1,721,026 research outputs found
Priors for Bayesian model selection: difficulties and remedies.
No full textLa scelta del modello rappresenta un'area di grande rilevanza nell'inferenza statistica. Ritengo che
l'impostazione bayesiana sia particolarmente adatta a questo fine, dal momento che può efficacemente
superare alcune difficoltà insite in quella frequentista.
Tuttavia anche l'impostazione bayesiana in questo campo presenta aspetti critici.
In particolare sostengo che non sia opportuno utlizzare
distribuzioni convenzionali, valide per l'inferenza condizionata ad un modello, quando si consideri una pluralità
di modelli.
Sviluppo la mia trattazione ricorrendo ad un semplice esempio, che tuttavia mette in evidenza le principali
questioni problematiche.
Termino con una discussione di alcuni progetti che mi vedono coinvolto e con l'indicazione di alcune tematiche che
meritano ulteriore studio e considerazione
Robust Bayesian Graphical Modeling Using Dirichlet t-Distributions Contributed Discussion
No full textThe paper we discuss provides both theoretical and computational results for robust structure estimation in decomposable graphical models. We will comment on prior speci cation, in order to add further insights. Notice that model choice results strongly depend on prior speci cation
Objective Bayesian Comparison of Order-Constrained Models in Contingency Tables.
Full text linkIn social and biomedical sciences, testing in contingency tables often involves order restrictions on cell
probabilities parameters. We develop objective Bayes methods for order-constrained testing and model
comparison when observations arise under product binomial or multinomial sampling. Specifically, we
consider tests for monotone order of the parameters against equality of all parameters. Our strategy
combines in a unified way both the intrinsic prior methodology and the encompassing prior approach in
order to compute Bayes factors and posterior model probabilities. Performance of our method is evaluated
on several simulation studies and real datasets
Model Determination for Directed Acyclic Graphs
No full textDirected acyclic graphs (DAGs) have become increasingly popular to communicate, model and manage complex systems efficiently. They also represent a major tool in probabilistic expert systems. We address the issue of model determination for DAGs, with respect to a given ordering of the variables, together with the corresponding parameter estimation, and show how this can be done in a simple way using available software for Bayesian data analysis, such as BUG
Objective Bayes model selection of Gaussian interventional essential graphs for the identification of signaling pathways
Full text linkA signalling pathway is a sequence of chemical reactions initiated by a stimulus which in turn affects a receptor, and then through some intermediate steps cascades down to the final cell response. Based on the technique of flow cytometry, samples of cell-by-cell measurements are collected under each experimental condition, resulting in a collection of interventional data (assuming no latent variables are involved). Usually several external interventions are applied at different points of the pathway, the ultimate aim being the structural recovery of the underlying signalling network which we model as a causal Directed Acyclic Graph (DAG) using intervention calculus. The advantage of using interventional data, rather than purely observational one, is that identifiability of the true data generating DAG is enhanced. More technically a Markov equivalence class of DAGs, whose members are statistically indistinguishable based on observational data alone, can be further decomposed, using additional interventional data, into smaller distinct Interventional Markov equivalence classes. We present a Bayesian methodology for structural learning of Interventional Markov equivalence classes based on observational and interventional samples of multivariate Gaussian observations. Our approach is objective, meaning that it is based on default parameter priors requiring no personal elicitation; some flexibility is however allowed through a tuning parameter which regulates sparsity in the prior on model space. Based on an analytical expression for the marginal likelihood of a given Interventional Essential Graph, and a suitable MCMC scheme, our analysis produces an approximate posterior distribution on the space of Interventional Markov equivalence classes, which can be used to provide uncertainty quantification for features of substantive scientific interest, such as the posterior probability of inclusion of selected edges, or paths
Discovering causal structures in Bayesian Gaussian directed acyclic graph models
No full textCausal directed acyclic graphs (DAGs) are naturally tailored to represent biological signalling pathways. However, a causal DAG is only identifiable up to Markov equivalence if only observational data are available. Interventional data, based on exogenous perturbations of the system, can greatly improve identifiability. Since the gain of an intervention crucially depends on the intervened variables, a natural issue is devising efficient strategies for optimal causal discovery. We present a Bayesian active learning procedure for Gaussian DAGs which requires no subjective specification on the side of the user, explicitly takes into account the uncertainty on the space of equivalence classes (through the posterior distribution) and sequentially proposes the choice of the optimal intervention variable. In simulation experiments our method, besides surpassing designs based on a random choice of intervention nodes, shows decisive improvements over currently available algorithms and is competitive with the best alternative benchmarks. An important reason behind this strong performance is that, unlike non-Bayesian algorithms, our utility function naturally incorporates graph estimation uncertainty through the posterior edge inclusion probability. We also reanalyse the Sachs data on protein signalling pathways from an active learning perspective and show that DAG identification can be achieved by using only a subset of the available intervention samples
Bayesian clustering of gene expression microarray data for subgroup identification.
