22,977 research outputs found
Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches
In the past two decades, functional Magnetic Resonance Imaging has been used
to relate neuronal network activity to cognitive processing and behaviour.
Recently this approach has been augmented by algorithms that allow us to infer
causal links between component populations of neuronal networks. Multiple
inference procedures have been proposed to approach this research question but
so far, each method has limitations when it comes to establishing whole-brain
connectivity patterns. In this work, we discuss eight ways to infer causality
in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality,
Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and
Transfer Entropy. We finish with formulating some recommendations for the
future directions in this area
Understanding predictive uncertainty in hydrologic modeling: The challenge of identifying input and structural errors
Meaningful quantification of data and structural uncertainties in conceptual rainfall-runoff modeling is a major scientific and engineering challenge. This paper focuses on the total predictive uncertainty and its decomposition into input and structural components under different inference scenarios. Several Bayesian inference schemes are investigated, differing in the treatment of rainfall and structural uncertainties, and in the precision of the priors describing rainfall uncertainty. Compared with traditional lumped additive error approaches, the quantification of the total predictive uncertainty in the runoff is improved when rainfall and/or structural errors are characterized explicitly. However, the decomposition of the total uncertainty into individual sources is more challenging. In particular, poor identifiability may arise when the inference scheme represents rainfall and structural errors using separate probabilistic models. The inference becomes illâposed unless sufficiently precise prior knowledge of data uncertainty is supplied; this illâposedness can often be detected from the behavior of the Monte Carlo sampling algorithm. Moreover, the priors on the data quality must also be sufficiently accurate if the inference is to be reliable and support meaningful uncertainty decomposition. Our findings highlight the inherent limitations of inferring inaccurate hydrologic models using rainfallârunoff data with large unknown errors. Bayesian total error analysis can overcome these problems using independent prior information. The need for deriving independent descriptions of the uncertainties in the input and output data is clearly demonstrated.Benjamin Renard, Dmitri Kavetski, George Kuczera, Mark Thyer, and Stewart W. Frank
Bayesian comparison of latent variable models: Conditional vs marginal likelihoods
Typical Bayesian methods for models with latent variables (or random effects)
involve directly sampling the latent variables along with the model parameters.
In high-level software code for model definitions (using, e.g., BUGS, JAGS,
Stan), the likelihood is therefore specified as conditional on the latent
variables. This can lead researchers to perform model comparisons via
conditional likelihoods, where the latent variables are considered model
parameters. In other settings, however, typical model comparisons involve
marginal likelihoods where the latent variables are integrated out. This
distinction is often overlooked despite the fact that it can have a large
impact on the comparisons of interest. In this paper, we clarify and illustrate
these issues, focusing on the comparison of conditional and marginal Deviance
Information Criteria (DICs) and Watanabe-Akaike Information Criteria (WAICs) in
psychometric modeling. The conditional/marginal distinction corresponds to
whether the model should be predictive for the clusters that are in the data or
for new clusters (where "clusters" typically correspond to higher-level units
like people or schools). Correspondingly, we show that marginal WAIC
corresponds to leave-one-cluster out (LOcO) cross-validation, whereas
conditional WAIC corresponds to leave-one-unit out (LOuO). These results lead
to recommendations on the general application of the criteria to models with
latent variables.Comment: Manuscript in press at Psychometrika; 31 pages, 8 figure
Contrasting Multiple Social Network Autocorrelations for Binary Outcomes, With Applications To Technology Adoption
The rise of socially targeted marketing suggests that decisions made by
consumers can be predicted not only from their personal tastes and
characteristics, but also from the decisions of people who are close to them in
their networks. One obstacle to consider is that there may be several different
measures for "closeness" that are appropriate, either through different types
of friendships, or different functions of distance on one kind of friendship,
where only a subset of these networks may actually be relevant. Another is that
these decisions are often binary and more difficult to model with conventional
approaches, both conceptually and computationally. To address these issues, we
present a hierarchical model for individual binary outcomes that uses and
extends the machinery of the auto-probit method for binary data. We demonstrate
the behavior of the parameters estimated by the multiple network-regime
auto-probit model (m-NAP) under various sensitivity conditions, such as the
impact of the prior distribution and the nature of the structure of the
network, and demonstrate on several examples of correlated binary data in
networks of interest to Information Systems, including the adoption of Caller
Ring-Back Tones, whose use is governed by direct connection but explained by
additional network topologies
Bayesian Item Response Modeling in R with brms and Stan
Item Response Theory (IRT) is widely applied in the human sciences to model
persons' responses on a set of items measuring one or more latent constructs.
While several R packages have been developed that implement IRT models, they
tend to be restricted to respective prespecified classes of models. Further,
most implementations are frequentist while the availability of Bayesian methods
remains comparably limited. We demonstrate how to use the R package brms
together with the probabilistic programming language Stan to specify and fit a
wide range of Bayesian IRT models using flexible and intuitive multilevel
formula syntax. Further, item and person parameters can be related in both a
linear or non-linear manner. Various distributions for categorical, ordinal,
and continuous responses are supported. Users may even define their own custom
response distribution for use in the presented framework. Common IRT model
classes that can be specified natively in the presented framework include 1PL
and 2PL logistic models optionally also containing guessing parameters, graded
response and partial credit ordinal models, as well as drift diffusion models
of response times coupled with binary decisions. Posterior distributions of
item and person parameters can be conveniently extracted and post-processed.
Model fit can be evaluated and compared using Bayes factors and efficient
cross-validation procedures.Comment: 54 pages, 16 figures, 3 table
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