Research Seminar

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Spring Semester 2022

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Speaker

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7 April 2022
16:15-17:15

Dominik Rothenhäusler
Stanford University

Event Details

Research Seminar in Statistics

Title	Calibrated inference: statistical inference that accounts for both sampling uncertainty and distributional uncertainty
Speaker, Affiliation	Dominik Rothenhäusler, Stanford University
Date, Time	7 April 2022, 16:15-17:15
Location	HG D 7.1
Abstract	During data analysis, analysts often have to make seemingly arbitrary decisions. For example during data pre-processing, there are a variety of options for dealing with outliers or inferring missing data. Similarly, many specifications and methods can be reasonable to address a certain domain question. This may be seen as a hindrance to reliable inference since conclusions can change depending on the analyst's choices. In this talk, I argue that this situation is an opportunity to construct confidence intervals that account not only for sampling uncertainty but also some type of distributional uncertainty. Distributional uncertainty is closely related to other issues in data analysis, ranging from dependence between observations to selection bias and confounding. We demonstrate the utility of the approach on simulated and real-world data. This is joint work with Yujin Jeong.

Calibrated inference: statistical inference that accounts for both sampling uncertainty and distributional uncertaintyread_more

HG D 7.1

22 June 2022
15:15-16:15

Rainer von Sachs
UC Louvain

Event Details

Research Seminar in Statistics

Title	Statistical inference for intrinsic wavelet estimators of covariance matrices in a log-Euclidean manifold
Speaker, Affiliation	Rainer von Sachs, UC Louvain
Date, Time	22 June 2022, 15:15-16:15
Location	HG G 19.1
Abstract	In this talk we treat statistical inference for an intrinsic wavelet estimator of curves of symmetric positive definite (SPD) matrices in a log-Euclidean manifold. Examples for these arise in Diffusion Tensor Imaging or related medical imaging problems as well as in computer vision and for neuroscience problems. Our proposed wavelet (kernel) estimator preserves positive-definiteness and enjoys permutation-equivariance, which is particularly relevant for covariance matrices. Our second-generation wavelet estimator is based on average-interpolation and allows the same powerful properties, including fast algorithms, known from nonparametric curve estimation with wavelets in standard Euclidean set-ups. The core of our work is the proposition of confidence sets for our high-level wavelet estimator in a non-Euclidean geometry. We derive asymptotic normality of this estimator, including explicit expressions of its asymptotic variance. This opens the door for constructing asymptotic confidence regions which we compare with our proposed bootstrap scheme for inference. Detailed numerical simulations confirm the appropriateness of our suggested inference schemes. This is joint work with Johannes Krebs, Eichstätt, and Daniel Rademacher, Heidelberg.

Statistical inference for intrinsic wavelet estimators of covariance matrices in a log-Euclidean manifoldread_more

HG G 19.1

19 July 2022
11:15-12:15

Andreas Buja
Flatiron Institute

Event Details

Research Seminar in Statistics

Title	Genetic Modeling of Autism
Speaker, Affiliation	Andreas Buja, Flatiron Institute
Date, Time	19 July 2022, 11:15-12:15
Location	HG G 19.1
Abstract	Autism, now called "Autism Spectrum Disorder" (ASD), is a neuro-developmental condition that is diagnosed in early childhood.It is heavily gender-biased as it affects by today's criteria about 1% of boys and 1/4% of girls. It also has a strong genetic basis as evidenced by studies of identical twins. Unfortunately, what we have learned today is discouraging: The number of genes causally related to ASD is in the hundreds, of which about 150 have been identified, each accounting for only a tiny fraction of ASD variability. While the search for causally linked genes is ongoing, we also have to ask more global questions: How can we think about the relative protection from ASD enjoyed by females? How can the gender bias be reconciled with known inheritance mechanisms? To answer such questions, Wigler et al. (2007) proposed a "Unified Theory" according to which females are the stores of damaging genetic variants for which they have relative protection, but cause ASD in their sons who lack this protection. To capture Wigler et al.'s theory and combine it with today's knowledge of the "polygenic" nature of ASD, we developed a scatter shot model of "damaging alleles" which have "lower penetrance" in females than males. In this model we are able to match the known "prevalences" of 1% in boys and 1/4% in girls, as well as other known global features such as the existence of high risk families. Most importantly, we are able to prove mathematically a prediction of Wigler et al.s' theory: genetic sharing among autistic male siblings is greater with the mother than the father. Surprisingly, the latest empirical evidence from Wigler's lab seems to indicate that genetic sharing among autistic male siblings is greater with the father than the mother. If this evidence can be firmed up, it refutes the Unified Theory and requires new ideas. One such idea involves the existence of "protecting alleles", which we are currently incorporating in our model.

Genetic Modeling of Autismread_more

HG G 19.1

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