over time as the model processes more input. We also investigate the learnability of verb semantic roles, a critical aspect of linking the syntax and semantics of verbs. In contrary to many existing linguistic theories and computational models which assume that semantic roles are innate and fixed, we show that general conceptions of semantic roles can be learned from the semantic properties of the verb arguments in the input usages. We represent each role as a semantic profile for an argument position in a general construction, where a profile is a probability distribution over a set of semantic properties that verb arguments can take. We extend this view to model the learning and use of verb selectional preferences, a phenomenon usually viewed as separate from verb semantic roles. Our experimental results show that the model learns intuitive profiles for both semantic roles and selectional preferences. Moreover, the learned profiles are shown to be useful in various language tasks as observed in reported experimental data on human subjects, such as resolving ambiguity in language comprehension and simulating human plausibility judgements.

The subject matter of this thesis can be summarized by a triplet of questions and answers. Showing what these questions and answers mean is, in essence, the goal of my project. The triplet goes like this: Q: How can we make progress in our understanding of social norms and norm compliance? A: Adopting a neurocomputational framework is one effective way to make progress in our understanding of social norms and norm compliance. Q: What could the neurocomputational mechanism of social norm compliance be? A: The mechanism of norm compliance probably consists of Bayesian - Reinforcement Learning algorithms implemented by activity in certain neural populations. Q: What could information about this mechanism tell us about social norms and social norm compliance? A: Information about this mechanism tells us that: a1: Social norms are uncertainty-minimizing devices. a2: Social norm compliance is one trick that agents employ to interact coadaptively and smoothly in their social environment. Most of the existing treatments of norms and norm compliance (e.g. Bicchieri 2006; Binmore 1993; Elster 1989; Gintis 2010; Lewis 1969; Pettit 1990; Sugden 1986; Ullmann‐Margalit 1977) consist in what Cristina Bicchieri (2006) refers to as “rational reconstructions.” A rational reconstruction of the concept of social norm “specifies in which sense one may say that norms are rational, or compliance with a norm is rational” (Ibid., pp. 10-11). What sets my project apart from these types of treatments is that it aims, first and foremost, at providing a description of some core aspects of the mechanism of norm compliance. The single most original idea put forth in my project is to bring an alternative explanatory framework to bear on social norm compliance. This is the framework of computational cognitive neuroscience. The chapters of this thesis describe some ways in which central issues concerning social norms can be fruitfully addressed within a neurocomputational framework. In order to qualify and articulate the triplet above, my strategy consists firstly in laying down the beginnings of a model of the mechanism of norm compliance behaviour, and then zooming in on specific aspects of the model. Such a model, the chapters of this thesis argue, explains apparently important features of the psychology and neuroscience of norm compliance, and helps us to understand the nature of the social norms we live by.

Bayesian modelling is a widely used, powerful approach for reducing absolute dating uncertainties in archaeological research. It is important that the methods used in chronology building are robust and reflect substantial prior knowledge. This thesis focuses on the development and evaluation of two novel, prior models: the trapezoidal phase model; and the Poisson process deposition model. Firstly, the limitations of the trapezoidal phase model were investigated by testing the model assumptions using simulations. It was found that a simple trapezoidal phase model does not reflect substantial prior knowledge and the addition of a non-informative element to the prior was proposed. An alternative parameterisation was also presented, to extend its use to a contiguous phase scenario. This method transforms the commonly-used abrupt transition model to allow for gradual changes. The second phase of this research evaluates the use of Bayesian model averaging in the Poisson process deposition model. The use of model averaging extends the application of the Poisson process model to remove the subjectivity involved in model selection. The last part of this thesis applies these models to different case studies, including attempts at resolving the Iron Age chronological debate in Israel, at determining the age of an important Quaternary tephra, at refining a cave chronology, and at more accurately modelling the mid-Holocene elm decline in the British Isles. The Bayesian methods discussed in this thesis are widely applicable in modelling situations where the associated prior assumptions are appropriate. Therefore, they are not limited to the case studies addressed in this thesis, nor are they limited to analysing radiocarbon chronologies.

Student Number: 9811822T - MSc Dissertation - School of Computational and Applied Mathematics - Faculty of Science / This dissertation reviews population dynamic type models of viral infection and introduces some new models to describe strain competition and the infected cell lifecycle. Laboratory data from a recent clinical trial, tracking drug resistant virus in patients given a short course of monotherapy is comprehensively analysed, paying particular attention to reproducibility. A Bayesian framework is introduced, which facilitates the inference of model parameters from the clinical data. It appears that the rapid emergence of resistance is a challenge to popular unstructured models of viral infection, and this challenge is partly addressed. In particular, it appears that minimal ordinary differential equations, with their implicit exponential lifetime (constant hazard) distributions in all compartments, lack the short transient timescales observed clinically. Directions for future work, both in terms of obtaining more informative data, and developing more systematic approaches to model building, are identified.