No full textLa tecnologia per la raccolta di dati genetici si sta sviluppando con grande
rapidit`a generando grandi basi di dati, con particolare riferimento alle osservazioni microarray
riferite all’ “espressione ” di geni. Sorge quindi l’esigenza di sviluppare analisi
statistiche capaci di raccogliere questa sfida, anche se finora queste rimangono spesso confinate
in un ambito descrittivo. Recentemente tuttavia sono stati proposti modelli ispirati
all’impostazione bayesiana che hanno il pregio di fornire una base probabilistica coerente
alle categorie concettuali impiegate (quali raggruppamento, profilo molecolare etc), oltre
a consentire stime pi`u efficienti, grazie al cosiddetto effetto di borrowing strength. In
particolare sono stati proposti modelli gerarchici bayesiani nei quali le osservazioni sono
generate da una distribuzione mistura a tre componenti (a seconda che il gene sia sottoespresso,
normalmente espresso e sovraespresso); le distribuzioni iniziali dei parametri
sono invece basate sull’ipotesi tradizionale di scambiabilit`a. In questo lavoro proponiamo
un modello gerarchico nel quale i parametri che rappresentano le probabilit`a che i
geni provengano dalla componente sotto- o sovraespressa non sono pi`u contraddistinti
dall’ipotesi di scambiabilit`a, ma piuttosto da una distribuzione mistura con un numero
aleatorio di componenti. In questo modo il modello consente di cogliere la presenza di
aspetti di eterogeneit`a conducendo di conseguenza ad un modello bayesiano di clustering
sia per quanto attiene ai geni che alle unit`a. Il modello viene applicato ad un insieme di
dati simulati e ad uno di osservazioni reali
Assessing replication success via skeptical mixture priors
No full textThere is growing interest in the analysis of replication studies aimed at reassessing
original findings across a wide range of scientific disciplines. In the context of hypothesis
testing for effect sizes, two Bayesian approaches stand out for their principled use
of the Bayes factor (BF): the replication BF and the skeptical BF. The latter, built
around the skeptical prior, represents the perspective of an investigator who remains
unconvinced by the original results and seeks to critically reassess them. In this paper,
we adopt the skeptical viewpoint and introduce a novel mixture prior that incorporates
skepticism while offering control over prior-data conflict. We study the consistency
properties of the resulting skeptical mixture Bayes factor and examine its relationship
to the standard skeptical BF. Through a focused simulation study, we conduct a sensitivity
analysis of the skeptical mixture BF with respect to prior-data conflict, covering
a range of plausible experimental scenarios. Our results show broad agreement with
the standard skeptical BF under typical conditions. However, in situations where the
standard skeptical BF suffers from severe prior-data conflict, our approach can yield
a meaningful adjustment in the reported strength of replication success. Finally,we
illustrate the practical application of our method using case studies from the Social
Sciences Replication Project
Bayesian clustering for row effects models
Full text linkWe deal with two-way contingency tables having ordered column categories. We use a row effects model wherein each interaction term is assumed to have a multiplicative form involving a row effect parameter and a fixed column score. We propose a methodology to cluster row effects in order to simplify the interaction structure and enhancing the interpretation of the model. Our method uses a product partition model with a suitable specification of the cohesion function, so that we can carry out our analysis on a collection of models of varying dimensions using a straightforward MCMC sampler. The methodology is illustrated with reference to simulated and real data sets
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