Construction of nonparametric Bayesian models from parametric Bayes equations

We consider the general problem of constructing nonparametric Bayesian models on infinite-dimensional random objects, such as functions, infinite graphs or infinite permutations. The problem has generated much interest in machine learning, where it is treated heuristically, but has not been studied in full generality in non-parametric Bayesian statistics, which tends to focus on models over probability distributions. Our approach applies a standard tool of stochastic process theory, the construction of stochastic processes from their finite-dimensional marginal distributions. The main contribution of the paper is a generalization of the classic Kolmogorov extension theorem to conditional probabilities. This extension allows a rigorous construction of nonparametric Bayesian models from systems of finite-dimensional, parametric Bayes equations. Using this approach, we show (i) how existence of a conjugate posterior for the nonparametric model can be guaranteed by choosing conjugate finite-dimensional models in the construction, (ii) how the mapping to the posterior parameters of the nonparametric model can be explicitly determined, and (iii) that the construction of conjugate models in essence requires the finite-dimensional models to be in the exponential family. As an application of our constructive framework, we derive a model on infinite permutations, the nonparametric Bayesian analogue of a model recently proposed for the analysis of rank data.

Inference in credal networks using multilinear programming

A credal network is a graphical tool for representation and manipulation of uncertainty, where probability values may be imprecise or indeterminate. A credal network associates a directed acyclic graph with a collection of sets of probability measures; in this context, inference is the computation of tight lower and upper bounds for conditional probabilities. In this paper we present new algorithms for inference in credal networks based on multilinear programming techniques. Experiments indicate that these new algorithms have better performance than existing ones, in the sense that they can produce more accurate results in larger networks.

Quantifying consistency of Event Related Potentials across subjects based on single-trial topographic analysis

Introduction: Non-invasive brain imaging techniques often contrast experimental conditions across a cohort of participants, obfuscating distinctions in individual performance and brain mechanisms that are better characterised by the inter-trial variability. To overcome such limitations, we developed topographic analysis methods for single-trial EEG data [1]. So far this was typically based on time-frequency analysis of single-electrode data or single independent components. The method's efficacy is demonstrated for event-related responses to environmental sounds, hitherto studied at an average event-related potential (ERP) level. Methods: Nine healthy subjects participated to the experiment. Auditory meaningful sounds of common objects were used for a target detection task [2]. On each block, subjects were asked to discriminate target sounds, which were living or man-made auditory objects. Continuous 64-channel EEG was acquired during the task. Two datasets were considered for each subject including single-trial of the two conditions, living and man-made. The analysis comprised two steps. In the first part, a mixture of Gaussians analysis [3] provided representative topographies for each subject. In the second step, conditional probabilities for each Gaussian provided statistical inference on the structure of these topographies across trials, time, and experimental conditions. Similar analysis was conducted at group-level. Results: Results show that the occurrence of each map is structured in time and consistent across trials both at the single-subject and at group level. Conducting separate analyses of ERPs at single-subject and group levels, we could quantify the consistency of identified topographies and their time course of activation within and across participants as well as experimental conditions. A general agreement was found with previous analysis at average ERP level. Conclusions: This novel approach to single-trial analysis promises to have impact on several domains. In clinical research, it gives the possibility to statistically evaluate single-subject data, an essential tool for analysing patients with specific deficits and impairments and their deviation from normative standards. In cognitive neuroscience, it provides a novel tool for understanding behaviour and brain activity interdependencies at both single-subject and at group levels. In basic neurophysiology, it provides a new representation of ERPs and promises to cast light on the mechanisms of its generation and inter-individual variability.

