The philosophical significance of Cox's theorem

Cox's theorem states that, under certain assumptions, any measure of belief is isomorphic to a probability measure. This theorem, although intended as a justification of the subjectivist interpretation of probability theory, is sometimes presented as an argument for more controversial theses. Of particular interest is the thesis that the only coherent means of representing uncertainty is via the probability calculus. In this paper I examine the logical assumptions of Cox's theorem and I show how these impinge on the philosophical conclusions thought to be supported by the theorem. I show that the more controversial thesis is not supported by Cox's theorem. (C) 2003 Elsevier Inc. All rights reserved.

Computational Techniques for Haplotype Inference and for Local Alignment Significance

This thesis which consists of an introduction and four peer-reviewed original publications studies the problems of haplotype inference (haplotyping) and local alignment significance. The problems studied here belong to the broad area of bioinformatics and computational biology. The presented solutions are computationally fast and accurate, which makes them practical in high-throughput sequence data analysis. Haplotype inference is a computational problem where the goal is to estimate haplotypes from a sample of genotypes as accurately as possible. This problem is important as the direct measurement of haplotypes is difficult, whereas the genotypes are easier to quantify. Haplotypes are the key-players when studying for example the genetic causes of diseases. In this thesis, three methods are presented for the haplotype inference problem referred to as HaploParser, HIT, and BACH. HaploParser is based on a combinatorial mosaic model and hierarchical parsing that together mimic recombinations and point-mutations in a biologically plausible way. In this mosaic model, the current population is assumed to be evolved from a small founder population. Thus, the haplotypes of the current population are recombinations of the (implicit) founder haplotypes with some point--mutations. HIT (Haplotype Inference Technique) uses a hidden Markov model for haplotypes and efficient algorithms are presented to learn this model from genotype data. The model structure of HIT is analogous to the mosaic model of HaploParser with founder haplotypes. Therefore, it can be seen as a probabilistic model of recombinations and point-mutations. BACH (Bayesian Context-based Haplotyping) utilizes a context tree weighting algorithm to efficiently sum over all variable-length Markov chains to evaluate the posterior probability of a haplotype configuration. Algorithms are presented that find haplotype configurations with high posterior probability. BACH is the most accurate method presented in this thesis and has comparable performance to the best available software for haplotype inference. Local alignment significance is a computational problem where one is interested in whether the local similarities in two sequences are due to the fact that the sequences are related or just by chance. Similarity of sequences is measured by their best local alignment score and from that, a p-value is computed. This p-value is the probability of picking two sequences from the null model that have as good or better best local alignment score. Local alignment significance is used routinely for example in homology searches. In this thesis, a general framework is sketched that allows one to compute a tight upper bound for the p-value of a local pairwise alignment score. Unlike the previous methods, the presented framework is not affeced by so-called edge-effects and can handle gaps (deletions and insertions) without troublesome sampling and curve fitting.

Optimal inference of sameness.

Deciding whether a set of objects are the same or different is a cornerstone of perception and cognition. Surprisingly, no principled quantitative model of sameness judgment exists. We tested whether human sameness judgment under sensory noise can be modeled as a form of probabilistically optimal inference. An optimal observer would compare the reliability-weighted variance of the sensory measurements with a set size-dependent criterion. We conducted two experiments, in which we varied set size and individual stimulus reliabilities. We found that the optimal-observer model accurately describes human behavior, outperforms plausible alternatives in a rigorous model comparison, and accounts for three key findings in the animal cognition literature. Our results provide a normative footing for the study of sameness judgment and indicate that the notion of perception as near-optimal inference extends to abstract relations.

Bayesian versus frequentist statistical inference for investi gating a one-off cancer cluster reported to a health department

Background The problem of silent multiple comparisons is one of the most difficult statistical problems faced by scientists. It is a particular problem for investigating a one-off cancer cluster reported to a health department because any one of hundreds, or possibly thousands, of neighbourhoods, schools, or workplaces could have reported a cluster, which could have been for any one of several types of cancer or any one of several time periods. Methods This paper contrasts the frequentist approach with a Bayesian approach for dealing with silent multiple comparisons in the context of a one-off cluster reported to a health department. Two published cluster investigations were re-analysed using the Dunn-Sidak method to adjust frequentist p-values and confidence intervals for silent multiple comparisons. Bayesian methods were based on the Gamma distribution. Results Bayesian analysis with non-informative priors produced results similar to the frequentist analysis, and suggested that both clusters represented a statistical excess. In the frequentist framework, the statistical significance of both clusters was extremely sensitive to the number of silent multiple comparisons, which can only ever be a subjective "guesstimate". The Bayesian approach is also subjective: whether there is an apparent statistical excess depends on the specified prior. Conclusion In cluster investigations, the frequentist approach is just as subjective as the Bayesian approach, but the Bayesian approach is less ambitious in that it treats the analysis as a synthesis of data and personal judgements (possibly poor ones), rather than objective reality. Bayesian analysis is (arguably) a useful tool to support complicated decision-making, because it makes the uncertainty associated with silent multiple comparisons explicit.

High-level concept annotation using ontology and probabilistic inference

Image annotation is a significant step towards semantic based image retrieval. Ontology is a popular approach for semantic representation and has been intensively studied for multimedia analysis. However, relations among concepts are seldom used to extract higher-level semantics. Moreover, the ontology inference is often crisp. This paper aims to enable sophisticated semantic querying of images, and thus contributes to 1) an ontology framework to contain both visual and contextual knowledge, and 2) a probabilistic inference approach to reason the high-level concepts based on different sources of information. The experiment on a natural scene database from LabelMe database shows encouraging results.

