This tutorial shows how to build, fit, and criticize disease transmission models in Stan, and should be useful to researchers interested in modeling the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pan...
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This tutorial shows how to build, fit, and criticize disease transmission models in Stan, and should be useful to researchers interested in modeling the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic and other infectious diseases in a bayesian framework. bayesian modeling provides a principled way to quantify uncertainty and incorporate both data and prior knowledge into the model estimates. Stan is an expressive probabilistic programming language that abstracts the inference and allows users to focus on the modeling. As a result, Stan code is readable and easily extensible, which makes the modeler's work more transparent. Furthermore, Stan's main inference engine, Hamiltonian Monte Carlo sampling, is amiable to diagnostics, which means the user can verify whether the obtained inference is reliable. In this tutorial, we demonstrate how to formulate, fit, and diagnose a compartmental transmission model in Stan, first with a simple susceptible-infected-recovered model, then with a more elaborate transmission model used during the SARS-CoV-2 pandemic. We also cover advanced topics which can further help practitioners fit sophisticated models;notably, how to use simulations to probe the model and priors, and computational techniques to scale-up models based on ordinary differential equations.
IoT networks are so voluminous that they cannot be treated as individual devices, but as populations. Main aim of the paper is to create a comprehensive method for predicting failures taking device variance into consi...
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IoT networks are so voluminous that they cannot be treated as individual devices, but as populations. Main aim of the paper is to create a comprehensive method for predicting failures taking device variance into consideration. We propose using data fusion of happen-stance observations (resets and failures) to better estimate device parameters. We propose using methods of population analysis in bayesian statistics to estimate failure times investigating only a part of the population. For this purpose, we use multilevel hierarchical bayesian model and provide it with post stratification. We propose model assumptions, construct the model and evaluate it, and perform computations using Hamiltonian Monte Carlo. This method is known as the bayesian workflow. We have analyzed three different models showing that, in case of small device variance, it can be ignored, or at least compensated, while significant differences require hierarchical modeling. We also show that hierarchical model shows significant robustness to a small amount of data. We have shown attractiveness of bayesian approach to modeling failures of IoT devices. Ability to diagnose and tune models, and assure their computational fidelity is a great advantage of bayesian workflow.
bayesian modeling provides a principled approach to quantifying uncertainty and has seen a surge of applications in recent years. Within the context of a bayesian workflow, we are concerned with model selection for th...
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bayesian modeling provides a principled approach to quantifying uncertainty and has seen a surge of applications in recent years. Within the context of a bayesian workflow, we are concerned with model selection for the purpose of finding models that best explain the data or underlying data generating process. Since insight into the true process is rare, what remains is incomplete causal knowledge and model predictions of the data. This leads to the important question of when the use of prediction as a proxy for explanation for the purpose of model selection is valid. We approach this question by means of large-scale simulations of bayesian generalized linear models where we investigate various causal and statistical misspecifications. Our results indicate that the use of prediction as proxy for explanation is valid and safe if the models under consideration are sufficiently consistent with the underlying causal structure of the true data generating process.
Simultaneous electroencephalography-functional MRI (EEG-fMRI) is a unique and noninvasive method for epilepsy presurgical evaluation. When selecting voxels by null-hypothesis tests, the conventional analysis may overe...
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Simultaneous electroencephalography-functional MRI (EEG-fMRI) is a unique and noninvasive method for epilepsy presurgical evaluation. When selecting voxels by null-hypothesis tests, the conventional analysis may overestimate fMRI response amplitudes related to interictal epileptic discharges (IEDs), especially when IEDs are rare. We aimed to estimate fMRI response amplitudes represented by blood oxygen level dependent (BOLD) percentage changes related to IEDs using a hierarchical model. It involves the local and distributed hemodynamic response homogeneity to regularize estimations. bayesian inference was applied to fit the model. Eighty-two epilepsy patients who underwent EEG-fMRI and subsequent surgery were included in this study. A conventional voxel-wise general linear model was compared to the hierarchical model on estimated fMRI response amplitudes and on the concordance between the highest response cluster and the surgical cavity. The voxel-wise model overestimated fMRI responses compared to the hierarchical model, evidenced by a practically and statistically significant difference between the estimated BOLD percentage changes. Only the hierarchical model differentiated brief and long-lasting IEDs with significantly different BOLD percentage changes. Overall, the hierarchical model outperformed the voxel-wise model on presurgical evaluation, measured by higher prediction performance. When compared with a previous study, the hierarchical model showed higher performance metric values, but the same or lower sensitivity. Our results demonstrated the capability of the hierarchical model of providing more physiologically reasonable and more accurate estimations of fMRI response amplitudes induced by IEDs. To enhance the sensitivity of EEG-fMRI for presurgical evaluation, it may be necessary to incorporate more appropriate spatial priors and bespoke decision strategies.
bayesian model criticism is an important part of the practice of bayesian statistics. Traditionally, model criticism methods have been based on the predictive check, an adaptation of goodness-of-fit testing to Bayesia...
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bayesian model criticism is an important part of the practice of bayesian statistics. Traditionally, model criticism methods have been based on the predictive check, an adaptation of goodness-of-fit testing to bayesian modeling and an effective method to understand how well a model captures the distribution of the data. In modern practice, however, researchers iteratively build and develop many models, exploring a space of models to help solve the problem at hand. While classical predictive checks can help assess each one, they cannot help the researcher understand how the models relate to each other. This paper introduces the posterior predictive null check (PPN), a method for bayesian model criticism that helps characterize the relationships between models. The idea behind the PPN is to check whether data from one model's predictive distribution can pass a predictive check designed for another model. This form of criticism complements the classical predictive check by providing a comparative tool. A collection of PPNs, which we call a PPN study, can help us understand which models are equivalent and which models provide different perspectives on the data. With mixture models, we demonstrate how a PPN study, along with traditional predictive checks, can help select the number of components by the principle of parsimony. With probabilistic factor models, we demonstrate how a PPN study can help understand relationships between different classes of models, such as linear models and models based on neural networks. Finally, we analyze data from the literature on predictive checks to show how a PPN study can improve the practice of bayesian model criticism.
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