arXiv subjects

Stefan Böhringer

Publications and source records attributed to Stefan Böhringer.

4 recordsLinked to original sources

arXiv2026

Plausibility: Exact inference in R

Plausbility is a theoretical framework that allows to conduct exact inference in general parametric families. We introduce R-packages {\em plausibility} that implements this framework for a wide class of regression models. Plausibility can also be used to test penalized regression models such as estimated by package {\em glmnet}. We illustrate the package using a number of R data sets Through a class-based mechanism, the package can be easily extended. We illustrate and discuss computation aspects of the implementation and their impact on real-data analysis.

stat.ME↗

arXiv2026

Evaluating HWE and Association in Genome Wide Association Studies: A Unified Procedure

In genome wide association studies (GWASs) based on a case-control design, single nucleotide polymorphisms (SNPs) are typically evaluated for an association test and a Hardy-Weinberg equilibrium (HWE) goodness-of-fit test. SNPs are then excluded from analysis based on a HWE cutoff to avoid false positives. In order to avoid cutoffs based on arbitrary threshold values, we propose a conditional genotype--based test that conditions the Pearson $χ^2$-statistic in the 3x2 contingency table on the $χ^2$-statistic for HWE in the control group, and develop the relevant asymptotic distribution theory. We show by simulations that our test in most scenarios is more powerful than two competing retrospective procedures. Another important advantage of the proposed method is a better ranking of SNPs in GWASs as HWE is accounted for in computing p-values of SNP association. We demonstrate this effect on a data set in an alopecia study. In conclusion, our test makes separate HWE testing superfluous by providing a unified framework and strictly improves on the standard procedure in terms of power and interpretability, thereby making replication more cost effective and improving subsequent fine mapping.\par

stat.ME↗

arXiv2026

ForwardFlow: Simulation only statistical inference using deep learning

Deep learning models are being used for the analysis of parametric statistical models based on simulation-only frameworks. Bayesian models using normalizing flows simulate data from a prior distribution and are composed of two deep neural networks: a summary network that learns a sufficient statistic for the parameter and a normalizing flow that conditional on the summary network can approximate the posterior distribution. Here, we explore frequentist models that are based on a single summary network. During training, input of the network is a simulated data set based on a parameter and the loss function minimizes the mean-square error between learned summary and parameter. The network thereby solves the inverse problem of parameter estimation. We propose a branched network structure that contains collapsing layers that reduce a data set to summary statistics that are further mapped through fully connected layers to approximate the parameter estimate. We motivate our choice of network structure by theoretical considerations. In simulations we demonstrate three desirable properties of parameter estimates: finite sample exactness, robustness to data contamination, and algorithm approximation. These properties are achieved offering the the network varying sample size, contaminated data, and data needing algorithmic reconstruction during the training phase. In our simulations an EM-algorithm for genetic data is automatically approximated by the network. Simulation only approaches seem to offer practical advantages in complex modeling tasks where the simpler data simulation part is left to the researcher and the more complex problem of solving the inverse problem is left to the neural network. Challenging future work includes offering pre-trained models that can be used in a wide variety of applications.

math.ST↗

arXiv2021

Exact model comparisons in the plausibility framework

Plausibility is a formalization of exact tests for parametric models and generalizes procedures such as Fisher's exact test. The resulting tests are based on cumulative probabilities of the probability density function and evaluate consistency with a parametric family while providing exact control of the $α$ level for finite sample size. Model comparisons are inefficient in this approach. We generalize plausibility by incorporating weighing which allows to perform model comparisons. We show that one weighing scheme is asymptotically equivalent to the likelihood ratio test (LRT) and has finite sample guarantees for the test size under the null hypothesis unlike the LRT. We confirm theoretical properties in simulations that mimic the data set of our data application. We apply the method to a retinoblastoma data set and demonstrate a parent-of-origin effect. Weighted plausibility also has applications in high-dimensional data analysis and P-values for penalized regression models can be derived. We demonstrate superior performance as compared to a data-splitting procedure in a simulation study. We apply weighted plausibility to a high-dimensional gene expression, case-control prostate cancer data set. We discuss the flexibility of the approach by relating weighted plausibility to targeted learning, the bootstrap, and sparsity selection.

math.ST↗