The quality of the mother-child relationship during collaborative problem solving /

The quality of the mother-child relationship was examined in relation to joint planning, maternal teaching strategies, maternal emotional support, mutual positive affect and attachment security. Fifty-five grade five children and their mothers participated in a laboratory session comprised of various activities and completed questionnaires to evaluate attachment security. Joint planning and social problem solving were assessed observationally during an origami task. Problem solving effectiveness was unrelated to maternal teaching strategies, maternal encouragement and mutual positive affect. A marginally significant relationship was found between maternal encouragement and active child participation. Attachment security was found to be significantly related to sharing of responsibility during local planning, but only for child autonomous performance. An examination of conditional probabilities revealed that mutual positive affect did not increase the likelihood of subsequent mother-child dyadic regulation. However, mutual positive affect was found to be significantly related to both active child participation and dyadic regulation. The hypothesis predicting a mediational model was not supported. The implications of these findings in the theoretical and empirical literature were considered and suggestions for future research were made.

A note on the accuracy of PAC-likelihood inference with microsatellite data

Stephens and Donnelly have introduced a simple yet powerful importance sampling scheme for computing the likelihood in population genetic models. Fundamental to the method is an approximation to the conditional probability of the allelic type of an additional gene, given those currently in the sample. As noted by Li and Stephens, the product of these conditional probabilities for a sequence of draws that gives the frequency of allelic types in a sample is an approximation to the likelihood, and can be used directly in inference. The aim of this note is to demonstrate the high level of accuracy of "product of approximate conditionals" (PAC) likelihood when used with microsatellite data. Results obtained on simulated microsatellite data show that this strategy leads to a negligible bias over a wide range of the scaled mutation parameter theta. Furthermore, the sampling variance of likelihood estimates as well as the computation time are lower than that obtained with importance sampling on the whole range of theta. It follows that this approach represents an efficient substitute to IS algorithms in computer intensive (e.g. MCMC) inference methods in population genetics. (c) 2006 Elsevier Inc. All rights reserved.

Essays on incentives, procurement and regulation

Esta tese é composta de três artigos. No primeiro artigo, "Simple Contracts under Simultaneous Adverse Selection and Moral Hazard", é considerado um problema de principal-agente sob a presença simultânea dos problemas de risco moral e seleção adversa, em que a dimensão de seleção adversa se dá sobre as distribuições de probabilidade condicionais as ações do agente. No segundo artigo, "Public-Private Partnerships in the Presence of Adverse Selection" é analisada a otimalidade de parcerias público-privadas sob a presença de seleção adversa. No terceiro artigo, "Regulation Under Stock Market Information Disclosure", por sua vez, é considerado o problema da regulação de firmas de capital aberto, onde as firmas possuem incentivos para mandar sinais opostos para o regulador e o mercado.

Analisi critica di modelli previsionali per le frane in Emilia Romagna

Questa tesi di dottorato è inserita nell’ambito della convenzione tra ARPA_SIMC (che è l’Ente finanziatore), l’Agenzia Regionale di Protezione Civile ed il Dipartimento di Scienze della Terra e Geologico - Ambientali dell’Ateneo di Bologna. L’obiettivo principale è la determinazione di possibili soglie pluviometriche di innesco per i fenomeni franosi in Emilia Romagna che possano essere utilizzate come strumento di supporto previsionale in sala operativa di Protezione Civile. In un contesto geologico così complesso, un approccio empirico tradizionale non è sufficiente per discriminare in modo univoco tra eventi meteo innescanti e non, ed in generale la distribuzione dei dati appare troppo dispersa per poter tracciare una soglia statisticamente significativa. È stato quindi deciso di applicare il rigoroso approccio statistico Bayesiano, innovativo poiché calcola la probabilità di frana dato un certo evento di pioggia (P(A|B)) , considerando non solo le precipitazioni innescanti frane (quindi la probabilità condizionata di avere un certo evento di precipitazione data l’occorrenza di frana, P(B|A)), ma anche le precipitazioni non innescanti (quindi la probabilità a priori di un evento di pioggia, P(A)). L’approccio Bayesiano è stato applicato all’intervallo temporale compreso tra il 1939 ed il 2009. Le isolinee di probabilità ottenute minimizzano i falsi allarmi e sono facilmente implementabili in un sistema di allertamento regionale, ma possono presentare limiti previsionali per fenomeni non rappresentati nel dataset storico o che avvengono in condizioni anomale. Ne sono esempio le frane superficiali con evoluzione in debris flows, estremamente rare negli ultimi 70 anni, ma con frequenza recentemente in aumento. Si è cercato di affrontare questo problema testando la variabilità previsionale di alcuni modelli fisicamente basati appositamente sviluppati a questo scopo, tra cui X – SLIP (Montrasio et al., 1998), SHALSTAB (SHALlow STABility model, Montgomery & Dietrich, 1994), Iverson (2000), TRIGRS 1.0 (Baum et al., 2002), TRIGRS 2.0 (Baum et al., 2008).

