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Browsing Statistics by Subject "Bayesian inference"

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    A Bayesian model for the identification of differentially expressed genes in Daphnia magna exposed to munition pollutants
    (Wiley, 2015) Cassese, Alberto; Guindani, Michele; Antczak, Philipp; Falciani, Francesco; Vannucci, Marina
    In this article we propose a Bayesian hierarchical model for the identification of differentially expressed genes in Daphnia magna organisms exposed to chemical compounds, specifically munition pollutants in water. The model we propose constitutes one of the very first attempts at a rigorous modeling of the biological effects of water purification. We have data acquired from a purification system that comprises four consecutive purification stages, which we refer to as "ponds," of progressively more contaminated water. We model the expected expression of a gene in a pond as the sum of the mean of the same gene in the previous pond plus a gene-pond specific difference. We incorporate a variable selection mechanism for the identification of the differential expressions, with a prior distribution on the probability of a change that accounts for the available information on the concentration of chemical compounds present in the water. We carry out posterior inference via MCMC stochastic search techniques. In the application, we reduce the complexity of the data by grouping genes according to their functional characteristics, based on the KEGG pathway database. This also increases the biological interpretability of the results. Our model successfully identifies a number of pathways that show differential expression between consecutive purification stages. We also find that changes in the transcriptional response are more strongly associated to the presence of certain compounds, with the remaining contributing to a lesser extent. We discuss the sensitivity of these results to the model parameters that measure the influence of the prior information on the posterior inference.
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    Bayesian Inference of Multiple Gaussian Graphical Models
    (Taylor & Francis, 2015) Peterson, Christine B.; Stingo, Francesco C.; Vannucci, Marina
    In this article, we propose a Bayesian approach to inference on multiple Gaussian graphical models. Specifically, we address the problem of inferring multiple undirected networks in situations where some of the networks may be unrelated, while others share common features. We link the estimation of the graph structures via a Markov random field (MRF) prior, which encourages common edges. We learn which sample groups have a shared graph structure by placing a spike-and-slab prior on the parameters that measure network relatedness. This approach allows us to share information between sample groups, when appropriate, as well as to obtain a measure of relative network similarity across groups. Our modeling framework incorporates relevant prior knowledge through an edge-specific informative prior and can encourage similarity to an established network. Through simulations, we demonstrate the utility of our method in summarizing relative network similarity and compare its performance against related methods. We find improved accuracy of network estimation, particularly when the sample sizes within each subgroup are moderate. We also illustrate the application of our model to infer protein networks for various cancer subtypes and under different experimental conditions.
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    Epilepsy as a dynamic disease: A Bayesian model for differentiating seizure risk from natural variability
    (Wiley, 2018) Chiang, Sharon; Vannucci, Marina; Goldenholz, Daniel M.; Moss, Robert; Stern, John M.
    Objective: A fundamental challenge in treating epilepsy is that changes in observed seizure frequencies do not necessarily reflect changes in underlying seizure risk. Rather, changes in seizure frequency may occur due to probabilistic variation around an underlying seizure risk state caused by normal fluctuations from natural history, leading to seizure unpredictability and potentially suboptimal medication adjustments in epilepsy management. However, no rigorous statistical approach exists to systematically distinguish expected changes in seizure frequency due to natural variability from changes in underlying seizure risk. Methods: Using data from SeizureTracker.com, a patient‐reported seizure diary tool containing over 1.2 million recorded seizures across 8 years, a novel epilepsy seizure risk assessment tool (EpiSAT) employing a Bayesian mixed‐effects hidden Markov model for zero‐inflated count data was developed to estimate changes in underlying seizure risk using patient‐reported seizure diary and clinical measurement data. Accuracy for correctly assessing underlying seizure risk was evaluated through a simulation comparison. Implications for the natural history of tuberous sclerosis complex (TSC) were assessed using data from SeizureTracker.com. Results: EpiSAT led to significant improvement in seizure risk assessment compared to traditional approaches relying solely on observed seizure frequencies. Applied to TSC, four underlying seizure risk states were identified. The expected duration of each state was <12 months, providing a data‐driven estimate of the amount of time a person with TSC would be expected to remain at the same seizure risk level according to the natural course of epilepsy. Significance: We propose a novel Bayesian statistical approach for evaluating seizure risk on an individual patient level using patient‐reported seizure diaries, which allows for the incorporation of external clinical variables to assess impact on seizure risk. This tool may improve the ability to distinguish true changes in seizure risk from natural variations in seizure frequency in clinical practice. Incorporation of systematic statistical approaches into antiepileptic drug (AED) management may help improve understanding of seizure unpredictability as well as timing of treatment interventions for people with epilepsy.