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1. A Bayesian non-parametric mixed-effects model of microbial growth curves

   https://doi.org/10.1371/journal.pcbi.1008366  

   Tonner, Peter D. ; Darnell, Cynthia L. ; Bushell, Francesca M. ; Lund, Peter A. ; Schmid, Amy K. ; Schmidler, Scott C. ( October 2020 , PLOS Computational Biology)

   Papin, Jason A. (Ed.)

   Substantive changes in gene expression, metabolism, and the proteome are manifested in overall changes in microbial population growth. Quantifying how microbes grow is therefore fundamental to areas such as genetics, bioengineering, and food safety. Traditional parametric growth curve models capture the population growth behavior through a set of summarizing parameters. However, estimation of these parameters from data is confounded by random effects such as experimental variability, batch effects or differences in experimental material. A systematic statistical method to identify and correct for such confounding effects in population growth data is not currently available. Further, our previous work has demonstrated that parametric models are insufficient to explain and predict microbial response under non-standard growth conditions. Here we develop a hierarchical Bayesian non-parametric model of population growth that identifies the latent growth behavior and response to perturbation, while simultaneously correcting for random effects in the data. This model enables more accurate estimates of the biological effect of interest, while better accounting for the uncertainty due to technical variation. Additionally, modeling hierarchical variation provides estimates of the relative impact of various confounding effects on measured population growth.
2. Assessing Ecosystem State Space Models: Identifiability and Estimation

   https://doi.org/10.1007/s13253-023-00531-8  

   Smith, Jr., J. W. ; Johnson, L. R. ; Thomas, R. Q. ( March 2023 , Journal of Agricultural, Biological and Environmental Statistics)

   Hierarchical probability models are being used more often than non-hierarchical deterministic process models in environmental prediction and forecasting, and Bayesian approaches to fitting such models are becoming increasingly popular. In particular, models describing ecosystem dynamics with multiple states that are autoregressive at each step in time can be treated as statistical state space models (SSMs). In this paper, we examine this subset of ecosystem models, embed a process-based ecosystem model into an SSM, and give closed form Gibbs sampling updates for latent states and process precision parameters when process and observation errors are normally distributed. Here, we use simulated data from an example model (DALECev) and study the effects changing the temporal resolution of observations on the states (observation data gaps), the temporal resolution of the state process (model time step), and the level of aggregation of observations on fluxes (measurements of transfer rates on the state process). We show that parameter estimates become unreliable as temporal gaps between observed state data increase. To improve parameter estimates, we introduce a method of tuning the time resolution of the latent states while still using higher-frequency driver information and show that this helps to improve estimates. Further, we show that datamore »cloning is a suitable method for assessing parameter identifiability in this class of models. Overall, our study helps inform the application of state space models to ecological forecasting applications where (1) data are not available for all states and transfers at the operational time step for the ecosystem model and (2) process uncertainty estimation is desired.

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3. Uncertainty Matters: Bayesian Probabilistic Forecasting for Residential Smart Meter Prediction, Segmentation, and Behavioral Measurement and Verification

   https://doi.org/10.3390/en14051481  

   Roth, Jonathan ; Chadalawada, Jayashree ; Jain, Rishee K. ; Miller, Clayton ( March 2021 , Energies)

