Related papers: Rising Above Chaotic Likelihoods
The maximum likelihood principle is widely used in statistics, and the associated estimators often display good properties. indeed maximum likelihood estimators are guaranteed to be asymptotically efficient under mild conditions. However in…
We propose currently feasible experiments using small, isolated systems of ultracold atoms to investigate the effects of dynamical chaos in the microscopic onset of irreversibility. A control parameter is tuned past a critical value, then…
There is an increasing amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. One approach is a set of algorithms known as Approximate Bayesian Computational (ABC) methods. One of the…
Polynomial chaos based methods enable the efficient computation of output variability in the presence of input uncertainty in complex models. Consequently, they have been used extensively for propagating uncertainty through a wide variety…
When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear state-space models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The…
Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated…
The research concerns the dynamics of complex autonomous Kauffman networks. The article defines and shows using simulation experiments half-chaotic networks, which exhibit features much more similar to typically modeled systems like a…
Multi-level modeling is an important approach for analyzing complex survey data using multi-stage sampling. However, estimation of multi-level models can be challenging when we combine several datasets with distinct hierarchies with…
We present a Bayesian hierarchical framework for a principled data analysis pipeline of peculiar velocity surveys, which makes explicit the inference problem of constraining cosmological parameters from redshift-independent distance…
We address the problem of monitoring a set of binary stochastic processes and generating an alert when the number of anomalies among them exceeds a threshold. For this, the decision-maker selects and probes a subset of the processes to…
Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…
Conventional approaches to cosmology inference from galaxy redshift surveys are based on n-point functions, which are under rigorous perturbative control on sufficiently large scales. Here, we present an alternative approach, which employs…
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…
A fundamental problem in analysis of complex systems is getting a reliable estimate of entropy of their probability distributions over the state space. This is difficult because unsampled states can contribute substantially to the entropy,…
Data assimilation leads naturally to a Bayesian formulation in which the posterior probability distribution of the system state, given the observations, plays a central conceptual role. The aim of this paper is to use this Bayesian…
High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…
On-line estimation plays an important role in process control and monitoring. Obtaining a theoretical solution to the simultaneous state-parameter estimation problem for non-linear stochastic systems involves solving complex…
When combining data sets to perform parameter inference, the results will be unreliable if there are unknown systematics in data or models. Here we introduce a flexible methodology, BACCUS: BAyesian Conservative Constraints and Unknown…
Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…
Physical parameterizations are used as representations of unresolved subgrid processes within weather and global climate models or coarse-scale turbulent models, whose resolutions are too coarse to resolve small-scale processes. These…