COVARIATE-ADJUSTED NONPARAMETRIC ANALYSIS OF MAGNETIC RESONANCE IMAGES USING MARKOV CHAIN MONTE CARLO

Permutation tests are useful for drawing inferences from imaging data because of their flexibility and ability to capture features of the brain that are difficult to capture parametrically. However, most implementations of permutation tests ignore important confounding covariates. To employ covariate control in a nonparametric setting we have developed a Markov chain Monte Carlo (MCMC) algorithm for conditional permutation testing using propensity scores. We present the first use of this methodology for imaging data. Our MCMC algorithm is an extension of algorithms developed to approximate exact conditional probabilities in contingency tables, logit, and log-linear models. An application of our non-parametric method to remove potential bias due to the observed covariates is presented.

Probabilistic versus incremental presynaptic learning in biological plausible synapses

In this paper, the presynaptic rule, a classical rule for hebbian learning, is revisited. It is shown that the presynaptic rule exhibits relevant synaptic properties like synaptic directionality, and LTP metaplasticity (long-term potentiation threshold metaplasticity). With slight modifications, the presynaptic model also exhibits metaplasticity of the long-term depression threshold, being also consistent with Artola, Brocher and Singer’s (ABS) influential model. Two asymptotically equivalent versions of the presynaptic rule were adopted for this analysis: the first one uses an incremental equation while the second, conditional probabilities. Despite their simplicity, both types of presynaptic rules exhibit sophisticated biological properties, specially the probabilistic version

Definition of HLA-DQ as a transplantation antigen

Recent studies have demonstrated the importance of recipient HLA-DRB1 allele disparity in the development of acute graft-versus-host disease (GVHD) after unrelated donor marrow transplantation. The role of HLA-DQB1 allele disparity in this clinical setting is unknown. To elucidate the biological importance of HLA-DQB1, we conducted a retrospective analysis of 449 HLA-A, -B, and -DR serologically matched unrelated donor transplants. Molecular typing of HLA-DRB1 and HLA-DQB1 alleles revealed 335 DRB1 and DQB1 matched pairs; 41 DRB1 matched and DQB1 mismatched pairs; 48 DRB1 mismatched and DQB1 matched pairs; and 25 DRB1 and DQB1 mismatched pairs. The conditional probabilities of grades III-IV acute GVHD were 0.42, 0.61, 0.55, and 0.71, respectively. The relative risk of acute GVHD associated with a single locus HLA-DQB1 mismatch was 1.8 (1.1, 2.7; P = 0.01), and the risk associated with any HLA-DQB1 and/or HLA-DRB1 mismatch was 1.6 (1.2, 2.2; P = 0.003). These results provide evidence that HLA-DQ is a transplant antigen and suggest that evaluation of both HLA-DQB1 and HLA-DRB1 is necessary in selecting potential donors.

Boosting the tree augmented naive bayes classifier

The Tree Augmented Naïve Bayes (TAN) classifier relaxes the sweeping independence assumptions of the Naïve Bayes approach by taking account of conditional probabilities. It does this in a limited sense, by incorporating the conditional probability of each attribute given the class and (at most) one other attribute. The method of boosting has previously proven very effective in improving the performance of Naïve Bayes classifiers and in this paper, we investigate its effectiveness on application to the TAN classifier.

