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Guido Consonni

Publications and source records attributed to Guido Consonni.

17 recordsLinked to original sources
arXiv2023

Assessing replication success via skeptical mixture priors

There is a growing interest in the analysis of replication studies of original findings across many disciplines. When testing a hypothesis for an effect size, two Bayesian approaches stand out for their principled use of the Bayes factor (BF), namely the replication BF and the skeptical BF. In particular, the latter BF is based on the skeptical prior, which represents the opinion of an investigator who is unconvinced by the original findings and wants to challenge them. We embrace the skeptical perspective, and elaborate a novel mixture prior which incorporates skepticism while at the same time controlling for prior-data conflict within the original data. Consistency properties of the resulting skeptical mixture BF are provided together with an extensive analysis of the main features of our proposal. Finally, we apply our methodology to data from the Social Sciences Replication Project. In particular we show that, for some case studies where prior-data conflict is an issue, our method uses a more realistic prior and leads to evidence-classification for replication success which differs from the standard skeptical approach.

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arXiv2023

Bayesian Approaches to Designing Replication Studies

Replication studies are essential for assessing the credibility of claims from original studies. A critical aspect of designing replication studies is determining their sample size; a too small sample size may lead to inconclusive studies whereas a too large sample size may waste resources that could be allocated better in other studies. Here, we show how Bayesian approaches can be used for tackling this problem. The Bayesian framework allows researchers to combine the original data and external knowledge in a design prior distribution for the underlying parameters. Based on a design prior, predictions about the replication data can be made, and the replication sample size can be chosen to ensure a sufficiently high probability of replication success. Replication success may be defined by Bayesian or non-Bayesian criteria, and different criteria may also be combined to meet distinct stakeholders and enable conclusive inferences based on multiple analysis approaches. We investigate sample size determination in the normal-normal hierarchical model where analytical results are available and traditional sample size determination is a special case where the uncertainty on parameter values is not accounted for. We use data from a multisite replication project of social-behavioral experiments to illustrate how Bayesian approaches can help design informative and cost-effective replication studies. Our methods can be used through the R package BayesRepDesign.

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arXiv2023

Joint structure learning and causal effect estimation for categorical graphical models

We consider a a collection of categorical random variables. Of special interest is the causal effect on an outcome variable following an intervention on another variable. Conditionally on a Directed Acyclic Graph (DAG), we assume that the joint law of the random variables can be factorized according to the DAG, where each term is a categorical distribution for the node-variable given a configuration of its parents. The graph is equipped with a causal interpretation through the notion of interventional distribution and the allied "do-calculus". From a modeling perspective, the likelihood is decomposed into a product over nodes and parents of DAG-parameters, on which a suitably specified collection of Dirichlet priors is assigned. The overall joint distribution on the ensemble of DAG-parameters is then constructed using global and local independence. We account for DAG-model uncertainty and propose a reversible jump Markov Chain Monte Carlo (MCMC) algorithm which targets the joint posterior over DAGs and DAG-parameters; from the output we are able to recover a full posterior distribution of any causal effect coefficient of interest, possibly summarized by a Bayesian Model Averaging (BMA) point estimate. We validate our method through extensive simulation studies, wherein comparisons with alternative state-of-the-art procedures reveal an outperformance in terms of estimation accuracy. Finally, we analyze a dataset relative to a study on depression and anxiety in undergraduate students.

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arXiv2023

Bayesian sample size determination for multi-site replication studies

An ongoing "reproducibility crisis" calls into question scientific discoveries across a variety of disciplines ranging from life to social sciences. Replication studies aim to investigate the validity of findings in published research, and try to assess whether the latter are statistically consistent with those in the replications. While the majority of replication projects are based on a single experiment, multiple independent replications of the same experiment conducted simultaneously at different sites are becoming more frequent. In connection with these types of projects, we deal with testing heterogeneity among sites; specifically, we focus on sample size determination suitable to deliver compelling evidence once the experimental data are gathered.

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arXiv2022

Bayesian sample size determination for causal discovery

Graphical models based on Directed Acyclic Graphs (DAGs) are widely used to answer causal questions across a variety of scientific and social disciplines. However, observational data alone cannot distinguish in general between DAGs representing the same conditional independence assertions (Markov equivalent DAGs); as a consequence the orientation of some edges in the graph remains indeterminate. Interventional data, produced by exogenous manipulations of variables in the network, enhance the process of structure learning because they allow to distinguish among equivalent DAGs, thus sharpening causal inference. Starting from an equivalence class of DAGs, a few procedures have been devised to produce a collection of variables to be manipulated in order to identify a causal DAG. Yet, these algorithmic approaches do not determine the sample size of the interventional data required to obtain a desired level of statistical accuracy. We tackle this problem from a Bayesian experimental design perspective, taking as input a sequence of target variables to be manipulated to identify edge orientation. We then propose a method to determine, at each intervention, the optimal sample size capable of producing a successful experiment based on a pre-experimental evaluation of the overall probability of substantial correct evidence.