Mid-level concept learning with visual contextual ontologies and probabilistic inference for image annotation

To date, automatic recognition of semantic information such as salient objects and mid-level concepts from images is a challenging task. Since real-world objects tend to exist in a context within their environment, the computer vision researchers have increasingly incorporated contextual information for improving object recognition. In this paper, we present a method to build a visual contextual ontology from salient objects descriptions for image annotation. The ontologies include not only partOf/kindOf relations, but also spatial and co-occurrence relations. A two-step image annotation algorithm is also proposed based on ontology relations and probabilistic inference. Different from most of the existing work, we specially exploit how to combine representation of ontology, contextual knowledge and probabilistic inference. The experiments show that image annotation results are improved in the LabelMe dataset.

A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent mean

Phase-type distributions represent the time to absorption for a finite state Markov chain in continuous time, generalising the exponential distribution and providing a flexible and useful modelling tool. We present a new reversible jump Markov chain Monte Carlo scheme for performing a fully Bayesian analysis of the popular Coxian subclass of phase-type models; the convenient Coxian representation involves fewer parameters than a more general phase-type model. The key novelty of our approach is that we model covariate dependence in the mean whilst using the Coxian phase-type model as a very general residual distribution. Such incorporation of covariates into the model has not previously been attempted in the Bayesian literature. A further novelty is that we also propose a reversible jump scheme for investigating structural changes to the model brought about by the introduction of Erlang phases. Our approach addresses more questions of inference than previous Bayesian treatments of this model and is automatic in nature. We analyse an example dataset comprising lengths of hospital stays of a sample of patients collected from two Australian hospitals to produce a model for a patient's expected length of stay which incorporates the effects of several covariates. This leads to interesting conclusions about what contributes to length of hospital stay with implications for hospital planning. We compare our results with an alternative classical analysis of these data.

Voter behaviour and constitutional change in Australia since 1967

Australian Constitutional referendums have been part of the Australian political system since federation. Up to the year 1999 (the time of the last referendum in Australia), constitutional change in Australia does not have a good history of acceptance. Since 1901, there have been 44 proposed constitutional changes with eight gaining the required acceptance according to section 128 of the Australian Constitution. In the modern era since 1967, there have been 20 proposals over seven referendum votes for a total of four changes. Over this same period, there have been 13 federal general elections which have realised change in government just five times. This research examines the electoral behaviour of Australian voters from 1967 to 1999 for each referendum. Party identification has long been a key indicator in general election voting. This research considers whether the dominant theory of voter behaviour in general elections (the Michigan Model) provides a plausible explanation for voting in Australian referendums. In order to explain electoral behaviour in each referendum, this research has utilised available data from the Australian Electoral Commission, the 1996 Australian Bureau of Statistics Census data, and the 1999 Australian Constitutional Referendum Study. This data has provided the necessary variables required to measure the impact of the Michigan Model of voter behaviour. Measurements have been conducted using bivariate and multivariate analyses. Each referendum provides an overview of the events at the time of the referendum as well as the =yes‘ and =no‘ cases at the time each referendum was initiated. Results from this research provide support for the Michigan Model of voter behaviour in Australian referendum voting. This research concludes that party identification, as a key variable of the Michigan Model, shows that voters continue to take their cues for voting from the political party they identify with in Australian referendums. However, the outcome of Australian referendums clearly shows that partisanship is only one of a number of contributory factors in constitutional referendums.

Approximate Bayesian computation using indirect inference

We present a novel approach for developing summary statistics for use in approximate Bayesian computation (ABC) algorithms by using indirect inference. ABC methods are useful for posterior inference in the presence of an intractable likelihood function. In the indirect inference approach to ABC the parameters of an auxiliary model fitted to the data become the summary statistics. Although applicable to any ABC technique, we embed this approach within a sequential Monte Carlo algorithm that is completely adaptive and requires very little tuning. This methodological development was motivated by an application involving data on macroparasite population evolution modelled by a trivariate stochastic process for which there is no tractable likelihood function. The auxiliary model here is based on a beta–binomial distribution. The main objective of the analysis is to determine which parameters of the stochastic model are estimable from the observed data on mature parasite worms.

Fault diagnosis of induction motor based on decision trees and adaptive neuro-fuzzy inference

This paper presents a fault diagnosis method based on adaptive neuro-fuzzy inference system (ANFIS) in combination with decision trees. Classification and regression tree (CART) which is one of the decision tree methods is used as a feature selection procedure to select pertinent features from data set. The crisp rules obtained from the decision tree are then converted to fuzzy if-then rules that are employed to identify the structure of ANFIS classifier. The hybrid of back-propagation and least squares algorithm are utilized to tune the parameters of the membership functions. In order to evaluate the proposed algorithm, the data sets obtained from vibration signals and current signals of the induction motors are used. The results indicate that the CART–ANFIS model has potential for fault diagnosis of induction motors.

Towards semantic search and inference in electronic medical records : an approach using concept-based information retrieval

For more than a decade research in the field of context aware computing has aimed to find ways to exploit situational information that can be detected by mobile computing and sensor technologies. The goal is to provide people with new and improved applications, enhanced functionality and better use experience (Dey, 2001). Early applications focused on representing or computing on physical parameters, such as showing your location and the location of people or things around you. Such applications might show where the next bus is, which of your friends is in the vicinity and so on. With the advent of social networking software and microblogging sites such as Facebook and Twitter, recommender systems and so on context-aware computing is moving towards mining the social web in order to provide better representations and understanding of context, including social context. In this paper we begin by recapping different theoretical framings of context. We then discuss the problem of context- aware computing from a design perspective.