Uncertainty in Statistical Computing

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Machine Learning methods have exploded in utility with the availability of software and graphics cards. Dealing with huge amounts of data requires approximations to statistical models, often relying on asymptotic arguments that likelihoods have decayed to near delta function shapes. The break down of traditional statistical methods for assessing models and assumptions are challenged by the size and the complexity of new data sources such as video, and text. Quantifying uncertainty from machine learning requires updating the underlying statistical models to consider the unique challenges from different data types. The overarching theme of this proposal is to advanced methods for dealing with large data sets while improving the measures of uncertainty and assessing assumptions therein. The research themes in this proposal consider i-Statistical Models for Video Data, ii-Spatial Models for Text Data, iii-Regression Models for Distributions of Covariates, and iv-Assessing Appropriateness of Model Assumptions in Machine Learning.******Project i With a combined 50 years worth of video of eagle behaviour from cameras inside dozens of nests around Coastal British Columbia, the Hancock Wildlife Foundation aims to understand eagle nesting, feeding, and rearing behaviour patterns as well as the factors influencing these behaviours. This work will smooth the output from machine learning models applied to video data to improve insights.******Project ii Here we intend inference on the geographic differences related to flavour characteristics of beer based on text reviews. Extensions to current Latent Dirichlet Allocation models will consider model beer style, brewery effects, and spatial variables in the topic allocations. The methods are expected to be extensible to topic model clusters for health records with physician, seasonal, long term time, and geographic effects.******Project iii Functional Regression (FR) has extended the statisticians toolbox by accounting for the smooth underlying process of some time series data sets and allowing them to be modelling in a regression context. This project considers extensions to FR to the case where some or all of the variables are smooth densities. Bernstein polynomials are a natural way to estimate densities and provide uncertainty thereof while respecting properties of densities. The associated uncertainty for different individuals based on different amounts of data would also be carried through the model allowing a natural weighted least squares regression. ******Project iv Probabilistic integration methods are fast ways of approximately numerically integrating functions while accounting for the approximation uncertainty. In this work we propose to use the Laplace approximation as a null hypothesis and then interrogate the likelihood at a set of points so as to check if the Laplace approximation falls within the uncertainty of the integrator.**