Perform linear regression taking errors in x,y into account (fit_standard)

[Gabriel-p]

--> How to fit a model to data, Hogg (2010) <--

(Is this the code used to perform the Bayesian, outlier model, 2D uncertainties fit?)

• Facebook post with lots of advice about linear regression
• My own FB post on the subject. Recommendations:
  • Fitting a simple model to data using MCMC (outliers not modelled independently)
  • Fitting a straight line with outliers (outliers known a priori?)
  • A Bayesian approach to linear regression with errors in both X and Y (linmix), article (apparently does not evaluate outliers)
• Robust Regression with Outlier Detection (PyMC3) (implements the Hogg, Bovy & Lang method using PyMC3)
• Two- and Multi-dimensional Curve Fitting using Bayesian Inference, Steiner (2017), an article that discusses this issue

OLD (below)

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Explore linear fitting methods for replicating fitparams

• Fitting data when both variables have uncertainties
• AutoCal: A software application for calibrating photometric data, Wium & Soelen 2017 (Zotero)
• Least squares regression with errors in both variables: case studies, Oliveira & Aguiar 2013 (Zotero) (OLS vs ODR, nice illustrative image)
• Orthogonal Distance Regression, Boggs & Roger 1990 (Zotero)
  • Estimate the standard deviation of fitted parameters in scipy.odr? How to properly calculate the standard deviations for the fitted parameters? (see comments in answer)
• BCES: Linear Regression for Astronomical Data with Measurement Errors and Intrinsic Scatter (Zotero)

Examples

1. Calculate uncertainty of linear regression slope based on data uncertainty
2. Fitting a Model to Data (emcee)
3. Line of Best Fit (Jake VanderPlas), emcee

StackOverflow

1. Standard deviation for fitted parameters with scipy.ODR, when data contains error
2. Linear fitting in python with uncertainty in both x and y coordinates
3. Linear fit including all errors with NumPy/SciPy
4. How to do linear regression, taking errorbars into account?
5. Python linear fitting with multiple error bars