A Bayesian destructive weighted Poisson cure rate model and an application to a cutaneous melanoma data

In this article, we propose a new Bayesian flexible cure rate survival model, which generalises the stochastic model of Klebanov et al. [Klebanov LB, Rachev ST and Yakovlev AY. A stochastic-model of radiation carcinogenesis - latent time distributions and their properties. Math Biosci 1993; 113: 51-75], and has much in common with the destructive model formulated by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)]. In our approach, the accumulated number of lesions or altered cells follows a compound weighted Poisson distribution. This model is more flexible than the promotion time cure model in terms of dispersion. Moreover, it possesses an interesting and realistic interpretation of the biological mechanism of the occurrence of the event of interest as it includes a destructive process of tumour cells after an initial treatment or the capacity of an individual exposed to irradiation to repair altered cells that results in cancer induction. In other words, what is recorded is only the damaged portion of the original number of altered cells not eliminated by the treatment or repaired by the repair system of an individual. Markov Chain Monte Carlo (MCMC) methods are then used to develop Bayesian inference for the proposed model. Also, some discussions on the model selection and an illustration with a cutaneous melanoma data set analysed by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)] are presented.

ABCtoolbox: a versatile toolkit for approximate Bayesian computations

Background The estimation of demographic parameters from genetic data often requires the computation of likelihoods. However, the likelihood function is computationally intractable for many realistic evolutionary models, and the use of Bayesian inference has therefore been limited to very simple models. The situation changed recently with the advent of Approximate Bayesian Computation (ABC) algorithms allowing one to obtain parameter posterior distributions based on simulations not requiring likelihood computations. Results Here we present ABCtoolbox, a series of open source programs to perform Approximate Bayesian Computations (ABC). It implements various ABC algorithms including rejection sampling, MCMC without likelihood, a Particle-based sampler and ABC-GLM. ABCtoolbox is bundled with, but not limited to, a program that allows parameter inference in a population genetics context and the simultaneous use of different types of markers with different ploidy levels. In addition, ABCtoolbox can also interact with most simulation and summary statistics computation programs. The usability of the ABCtoolbox is demonstrated by inferring the evolutionary history of two evolutionary lineages of Microtus arvalis. Using nuclear microsatellites and mitochondrial sequence data in the same estimation procedure enabled us to infer sex-specific population sizes and migration rates and to find that males show smaller population sizes but much higher levels of migration than females. Conclusion ABCtoolbox allows a user to perform all the necessary steps of a full ABC analysis, from parameter sampling from prior distributions, data simulations, computation of summary statistics, estimation of posterior distributions, model choice, validation of the estimation procedure, and visualization of the results.

Bayesian Geostatistical Design

This paper describes the use of model-based geostatistics for choosing the optimal set of sampling locations, collectively called the design, for a geostatistical analysis. Two types of design situations are considered. These are retrospective design, which concerns the addition of sampling locations to, or deletion of locations from, an existing design, and prospective design, which consists of choosing optimal positions for a new set of sampling locations. We propose a Bayesian design criterion which focuses on the goal of efficient spatial prediction whilst allowing for the fact that model parameter values are unknown. The results show that in this situation a wide range of inter-point distances should be included in the design, and the widely used regular design is therefore not the optimal choice.

Bayesian change-point analysis in linear regression model with scale mixtures of normal distributions

In this thesis, we consider Bayesian inference on the detection of variance change-point models with scale mixtures of normal (for short SMN) distributions. This class of distributions is symmetric and thick-tailed and includes as special cases: Gaussian, Student-t, contaminated normal, and slash distributions. The proposed models provide greater flexibility to analyze a lot of practical data, which often show heavy-tail and may not satisfy the normal assumption. As to the Bayesian analysis, we specify some prior distributions for the unknown parameters in the variance change-point models with the SMN distributions. Due to the complexity of the joint posterior distribution, we propose an efficient Gibbs-type with Metropolis- Hastings sampling algorithm for posterior Bayesian inference. Thereafter, following the idea of [1], we consider the problems of the single and multiple change-point detections. The performance of the proposed procedures is illustrated and analyzed by simulation studies. A real application to the closing price data of U.S. stock market has been analyzed for illustrative purposes.