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arXiv2022

Bayesian graphical modeling for heterogeneous causal effects

Our motivation stems from current medical research aiming at personalized treatment using a molecular-based approach. The broad goal is to develop a more precise and targeted decision making process, relative to traditional treatments based primarily on clinical diagnoses. Specifically, we consider patients affected by Acute Myeloid Leukemia (AML), an hematological cancer characterized by uncontrolled proliferation of hematopoietic stem cells in the bone marrow. Because AML responds poorly to chemoterapeutic treatments, the development of targeted therapies is essential to improve patients' prospects. In particular, the dataset we analyze contains the levels of proteins involved in cell cycle regulation and linked to the progression of the disease. We analyse treatment effects within a causal framework represented by a Directed Acyclic Graph (DAG) model, whose vertices are the protein levels in the network. A major obstacle in implementing the above program is however represented by individual heterogeneity. We address this issue through a Dirichlet Process (DP) mixture of Gaussian DAG-models where both the graphical structure as well as the allied model parameters are regarded as uncertain. Our procedure determines a clustering structure of the units reflecting the underlying heterogeneity, and produces subject-specific estimates of causal effects based on Bayesian model averaging. With reference to the AML dataset, we identify different effects of protein regulation among individuals; moreover, our method clusters patients into groups that exhibit only mild similarities with traditional categories based on morphological features.

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arXiv2020

Bayesian causal inference in probit graphical models

We consider a binary response which is potentially affected by a set of continuous variables. Of special interest is the causal effect on the response due to an intervention on a specific variable. The latter can be meaningfully determined on the basis of observational data through suitable assumptions on the data generating mechanism. In particular we assume that the joint distribution obeys the conditional independencies (Markov properties) inherent in a Directed Acyclic Graph (DAG), and the DAG is given a causal interpretation through the notion of interventional distribution. We propose a DAG-probit model where the response is generated by discretization through a random threshold of a continuous latent variable and the latter, jointly with the remaining continuous variables, has a distribution belonging to a zero-mean Gaussian model whose covariance matrix is constrained to satisfy the Markov properties of the DAG. Our model leads to a natural definition of causal effect conditionally on a given DAG. Since the DAG which generates the observations is unknown, we present an efficient MCMC algorithm whose target is the posterior distribution on the space of DAGs, the Cholesky parameters of the concentration matrix, and the threshold linking the response to the latent. Our end result is a Bayesian Model Averaging estimate of the causal effect which incorporates parameter, as well as model, uncertainty. The methodology is assessed using simulation experiments and applied to a gene expression data set originating from breast cancer stem cells.

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arXiv2018

Objective Bayesian Comparison of Order-Constrained Models in Contingency Tables

In 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.

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arXiv2014

Objective Bayesian Comparison of Constrained Analysis of Variance Models

In the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints. For instance, when examining three group means $\{ μ_1, μ_2, μ_3\}$ through an analysis of variance (ANOVA), a model may specify that $μ_1<μ_2<μ_3$, while another one may state that $\{ μ_1=μ_3\} <μ_2$, and finally a third model may instead suggest that all means are unrestricted. This is a challenging problem, because it involves a combination of non-nested models, as well as nested models having the same dimension. We adopt an objective Bayesian approach, and derive the posterior probability of each model under consideration. Our method is based on the intrinsic prior methodology, with suitably modifications to accommodate equality and inequality constraints. Focussing on normal ANOVA models, a comparative assessment is carried out through simulation studies, showing that correct model identification is possible even in situations where frequentist power is low. We also present an application to real data collected in a psychological experiment.

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arXiv2014

Objective Bayesian Model Discrimination in Follow-up Experimental Designs

An initial screening experiment may lead to ambiguous conclusions regarding the factors which are active in explaining the variation of an outcome variable: thus adding follow-up runs becomes necessary. We propose a fully Bayes objective approach to follow-up designs, using prior distributions suitably tailored to model selection. We adopt a model criterion based on a weighted average of Kullback-Leibler divergences between predictive distributions for all possible pairs of models. When applied to real data, our method produces results which compare favorably to previous analyses based on subjective weakly informative priors.

