Giusi Moffa

Partition MCMC for Inference on Acyclic Digraphs

ABSTRACT Acyclic digraphs are the underlying representation of Bayesian networks, a widely used class of probabilistic graphical models. Learning the underlying graph from data is a way of gaining insights about the structural properties of a domain. Structure learning forms one of the inference challenges of statistical graphical models. Markov chain Monte Carlo (MCMC) methods, notably structure MCMC, to sample graphs from the posterior distribution given the data are probably the only viable option for Bayesian model averaging. Score modularity and restrictions on the number of parents of each node allow the graphs to be grouped into larger collections, which can be scored as a whole to improve the chain’s convergence. Current examples of algorithms taking advantage of grouping are the biased order MCMC, which acts on the alternative space of permuted triangular matrices, and nonergodic edge reversal moves. Here, we propose a novel algorithm, which employs the underlying combinatorial structure of DAGs to define a new grouping. As a result convergence is improved compared to structure MCMC, while still retaining the property of producing an unbiased sample. Finally, the method can be combined with edge reversal moves to improve the sampler further. Supplementary materials for this article are available online.

Using Directed Acyclic Graphs in Epidemiological Research in Psychosis: An Analysis of the Role of Bullying in Psychosis.

Abstract Modern psychiatric epidemiology researches complex interactions between multiple variables in large datasets. This creates difficulties for causal inference. We argue for the use of probabilistic models represented by directed acyclic graphs (DAGs). These capture the dependence structure of multiple variables and, used appropriately, allow more robust conclusions about the direction of causation. We analyzed British national survey data to assess putative mediators of the association between bullying victimization and persecutory ideation. We compared results using DAGs and the Karlson–Holm–Breen (KHB) logistic regression commands in STATA. We analyzed data from the 2007 English National Survey of Psychiatric Morbidity, using the equivalent 2000 survey in an instant replication. Additional details of methods and results are provided in the supplementary material. DAG analysis revealed a richer structure of relationships than could be inferred using the KHB logistic regression commands. Thus, bullying had direct effects on worry, persecutory ideation, mood instability, and drug use. Depression, sleep and anxiety lay downstream, and therefore did not mediate the link between bullying and persecutory ideation. Mediation by worry and mood instability could not be definitively ascertained. Bullying led to hallucinations indirectly, via persecutory ideation and depression. DAG analysis of the 2000 dataset suggested the technique generates stable results. While causality cannot be fully determined from cross-sectional data, DAGs indicate the relationships providing the best fit. They thereby advance investigation of the complex interactions seen in psychiatry, including the mechanisms underpinning psychiatric symptoms. It may consequently be used to optimize the choice of intervention targets.

Sequential Monte Carlo EM for multivariate probit models

Multivariate probit models have the appealing feature of capturing some of the dependence structure between the components of multidimensional binary responses. The key for the dependence modelling is the covariance matrix of an underlying latent multivariate Gaussian. Most approaches to maximum likelihood estimation in multivariate probit regression rely on Monte Carlo EM algorithms to avoid computationally intensive evaluations of multivariate normal orthant probabilities. As an alternative to the much used Gibbs sampler a new sequential Monte Carlo (SMC) sampler for truncated multivariate normals is proposed. The algorithm proceeds in two stages where samples are first drawn from truncated multivariate Student t distributions and then further evolved towards a Gaussian. The sampler is then embedded in a Monte Carlo EM algorithm. The sequential nature of SMC methods can be exploited to design a fully sequential version of the EM, where the samples are simply updated from one iteration to the next rather than resampled from scratch. Recycling the samples in this manner significantly reduces the computational cost. An alternative view of the standard conditional maximisation step provides the basis for an iterative procedure to fully perform the maximisation needed in the EM algorithm. The identifiability of multivariate probit models is also thoroughly discussed. In particular, the likelihood invariance can be embedded in the EM algorithm to ensure that constrained and unconstrained maximisations are equivalent. A simple iterative procedure is then derived for either maximisation which takes effectively no computational time. The method is validated by applying it to the widely analysed Six Cities dataset and on a higher dimensional simulated example. Previous approaches to the Six Cities dataset overly restrict the parameter space but, by considering the correct invariance, the maximum likelihood is quite naturally improved when treating the full unrestricted model.