Bayesian generalized linear models for meta-analysis of diagnostic tests

With the recognition of the importance of evidence-based medicine, there is an emerging need for methods to systematically synthesize available data. Specifically, methods to provide accurate estimates of test characteristics for diagnostic tests are needed to help physicians make better clinical decisions. To provide more flexible approaches for meta-analysis of diagnostic tests, we developed three Bayesian generalized linear models. Two of these models, a bivariate normal and a binomial model, analyzed pairs of sensitivity and specificity values while incorporating the correlation between these two outcome variables. Noninformative independent uniform priors were used for the variance of sensitivity, specificity and correlation. We also applied an inverse Wishart prior to check the sensitivity of the results. The third model was a multinomial model where the test results were modeled as multinomial random variables. All three models can include specific imaging techniques as covariates in order to compare performance. Vague normal priors were assigned to the coefficients of the covariates. The computations were carried out using the 'Bayesian inference using Gibbs sampling' implementation of Markov chain Monte Carlo techniques. We investigated the properties of the three proposed models through extensive simulation studies. We also applied these models to a previously published meta-analysis dataset on cervical cancer as well as to an unpublished melanoma dataset. In general, our findings show that the point estimates of sensitivity and specificity were consistent among Bayesian and frequentist bivariate normal and binomial models. However, in the simulation studies, the estimates of the correlation coefficient from Bayesian bivariate models are not as good as those obtained from frequentist estimation regardless of which prior distribution was used for the covariance matrix. The Bayesian multinomial model consistently underestimated the sensitivity and specificity regardless of the sample size and correlation coefficient. In conclusion, the Bayesian bivariate binomial model provides the most flexible framework for future applications because of its following strengths: (1) it facilitates direct comparison between different tests; (2) it captures the variability in both sensitivity and specificity simultaneously as well as the intercorrelation between the two; and (3) it can be directly applied to sparse data without ad hoc correction. ^

Distributed Fault Diagnosis Using Bayesian Reasoning in MAGNETO

Many of the emerging telecom services make use of Outer Edge Networks, in particular Home Area Networks. The configuration and maintenance of such services may not be under full control of the telecom operator which still needs to guarantee the service quality experienced by the consumer. Diagnosing service faults in these scenarios becomes especially difficult since there may be not full visibility between different domains. This paper describes the fault diagnosis solution developed in the MAGNETO project, based on the application of Bayesian Inference to deal with the uncertainty. It also takes advantage of a distributed framework to deploy diagnosis components in the different domains and network elements involved, spanning both the telecom operator and the Outer Edge networks. In addition, MAGNETO features self-learning capabilities to automatically improve diagnosis knowledge over time and a partition mechanism that allows breaking down the overall diagnosis knowledge into smaller subsets. The MAGNETO solution has been prototyped and adapted to a particular outer edge scenario, and has been further validated on a real testbed. Evaluation of the results shows the potential of our approach to deal with fault management of outer edge networks.

Probabilistic reasoning with a bayesian DNA device based on strand displacement

We present a computing model based on the DNA strand displacement technique which performs Bayesian inference. The model will take single stranded DNA as input data, representing the presence or absence of a specific molecular signal (evidence). The program logic encodes the prior probability of a disease and the conditional probability of a signal given the disease playing with a set of different DNA complexes and their ratios. When the input and program molecules interact, they release a different pair of single stranded DNA species whose relative proportion represents the application of Bayes? Law: the conditional probability of the disease given the signal. The models presented in this paper can empower the application of probabilistic reasoning in genetic diagnosis in vitro.

A multi-agent system with distributed bayesian reasoning for network fault diagnosis

In this paper, an innovative approach to perform distributed Bayesian inference using a multi-agent architecture is presented. The final goal is dealing with uncertainty in network diagnosis, but the solution can be of applied in other fields. The validation testbed has been a P2P streaming video service. An assessment of the work is presented, in order to show its advantages when it is compared with traditional manual processes and other previous systems.

B2DI a bayesian BDI agent model with causal belief updating based on MSBN

In this paper, we introduce B2DI model that extends BDI model to perform Bayesian inference under uncertainty. For scalability and flexibility purposes, Multiply Sectioned Bayesian Network (MSBN) technology has been selected and adapted to BDI agent reasoning. A belief update mechanism has been defined for agents, whose belief models are connected by public shared beliefs, and the certainty of these beliefs is updated based on MSBN. The classical BDI agent architecture has been extended in order to manage uncertainty using Bayesian reasoning. The resulting extended model, so-called B2DI, proposes a new control loop. The proposed B2DI model has been evaluated in a network fault diagnosis scenario. The evaluation has compared this model with two previously developed agent models. The evaluation has been carried out with a real testbed diagnosis scenario using JADEX. As a result, the proposed model exhibits significant improvements in the cost and time required to carry out a reliable diagnosis.

Bayesian model selection of structural explanatory models: Application to road accident data

Using the Bayesian approach as the model selection criteria, the main purpose in this study is to establish a practical road accident model that can provide a better interpretation and prediction performance. For this purpose we are using a structural explanatory model with autoregressive error term. The model estimation is carried out through Bayesian inference and the best model is selected based on the goodness of fit measures. To cross validate the model estimation further prediction analysis were done. As the road safety measures the number of fatal accidents in Spain, during 2000-2011 were employed. The results of the variable selection process show that the factors explaining fatal road accidents are mainly exposure, economic factors, and surveillance and legislative measures. The model selection shows that the impact of economic factors on fatal accidents during the period under study has been higher compared to surveillance and legislative measures.

