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Mathematical models are indispensable to the system biology toolkit for studying the structure and behavior of intracellular signaling networks. A common approach to modeling is to develop a system of equations that encode the known biology…
Simulation methods are among the most ubiquitous methodological tools in statistical science. In particular, statisticians often is simulation to explore properties of statistical functionals in models for which developed statistical theory…
We present a common framework for Bayesian emulation methodologies for multivariate-output simulators, or computer models, that employ either parametric linear models or nonparametric Gaussian processes. Novel diagnostics suitable for…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
Approximate Bayesian computation is an established and popular method for likelihood-free inference with applications in many disciplines. The effectiveness of the method depends critically on the availability of well performing summary…
The problem of model selection with a limited number of experimental trials has received considerable attention in cognitive science, where the role of experiments is to discriminate between theories expressed as computational models.…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…
Understanding the mechanisms of interactions within cells, tissues, and organisms is crucial to driving developments across biology and medicine. Mathematical modeling is an essential tool for simulating biological systems and revealing…
The choice of the summary statistics used in Bayesian inference and in particular in ABC algorithms has bearings on the validation of the resulting inference. Those statistics are nonetheless customarily used in ABC algorithms without…
Closed-form, interpretable mathematical models have been instrumental for advancing our understanding of the world; with the data revolution, we may now be in a position to uncover new such models for many systems from physics to the social…
The increase in complexity of autonomous systems is accompanied by a need of data-driven development and validation strategies. Advances in computer graphics and cloud clusters have opened the way to massive parallel high fidelity…
Performing optimal Bayesian design for discriminating between competing models is computationally intensive as it involves estimating posterior model probabilities for thousands of simulated datasets. This issue is compounded further when…
Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…
This paper describes a Bayesian method for learning causal networks using samples that were selected in a non-random manner from a population of interest. Examples of data obtained by non-random sampling include convenience samples and…
Engineers are often faced with the decision to select the most appropriate model for simulating the behavior of engineered systems, among a candidate set of models. Experimental monitoring data can generate significant value by supporting…
Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling…
System identification of complex and nonlinear systems is a central problem for model predictive control and model-based reinforcement learning. Despite their complexity, such systems can often be approximated well by a set of linear…
Model selection aims to determine which theoretical models are most plausible given some data, without necessarily asking about the preferred values of the model parameters. A common model selection question is to ask when new data require…
For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…