Lecture

Assumption-lean Inference: Generalised Linear Model Parameters

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture by the instructor focuses on the challenges of model misspecification in statistical inference, proposing a shift from model-based to estimand-based approaches. The discussion covers the definition of estimands, main effect estimands, interaction estimands, and survival analysis estimands. The lecture emphasizes the importance of choosing estimands that are well-defined and generic, allowing for robust inference. Various criteria for selecting estimands are explored, along with the limitations of plug-in estimators and the benefits of data-adaptive inference. The presentation concludes by highlighting the advantages of assumption-lean inference and the implications for practical applications.

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related concepts (32)

Statistical inference

Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population.

Frequentist inference

Frequentist inference is a type of statistical inference based in frequentist probability, which treats “probability” in equivalent terms to “frequency” and draws conclusions from sample-data by means of emphasizing the frequency or proportion of findings in the data. Frequentist-inference underlies frequentist statistics, in which the well-established methodologies of statistical hypothesis testing and confidence intervals are founded. The primary formulation of frequentism stems from the presumption that statistics could be perceived to have been a probabilistic frequency.

Bayesian inference

Bayesian inference (ˈbeɪziən or ˈbeɪʒən ) is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law.

Estimator

In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the sample mean is a commonly used estimator of the population mean. There are point and interval estimators. The point estimators yield single-valued results. This is in contrast to an interval estimator, where the result would be a range of plausible values.

Statistical assumption

Statistics, like all mathematical disciplines, does not infer valid conclusions from nothing. Inferring interesting conclusions about real statistical populations almost always requires some background assumptions. Those assumptions must be made carefully, because incorrect assumptions can generate wildly inaccurate conclusions. Here are some examples of statistical assumptions: Independence of observations from each other (this assumption is an especially common error). Independence of observational error from potential confounding effects.

Related lectures (64)

Confidence Intervals: Definition and Estimation

Explains confidence intervals, parameter estimation methods, and the central limit theorem in statistical inference.

Probabilistic Models for Linear Regression

Covers the probabilistic model for linear regression and its applications in nuclear magnetic resonance and X-ray imaging.

Linear Regression: Statistical Inference and Regularization

Covers the probabilistic model for linear regression and the importance of regularization techniques.

Parameter Estimation

Introduces statistical inference concepts, focusing on parameter estimation, unbiased estimators, and mean estimation using independent random variables.

Statistical Theory: Inference and Optimality