Inference by replication in densely connected systems

An efficient Bayesian inference method for problems that can be mapped onto dense graphs is presented. The approach is based on message passing where messages are averaged over a large number of replicated variable systems exposed to the same evidential nodes. An assumption about the symmetry of the solutions is required for carrying out the averages; here we extend the previous derivation based on a replica-symmetric- (RS)-like structure to include a more complex one-step replica-symmetry-breaking-like (1RSB-like) ansatz. To demonstrate the potential of the approach it is employed for studying critical properties of the Ising linear perceptron and for multiuser detection in code division multiple access (CDMA) under different noise models. Results obtained under the RS assumption in the noncritical regime give rise to a highly efficient signal detection algorithm in the context of CDMA; while in the critical regime one observes a first-order transition line that ends in a continuous phase transition point. Finite size effects are also observed. While the 1RSB ansatz is not required for the original problems, it was applied to the CDMA signal detection problem with a more complex noise model that exhibits RSB behavior, resulting in an improvement in performance. © 2007 The American Physical Society.

A Note on Bayesian Estimation for the Negative-Binomial Model

2000 Mathematics Subject Classification: 62F15.

Bayesian alignment of continuous molecular shapes using random fields

Statistical methodology is proposed for comparing molecular shapes. In order to account for the continuous nature of molecules, classical shape analysis methods are combined with techniques used for predicting random fields in spatial statistics. Applying a modification of Procrustes analysis, Bayesian inference is carried out using Markov chain Monte Carlo methods for the pairwise alignment of the resulting molecular fields. Superimposing entire fields rather than the configuration matrices of nuclear positions thereby solves the problem that there is usually no clear one--to--one correspondence between the atoms of the two molecules under consideration. Using a similar concept, we also propose an adaptation of the generalised Procrustes analysis algorithm for the simultaneous alignment of multiple molecular fields. The methodology is applied to a dataset of 31 steroid molecules.

New perspectives in statistical mechanics and high-dimensional inference

The main purpose of this thesis is to go beyond two usual assumptions that accompany theoretical analysis in spin-glasses and inference: the i.i.d. (independently and identically distributed) hypothesis on the noise elements and the finite rank regime. The first one appears since the early birth of spin-glasses. The second one instead concerns the inference viewpoint. Disordered systems and Bayesian inference have a well-established relation, evidenced by their continuous cross-fertilization. The thesis makes use of techniques coming both from the rigorous mathematical machinery of spin-glasses, such as the interpolation scheme, and from Statistical Physics, such as the replica method. The first chapter contains an introduction to the Sherrington-Kirkpatrick and spiked Wigner models. The first is a mean field spin-glass where the couplings are i.i.d. Gaussian random variables. The second instead amounts to establish the information theoretical limits in the reconstruction of a fixed low rank matrix, the “spike”, blurred by additive Gaussian noise. In chapters 2 and 3 the i.i.d. hypothesis on the noise is broken by assuming a noise with inhomogeneous variance profile. In spin-glasses this leads to multi-species models. The inferential counterpart is called spatial coupling. All the previous models are usually studied in the Bayes-optimal setting, where everything is known about the generating process of the data. In chapter 4 instead we study the spiked Wigner model where the prior on the signal to reconstruct is ignored. In chapter 5 we analyze the statistical limits of a spiked Wigner model where the noise is no longer Gaussian, but drawn from a random matrix ensemble, which makes its elements dependent. The thesis ends with chapter 6, where the challenging problem of high-rank probabilistic matrix factorization is tackled. Here we introduce a new procedure called "decimation" and we show that it is theoretically to perform matrix factorization through it.

Hierarchical active inference for cognitive architectures

This thesis explores the methods based on the free energy principle and active inference for modelling cognition. Active inference is an emerging framework for designing intelligent agents where psychological processes are cast in terms of Bayesian inference. Here, I appeal to it to test the design of a set of cognitive architectures, via simulation. These architectures are defined in terms of generative models where an agent executes a task under the assumption that all cognitive processes aspire to the same objective: the minimization of variational free energy. Chapter 1 introduces the free energy principle and its assumptions about self-organizing systems. Chapter 2 describes how from the mechanics of self-organization can emerge a minimal form of cognition able to achieve autopoiesis. In chapter 3 I present the method of how I formalize generative models for action and perception. The architectures proposed allow providing a more biologically plausible account of more complex cognitive processing that entails deep temporal features. I then present three simulation studies that aim to show different aspects of cognition, their associated behavior and the underlying neural dynamics. In chapter 4, the first study proposes an architecture that represents the visuomotor system for the encoding of actions during action observation, understanding and imitation. In chapter 5, the generative model is extended and is lesioned to simulate brain damage and neuropsychological patterns observed in apraxic patients. In chapter 6, the third study proposes an architecture for cognitive control and the modulation of attention for action selection. At last, I argue how active inference can provide a formal account of information processing in the brain and how the adaptive capabilities of the simulated agents are a mere consequence of the architecture of the generative models. Cognitive processing, then, becomes an emergent property of the minimization of variational free energy.