   As new grid edge technologies emerge—such as rooftop solar panels, battery storage, and controllable water heaters—quantifying the uncertainties of building load forecasts is becoming more critical. The recent adoption of smart meter infrastructures provided new granular data streams, largely unavailable just ten years ago, that can be utilized to better forecast building-level demand. This paper uses Bayesian Structural Time Series for probabilistic load forecasting at the residential building level to capture uncertainties in forecasting. We use sub-hourly electrical submeter data from 120 residential apartments in Singapore that were part of a behavioral intervention study. The proposed model addresses several fundamental limitations through its flexibility to handle univariate and multivariate scenarios, perform feature selection, and include either static or dynamic effects, as well as its inherent applicability for measurement and verification. We highlight the benefits of this process in three main application areas: (1) Probabilistic Load Forecasting for Apartment-Level Hourly Loads; (2) Submeter Load Forecasting and Segmentation; (3) Measurement and Verification for Behavioral Demand Response. Results show the model achieves a similar performance to ARIMA, another popular time series model, when predicting individual apartment loads, and superior performance when predicting aggregate loads. Furthermore, we show that the model robustly captures uncertaintiesmore »in the forecasts while providing interpretable results, indicating the importance of, for example, temperature data in its predictions. Finally, our estimates for a behavioral demand response program indicate that it achieved energy savings; however, the confidence interval provided by the probabilistic model is wide. Overall, this probabilistic forecasting model accurately measures uncertainties in forecasts and provides interpretable results that can support building managers and policymakers with the goal of reducing energy use.« less
4. Modeling of Composite MRFs with CFT Columns and WF Beams

   https://doi.org/10.12989/scs.2022.43.3.000  

   Herrera, R. ( May 2022 , Steel And Composite Structures)

   A vast amount of experimental and analytical research has been conducted related to the seismic behavior and performance of concrete filled steel tubular (CFT) columns. This research has resulted in a wealth of information on the component behavior. However, analytical and experimental data for structural systems with CFT columns is limited, and the well known behavior of steel or concrete structures is assumed valid for designing these systems. This paper presents the development of an analytical model for nonlinear analysis of composite moment resisting frame (CFT MRF) systems with CFT columns and steel wide flange (WF) beams under seismic loading. The model integrates component models for steel WF beams, CFT columns, connections between CFT columns and WF beams, and CFT panel zones. These component models account for nonlinear behavior due to steel yielding and local buckling in the beams and columns, concrete cracking and crushing in the columns, and yielding of panel zones and connections. Component tests were used to validate the component models. The model for a CFT MRF considers second order geometric effects from the gravity load bearing system using a lean on column. The experimental results from the testing of a four story CFT MRF test structuremore »are used as a benchmark to validate the modeling procedure. An analytical model of the test structure was created using the modeling procedure and imposed displacement analyses were used to reproduce the tests with the analytical model of the test structure. Good agreement was found at the global and local level. The model reproduced reasonably well the story shear story drift response as well as the column, beam and connection moment rotation response, but overpredicted the inelastic deformation of the panel zone.« less
5. Discovery of interpretable structural model errors by combining Bayesian sparse regression and data assimilation: A chaotic Kuramoto–Sivashinsky test case

   https://doi.org/10.1063/5.0091282  

   Mojgani, Rambod ; Chattopadhyay, Ashesh ; Hassanzadeh, Pedram ( June 2022 , Chaos: An Interdisciplinary Journal of Nonlinear Science)

   Models of many engineering and natural systems are imperfect. The discrepancy between the mathematical representations of a true physical system and its imperfect model is called the model error. These model errors can lead to substantial differences between the numerical solutions of the model and the state of the system, particularly in those involving nonlinear, multi-scale phenomena. Thus, there is increasing interest in reducing model errors, particularly by leveraging the rapidly growing observational data to understand their physics and sources. Here, we introduce a framework named MEDIDA: Model Error Discovery with Interpretability and Data Assimilation. MEDIDA only requires a working numerical solver of the model and a small number of noise-free or noisy sporadic observations of the system. In MEDIDA, first, the model error is estimated from differences between the observed states and model-predicted states (the latter are obtained from a number of one-time-step numerical integrations from the previous observed states). If observations are noisy, a data assimilation technique, such as the ensemble Kalman filter, is employed to provide the analysis state of the system, which is then used to estimate the model error. Finally, an equation-discovery technique, here the relevance vector machine, a sparsity-promoting Bayesian method, is used tomore »identify an interpretable, parsimonious, and closed-form representation of the model error. Using the chaotic Kuramoto–Sivashinsky system as the test case, we demonstrate the excellent performance of MEDIDA in discovering different types of structural/parametric model errors, representing different types of missing physics, using noise-free and noisy observations.

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