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Open AccessProceedings ArticleDOI

Frequentism and Bayesianism: A Python-driven Primer

TLDR
This paper presents a brief, semi-technical comparison of the essential features of the frequentist and Bayesian approaches to statistical inference, with several illustrative examples implemented in Python.
Abstract
This paper presents a brief, semi-technical comparison of the es- sential features of the frequentist and Bayesian approaches to statistical infer- ence, with several illustrative examples implemented in Python. The differences between frequentism and Bayesianism fundamentally stem from differing defini- tions of probability, a philosophical divide which leads to distinct approaches to the solution of statistical problems as well as contrasting ways of asking and answering questions about unknown parameters. After an example-driven discussion of these differences, we briefly compare several leading Python sta- tistical packages which implement frequentist inference using classical methods and Bayesian inference using Markov Chain Monte Carlo. 1

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Journal ArticleDOI

Probabilistic Programming in Python using PyMC3

TL;DR: This paper is a tutorial-style introduction to PyMC3, a new open source Probabilistic Programming framework written in Python that uses Theano to compute gradients via automatic dierentiation as well as compile probabilistic programs on-the-fly to C for increased speed.
Journal ArticleDOI

A Primer for Model Selection: The Decisive Role of Model Complexity

TL;DR: A classification scheme for model selection criteria that helps to find the right criterion for a specific goal, i.e., which employs the correct complexity interpretation, is proposed and guidance on choosing the right type of criteria for specific model selection tasks is provided.
Book

Income Distribution Dynamics of Economic Systems: An Econophysical Approach

TL;DR: In this paper, the authors used the econophysics perspective to focus on the income distributive dynamics of economic systems and provided empirical characterization and dynamics of income distribution from the epistemological and practical perspectives of contemporary physics.
Proceedings ArticleDOI

Bayesian concepts in software testing: an initial review

TL;DR: This work summarizes the main topics that have been researched in the area of software testing under the umbrella of ``Bayesian approaches'' since 2010 and selected around 40 references applying Bayesian approaches in the field of softwareTesting since 2010 to foster better focused research.
References
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Book

Bayesian Data Analysis

TL;DR: Detailed notes on Bayesian Computation Basics of Markov Chain Simulation, Regression Models, and Asymptotic Theorems are provided.
Journal ArticleDOI

emcee: The MCMC Hammer

TL;DR: The emcee algorithm as mentioned in this paper is a Python implementation of the affine-invariant ensemble sampler for Markov chain Monte Carlo (MCMC) proposed by Goodman & Weare (2010).
Proceedings ArticleDOI

Statsmodels: Econometric and Statistical Modeling with Python

TL;DR: The current relationship between statistics and Python and open source more generally is discussed, outlining how the statsmodels package fills a gap in this relationship.
Journal ArticleDOI

Ensemble samplers with affine invariance

TL;DR: A family of Markov chain Monte Carlo methods whose performance is unaffected by affine tranformations of space is proposed, and computational tests show that the affine invariant methods can be significantly faster than standard MCMC methods on highly skewed distributions.
Journal ArticleDOI

An invariant form for the prior probability in estimation problems.

TL;DR: It is shown that a certain differential form depending on the values of the parameters in a law of chance is invariant for all transformations of the parameter when the law is differentiable with regard to all parameters.