Mutational interactions define novel cancer subgroups

Large-scale genomic data highlight the complexity and diversity of the molecular changes that drive cancer progression. Statistical analysis of cancer data from different tissues can guide drug repositioning as well as the design of targeted treatments. Here, we develop an improved Bayesian network model for tumour mutational profiles and apply it to 8198 patient samples across 22 cancer types from TCGA. For each cancer type, we identify the interactions between mutated genes, capturing signatures beyond mere mutational frequencies. When comparing mutation networks, we find genes which interact both within and across cancer types. To detach cancer classification from the tissue type we perform de novo clustering of the pancancer mutational profiles based on the Bayesian network models. We find 22 novel clusters which significantly improve survival prediction beyond clinical information. The models highlight key gene interactions for each cluster potentially allowing genomic stratification for clinical trials and identifying drug targets.Tumour heterogeneity hinders translation of large-scale genomic data into the clinic. Here the authors develop a method for the stratification of cancer patients based on the molecular gene status, including genetic interactions, rather than clinico-histological data, and apply it to TCGA data for over 8000 cases across 22 cancer types.

Using directed acyclic graphs in Epidemiological research in psychosis

Abstract Modern psychiatric epidemiology researches complex interactions between multiple variables in large datasets. This creates difficulties for causal inference. We argue for the use of probabilistic models represented by directed acyclic graphs (DAGs). These capture the dependence structure of multiple variables and, used appropriately, allow more robust conclusions about the direction of causation. We analyzed British national survey data to assess putative mediators of the association between bullying victimization and persecutory ideation. We compared results using DAGs and the Karlson–Holm–Breen (KHB) logistic regression commands in STATA. We analyzed data from the 2007 English National Survey of Psychiatric Morbidity, using the equivalent 2000 survey in an instant replication. Additional details of methods and results are provided in the supplementary material. DAG analysis revealed a richer structure of relationships than could be inferred using the KHB logistic regression commands. Thus, bullying had direct effects on worry, persecutory ideation, mood instability, and drug use. Depression, sleep and anxiety lay downstream, and therefore did not mediate the link between bullying and persecutory ideation. Mediation by worry and mood instability could not be definitively ascertained. Bullying led to hallucinations indirectly, via persecutory ideation and depression. DAG analysis of the 2000 dataset suggested the technique generates stable results. While causality cannot be fully determined from cross-sectional data, DAGs indicate the relationships providing the best fit. They thereby advance investigation of the complex interactions seen in psychiatry, including the mechanisms underpinning psychiatric symptoms. It may consequently be used to optimize the choice of intervention targets.

Using directed acyclic graphs in Epidemiological research in psychosis: the role of bullying in psychosis

Abstract Modern psychiatric epidemiology researches complex interactions between multiple variables in large datasets. This creates difficulties for causal inference. We argue for the use of probabilistic models represented by directed acyclic graphs (DAGs). These capture the dependence structure of multiple variables and, used appropriately, allow more robust conclusions about the direction of causation. We analyzed British national survey data to assess putative mediators of the association between bullying victimization and persecutory ideation. We compared results using DAGs and the Karlson–Holm–Breen (KHB) logistic regression commands in STATA. We analyzed data from the 2007 English National Survey of Psychiatric Morbidity, using the equivalent 2000 survey in an instant replication. Additional details of methods and results are provided in the supplementary material. DAG analysis revealed a richer structure of relationships than could be inferred using the KHB logistic regression commands. Thus, bullying had direct effects on worry, persecutory ideation, mood instability, and drug use. Depression, sleep and anxiety lay downstream, and therefore did not mediate the link between bullying and persecutory ideation. Mediation by worry and mood instability could not be definitively ascertained. Bullying led to hallucinations indirectly, via persecutory ideation and depression. DAG analysis of the 2000 dataset suggested the technique generates stable results. While causality cannot be fully determined from cross-sectional data, DAGs indicate the relationships providing the best fit. They thereby advance investigation of the complex interactions seen in psychiatry, including the mechanisms underpinning psychiatric symptoms. It may consequently be used to optimize the choice of intervention targets.