Modelling wind direction from satellite scatterometer data

Most of the common techniques for estimating conditional probability densities are inappropriate for applications involving periodic variables. In this paper we apply two novel techniques to the problem of extracting the distribution of wind vector directions from radar scatterometer data gathered by a remote-sensing satellite.

Controlling protein molecular dynamics:how to accelerate folding while preserving the native state

The dynamics of peptides and proteins generated by classical molecular dynamics (MD) is described by using a Markov model. The model is built by clustering the trajectory into conformational states and estimating transition probabilities between the states. Assuming that it is possible to influence the dynamics of the system by varying simulation parameters, we show how to use the Markov model to determine the parameter values that preserve the folded state of the protein and at the same time, reduce the folding time in the simulation. We investigate this by applying the method to two systems. The first system is an imaginary peptide described by given transition probabilities with a total folding time of 1 micros. We find that only small changes in the transition probabilities are needed to accelerate (or decelerate) the folding. This implies that folding times for slowly folding peptides and proteins calculated using MD cannot be meaningfully compared to experimental results. The second system is a four residue peptide valine-proline-alanine-leucine in water. We control the dynamics of the transitions by varying the temperature and the atom masses. The simulation results show that it is possible to find the combinations of parameter values that accelerate the dynamics and at the same time preserve the native state of the peptide. A method for accelerating larger systems without performing simulations for the whole folding process is outlined.

Real-time process plant fault diagnosis

Operators can become confused while diagnosing faults in process plant while in operation. This may prevent remedial actions being taken before hazardous consequences can occur. The work in this thesis proposes a method to aid plant operators in systematically finding the causes of any fault in the process plant. A computer aided fault diagnosis package has been developed for use on the widely available IBM PC compatible microcomputer. The program displays a coloured diagram of a fault tree on the VDU of the microcomputer, so that the operator can see the link between the fault and its causes. The consequences of the fault and the causes of the fault are also shown to provide a warning of what may happen if the fault is not remedied. The cause and effect data needed by the package are obtained from a hazard and operability (HAZOP) study on the process plant. The result of the HAZOP study is recorded as cause and symptom equations which are translated into a data structure and stored in the computer as a file for the package to access. Probability values are assigned to the events that constitute the basic causes of any deviation. From these probability values, the a priori probabilities of occurrence of other events are evaluated. A top-down recursive algorithm, called TDRA, for evaluating the probability of every event in a fault tree has been developed. From the a priori probabilities, the conditional probabilities of the causes of the fault are then evaluated using Bayes' conditional probability theorem. The posteriori probability values could then be used by the operators to check in an orderly manner the cause of the fault. The package has been tested using the results of a HAZOP study on a pilot distillation plant. The results from the test show how easy it is to trace the chain of events that leads to the primary cause of a fault. This method could be applied in a real process environment.

Supporting decision-making for self-adaptive systems:from goal models to dynamic decision networks

Context/Motivation - Different modeling techniques have been used to model requirements and decision-making of self-adaptive systems (SASs). Specifically, goal models have been prolific in supporting decision-making depending on partial and total fulfilment of functional (goals) and non-functional requirements (softgoals). Different goalrealization strategies can have different effects on softgoals which are specified with weighted contribution-links. The final decision about what strategy to use is based, among other reasons, on a utility function that takes into account the weighted sum of the different effects on softgoals. Questions/Problems - One of the main challenges about decisionmaking in self-adaptive systems is to deal with uncertainty during runtime. New techniques are needed to systematically revise the current model when empirical evidence becomes available from the deployment. Principal ideas/results - In this paper we enrich the decision-making supported by goal models by using Dynamic Decision Networks (DDNs). Goal realization strategies and their impact on softgoals have a correspondence with decision alternatives and conditional probabilities and expected utilities in the DDNs respectively. Our novel approach allows the specification of preferences over the softgoals and supports reasoning about partial satisfaction of softgoals using probabilities. We report results of the application of the approach on two different cases. Our early results suggest the decision-making process of SASs can be improved by using DDNs. © 2013 Springer-Verlag.