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arXiv2013

The Whetstone and the Alum Block: Balanced Objective Bayesian Comparison of Nested Models for Discrete Data

When two nested models are compared, using a Bayes factor, from an objective standpoint, two seemingly conflicting issues emerge at the time of choosing parameter priors under the two models. On the one hand, for moderate sample sizes, the evidence in favor of the smaller model can be inflated by diffuseness of the prior under the larger model. On the other hand, asymptotically, the evidence in favor of the smaller model typically accumulates at a slower rate. With reference to finitely discrete data models, we show that these two issues can be dealt with jointly, by combining intrinsic priors and nonlocal priors in a new unified class of priors. We illustrate our ideas in a running Bernoulli example, then we apply them to test the equality of two proportions, and finally we deal with the more general case of logistic regression models.

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arXiv2011

Compatibility of Prior Specifications Across Linear Models

Bayesian model comparison requires the specification of a prior distribution on the parameter space of each candidate model. In this connection two concerns arise: on the one hand the elicitation task rapidly becomes prohibitive as the number of models increases; on the other hand numerous prior specifications can only exacerbate the well-known sensitivity to prior assignments, thus producing less dependable conclusions. Within the subjective framework, both difficulties can be counteracted by linking priors across models in order to achieve simplification and compatibility; we discuss links with related objective approaches. Given an encompassing, or full, model together with a prior on its parameter space, we review and summarize a few procedures for deriving priors under a submodel, namely marginalization, conditioning, and Kullback--Leibler projection. These techniques are illustrated and discussed with reference to variable selection in linear models adopting a conventional $g$-prior; comparisons with existing standard approaches are provided. Finally, the relative merits of each procedure are evaluated through simulated and real data sets.

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arXiv2009

Reconciling Model Selection and Prediction

It is known that there is a dichotomy in the performance of model selectors. Those that are consistent (having the "oracle property") do not achieve the asymptotic minimax rate for prediction error. We look at this phenomenon closely, and argue that the set of parameters on which this dichotomy occurs is extreme, even pathological, and should not be considered when evaluating model selectors. We characterize this set, and show that, when such parameters are dismissed from consideration, consistency and asymptotic minimaxity can be attained simultaneously.

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arXiv2007

Alternative parametrizations and reference priors for decomposable discrete graphical models

For a given discrete decomposable graphical model, we identify several alternative parametrizations, and construct the corresponding reference priors for suitable groupings of the parameters. Specifically, assuming that the cliques of the graph are arranged in a perfect order, the parameters we consider are conditional probabilities of clique-residuals given separators, as well as generalized log-odds-ratios. We also consider a parametrization associated to a collection of variables representing a cut for the statistical model. The reference priors we obtain do not depend on the order of the groupings, belong to a conjugate family, and are proper.

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arXiv2007

Intrinsic tests for the equality of two correlated proportions

Correlated proportions arise in longitudinal (panel) studies. A typical example is the ``opinion swing'' problem: ``Has the proportion of people favoring a politician changed after his recent speech to the nation on TV?''. Since the same group of individuals is interviewed before and after the speech, the two proportions are correlated. A natural null hypothesis to be tested is whether the corresponding population proportions are equal. A standard Bayesian approach to this problem has already been considered in the literature, based on a Dirichlet prior for the cell-probabilities of the underlying two-by-two table under the alternative hypothesis, together with an induced prior under the null. In lack of specific prior information, a diffuse (e.g. uniform) distribution may be used. We claim that this approach is not satisfactory, since in a testing problem one should make sure that the prior under the alternative be adequately centered around the region specified by the null, in order to obtain a fair comparison between the two hypotheses. Following an intrinsic prior methodology, we develop two strategies for the construction of a collection of objective priors increasingly peaked around the null. We provide a simple interpretation of their structure in terms of weighted imaginary sample scenarios. We illustrate our method by means of three examples, carrying out sensitivity analysis and providing comparison with existing results.

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arXiv2007

Algebraic Bayesian analysis of contingency tables with possibly zero-probability cells

In this paper we consider a Bayesian analysis of contingency tables allowing for the possibility that cells may have probability zero. In this sense we depart from standard log-linear modeling that implicitly assumes a positivity constraint. Our approach leads us to consider mixture models for contingency tables, where the components of the mixture, which we call model-instances, have distinct support. We rely on ideas from polynomial algebra in order to identify the various model instances. We also provide a method to assign prior probabilities to each instance of the model, as well as describing methods for constructing priors on the parameter space of each instance. We illustrate our methodology through a $5 \times 2$ table involving two structural zeros, as well as a zero count. The results we obtain show that our analysis may lead to conclusions that are substantively different from those that would obtain in a standard framework, wherein the possibility of zero-probability cells is not explicitly accounted for.

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