# Data analysis recipes: Probability calculus for inference

@article{Hogg2012DataAR, title={Data analysis recipes: Probability calculus for inference}, author={David W. Hogg}, journal={arXiv: Data Analysis, Statistics and Probability}, year={2012} }

In this pedagogical text aimed at those wanting to start thinking about or brush up on probabilistic inference, I review the rules by which probability distribution functions can (and cannot) be combined. I connect these rules to the operations performed in probabilistic data analysis. Dimensional analysis is emphasized as a valuable tool for helping to construct non-wrong probabilistic statements. The applications of probability calculus in constructing likelihoods, marginalized likelihoods…

## 11 Citations

Data Analysis Recipes: Using Markov Chain Monte Carlo

- Mathematics
- 2017

It is argued that autocorrelation time is the most important test for convergence, as it directly connects to the uncertainty on the sampling estimate of any quantity of interest.

Data Analysis Recipes: Products of multivariate Gaussians in Bayesian inferences

- Computer Science
- 2020

The solutions, discussion, and exercises in this Note are aimed at someone who is already familiar with the basic ideas of Bayesian inference and probability, and connected to inferences that arise frequently in physics and astronomy.

New theory about old evidence

- EconomicsSynthese
- 2014

We present a conservative extension of a Bayesian account of confirmation that can deal with the problem of old evidence and new theories. So-called open-minded Bayesianism challenges the…

A framework for open-minded Bayesianism

- Computer Science
- 2016

A conservative extension of a Bayesian account of confirmation that can deal with the problem of old evidence and new theories and allows for old evidence to confirm a new hypothesis due to a shift in the theoretical context is presented.

A likelihood function for the Gaia Data

- Computer Science
- 2018

The recommendation is to assume (for, say, the parallax) that the Catalog-reported value and uncertainty are the mean and root-variance of a Gaussian function that can stand in for the true likelihood function.

Basics of Astrostatistics

- Physics
- 2020

This chapter introduces the key statistical concepts that are necessary to understand and analyze high-energy astronomical data so that a reader may learn to judge the quality of their inferences and properly evaluate claims made in the literature.

Probabilistic Catalogs for Crowded Stellar Fields

- Physics, Computer Science
- 2012

A probabilistic (Bayesian) method for producing catalogs from images of stellar fields capable of inferring the number of sources N in the image and can also handle the challenges introduced by noise, overlapping sources, and an unknown point-spread function.

How not to obtain the redshift distribution from probabilistic redshift estimates: Under what conditions is it not inappropriate to estimate the redshift distribution
N(z)
by stacking photo-
z
PDFs?

- Physics
- 2021

The scientific impact of current and upcoming photometric galaxy surveys is contingent on our ability to obtain redshift estimates for large numbers of faint galaxies. In the absence of…

RUN DMC: AN EFFICIENT, PARALLEL CODE FOR ANALYZING RADIAL VELOCITY OBSERVATIONS USING N-BODY INTEGRATIONS AND DIFFERENTIAL EVOLUTION MARKOV CHAIN MONTE CARLO

- Physics, Geology
- 2013

This work improves upon the random walk proposal distribution of the traditional MCMC by using an ensemble of Markov chains to adaptively improve the proposal distribution, and offers recommendations for choosing the DEMCMC algorithm's algorithmic parameters that result in excellent performance for a wide variety of planetary systems.

The 31 yr Rotation History of the Millisecond Pulsar J1939+2134 (B1937+21)

- PhysicsThe Astrophysical Journal
- 2020

The timing properties of the millisecond pulsar PSR J1939+2134—very high rotation frequency, very low time derivative of rotation frequency, no timing glitches, and relatively low timing noise—are…

## References

SHOWING 1-5 OF 5 REFERENCES

Data analysis recipes: Fitting a model to data

- Geology
- 2010

We go through the many considerations involved in fitting a model to data, using as an example the fit of a straight line to a set of points in a two-dimensional plane. Standard weighted…

Data analysis : a Bayesian tutorial

- Mathematics
- 1996

This tutorial jumps right in to the power ofparameter estimation without dragging you through the basic concepts of parameter estimation.

Is cosmology just a plausibility argument

- Philosophy
- 2009

I review the basis and limitations of plausible inference in cosmology, in particular the limitation that it can only provide fundamentally true inferences when the hypotheses under consideration…

INFERRING THE ECCENTRICITY DISTRIBUTION

- Physics
- 2010

Standard maximum-likelihood estimators for binary-star and exoplanet eccentricities are biased high, in the sense that the estimated eccentricity tends to be larger than the true eccentricity. As…

2010b, “Inferring the eccentricity

- 2010