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We examine the influence of input data representations on learning complexity. For learning, we posit that each model implicitly uses a candidate model distribution for unexplained variations in the data, its noise model. If the model…

Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data…

Equation learning aims to infer differential equation models from data. While a number of studies have shown that differential equation models can be successfully identified when the data are sufficiently detailed and corrupted with…

Bayesian inference is applied to the level fluctuations of two coupled microwave billiards in order to extract the coupling strength. The coupled resonators provide a model of a chaotic quantum system containing two coupled symmetry classes…

Scientific claims gain credibility by replicability, especially if replication under different circumstances and varying designs yields equivalent results. Aggregating results over multiple studies is, however, not straightforward, and when…

A method is presented for performing joint analyses of cosmological datasets, in which the weight assigned to each dataset is determined directly by it own statistical properties. The weights are considered in a Bayesian context as a set of…

Cosmological experiments often employ Bayesian workflows to derive constraints on cosmological and astrophysical parameters from their data. It has been shown that these constraints can be combined across different probes such as Planck and…

Aleatoric uncertainty captures the inherent randomness of the data, such as measurement noise. In Bayesian regression, we often use a Gaussian observation model, where we control the level of aleatoric uncertainty with a noise variance…

This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum…

Environmental variations can significantly influence how populations compete for resources, and hence shape their evolution. Here, we study population dynamics subject to a fluctuating environment modeled by a varying carrying capacity…

This work considers an estimation task in compressive sensing, where the goal is to estimate an unknown signal from compressive measurements that are corrupted by additive pre-measurement noise (interference, or clutter) as well as…

Noise is an unavoidable part of most measurements which can hinder a correct interpretation of the data. Uncertainties propagate in the data analysis and can lead to biased results even in basic descriptive statistics such as the central…

Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many model variations can frequently be…

Network-linked data, where multivariate observations are interconnected by a network, are becoming increasingly prevalent in fields such as sociology and biology. These data often exhibit inherent noise and complex relational structures,…

Confirmation bias, the tendency to interpret information in a way that aligns with one's preconceptions, can profoundly impact scientific research, leading to conclusions that reflect the researcher's hypotheses even when the observational…

Evidence synthesis models combine multiple data sources to estimate latent quantities of interest, enabling reliable inference on parameters that are difficult to measure directly. However, shared parameters across data sources can induce…

A general theory is presented for the photodetection statistics of coherent radiation that has been amplified by a disordered medium. The beating of the coherent radiation with the spontaneous emission increases the noise above the…

Perceptual judgments of sequential stimuli are systematically biased by prior expectations and by the temporal structure of sensory input. In haptic discrimination tasks, these effects often manifest as time-order asymmetries, whereby the…

Bayesian model comparison is often based on the posterior distribution over the set of compared models. This distribution is often observed to concentrate on a single model even when other measures of model fit or forecasting ability…

We study the long-time effect of noise on pattern formation for the aggregation model. We consider aggregation kernels that generate patterns consisting of two delta-concentrations. Without noise, there is a one-parameter family of…