Journal ArticleDOI
A Bayesian Look at Inverse Linear Regression
Reads0
Chats0
TLDR
In this article, the problem of making statistical inferences about an unknown value of x corresponding to one or more additional observed values of y is considered, and it is shown that the inverse estimator is Bayes with respect to a particular informative prior.Abstract:
The model considered in this paper is simple linear regression , and the problem is to make statistical inferences about an unknown value of x corresponding to one or more additional observed values of y. The maximum likelihood estimator x of x and the classical (1 - α) 100% confidence set S for x have some undesirable properties. For example, has infinite mean square error and > 0. The purpose of this paper is to demonstrate that insight and understanding, as well as a useful class of solutions, can be obtained by looking at the problem from a Bayesian point of view. A result which follows from a general Bayes solution is that the inverse estimator [4] is Bayes with respect to a particular informative prior.read more
Citations
More filters
Journal ArticleDOI
An Introduction to Bayesian Inference for Ecological Research and Environmental Decision‐Making
TL;DR: It is argued that a "Bayesian ecology" would make better use of pre-existing data; allow stronger conclusions to be drawn from large-scale experiments with few replicates; and be more relevant to environmental decision-making.
Journal ArticleDOI
Statistical Calibration: A Review
TL;DR: In this paper, a wide variety of approaches to both univariate and multivariate calibration are reviewed, including the classical, inverse, Bayesian and non-parametric approaches together with the approaches via tolerance regions.
Proceedings ArticleDOI
Blind calibration of sensor networks
Laura Balzano,Robert Nowak +1 more
TL;DR: It is shown that as long as the sensors slightly oversample the signals of interest, then unknown sensor gains can be perfectly recovered and neither a controlled stimulus nor a dense deployment is required.
Journal ArticleDOI
Predicting mosquito infection from Plasmodium falciparum gametocyte density and estimating the reservoir of infection
Thomas S. Churcher,Teun Bousema,Teun Bousema,Martin Walker,Chris Drakeley,Petra Schneider,André Lin Ouédraogo,María-Gloria Basáñez +7 more
TL;DR: In a site in Burkina Faso, children harbour more gametocytes than adults though the non-linear relationship between gametocyte density and mosquito infection means that (per person) they only contribute slightly more to transmission.
Journal ArticleDOI
Stature estimation and calibration: Bayesian and maximum likelihood perspectives in physical anthropology
TL;DR: It is shown that inverse calibration (regression of stature on bone length) is generally preferred when the stature distribution for a reference sample forms a reasonable prior, while classical calibration is preferred when there is reason to suspect that the estimated stature will be an extrapolation beyond the useful limits of the reference sample statures.
References
More filters
Book
Introduction to the Theory of Statistics
TL;DR: In this article, a tabular summary of parametric families of distributions is presented, along with a parametric point estimation method and a nonparametric interval estimation method for point estimation.
Journal ArticleDOI
Introduction to the Theory of Statistics.
Jacob Wolfowitz,A. M. Mood +1 more
TL;DR: In this article, a tabular summary of parametric families of distributions is presented, along with a parametric point estimation method and a nonparametric interval estimation method for point estimation.
Journal ArticleDOI
Applied Statistical Decision Theory
Journal ArticleDOI
Some problems in interval estimation
TL;DR: In this article, the fiducial distributions of a simple equation (i.e., a ratio), and the roots of a quadratic equation with variable coefficients with respect to the region of the (aC, t2) plane lying above the curve are investigated.
Journal ArticleDOI
Classical and Inverse Regression Methods of Calibration
TL;DR: In this article, the classical and Inverse least squares methods of linear calibration are compared by Monte Carlo methods and the Inverse approach is found to be superior to the classical approach from a mean squared error point of view.