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Last updated: 2026-02-05

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Knit directory: fiveMinuteStats/analysis/

This reproducible R Markdown analysis was created with workflowr (version 1.7.1). The Checks tab describes the reproducibility checks that were applied when the results were created. The Past versions tab lists the development history.

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R Markdown file: uncommitted changes

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Repository version: b794700

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Unstaged changes:
    Modified:   Makefile
    Modified:   analysis/bernoulli_poisson_process.Rmd
    Modified:   analysis/index.Rmd

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These are the previous versions of the repository in which changes were made to the R Markdown (analysis/index.Rmd) and HTML (docs/index.html) files. If you’ve configured a remote Git repository (see ?wflow_git_remote), click on the hyperlinks in the table below to view the files as they were in that past version.

File	Version	Author	Date	Message
Rmd	b794700	Peter Carbonetto	2026-02-05	Created pdf version of hmm vignette.
html	b794700	Peter Carbonetto	2026-02-05	Created pdf version of hmm vignette.
html	2b6b758	Peter Carbonetto	2026-01-23	Build site.
Rmd	d8b565d	Peter Carbonetto	2026-01-23	wflow_publish("analysis/index.Rmd")
html	2a7ca9c	Peter Carbonetto	2026-01-23	Build site.
Rmd	a50142b	Peter Carbonetto	2026-01-23	wflow_publish("analysis/index.Rmd")
html	4c77a1c	Peter Carbonetto	2026-01-23	Build site.
Rmd	4bc1378	Peter Carbonetto	2026-01-23	wflow_publish("analysis/index.Rmd")
html	a641c10	Peter Carbonetto	2026-01-15	Build site.
Rmd	cc90f59	Peter Carbonetto	2026-01-15	wflow_publish("analysis/index.Rmd")
html	a221240	Peter Carbonetto	2026-01-09	Push a bunch of updates to the webpages.
Rmd	a7c1413	Peter Carbonetto	2026-01-09	Added pdf version of em_variational vignette.
Rmd	4e44239	Peter Carbonetto	2026-01-09	Added pdf versions of mixture_models_01 and em_algorithm_01 vignettes.
Rmd	869a274	Peter Carbonetto	2026-01-09	Added a link to one of the pdfs.
Rmd	788b7d8	Peter Carbonetto	2026-01-08	Added pdf version of bayes_conjugate vignette.
Rmd	25e1cf5	Peter Carbonetto	2026-01-08	Adding pdf versions of three other vignettes.
html	a473a0f	Peter Carbonetto	2026-01-07	Ran wflow_publish("analysis/index.Rmd").
Rmd	aae635b	Peter Carbonetto	2026-01-07	wflow_publish("analysis/index.Rmd")
html	8a67ea4	Peter Carbonetto	2026-01-05	A few more minor fixes to the importance sampling vignette.
Rmd	224feb1	Peter Carbonetto	2025-12-29	A few small fixes.
Rmd	9d1c6ee	Peter Carbonetto	2025-12-29	Created pdf version of importance sampling vignette.
html	9d1c6ee	Peter Carbonetto	2025-12-29	Created pdf version of importance sampling vignette.
Rmd	e9dea3a	Peter Carbonetto	2025-12-29	Small fix.
Rmd	4f2f8a7	Peter Carbonetto	2025-12-29	Added a link.
html	4f2f8a7	Peter Carbonetto	2025-12-29	Added a link.
Rmd	fb6ff87	Peter Carbonetto	2025-12-29	Added pdf version of integral vignette.
html	fb6ff87	Peter Carbonetto	2025-12-29	Added pdf version of integral vignette.
Rmd	d1623a0	Peter Carbonetto	2025-12-29	fixed a link.
html	d1623a0	Peter Carbonetto	2025-12-29	fixed a link.
Rmd	cb29296	Peter Carbonetto	2025-12-29	Added pdf version of likelihood_ratio_simple_continuous_data vignette.
html	cb29296	Peter Carbonetto	2025-12-29	Added pdf version of likelihood_ratio_simple_continuous_data vignette.
Rmd	cb4b7d5	Peter Carbonetto	2025-12-29	Created pdf version of r_simplemix vignette.
html	cb4b7d5	Peter Carbonetto	2025-12-29	Created pdf version of r_simplemix vignette.
Rmd	b2fbf16	Peter Carbonetto	2025-12-29	Fixed a couple links.
html	b2fbf16	Peter Carbonetto	2025-12-29	Fixed a couple links.
Rmd	b705a3f	Peter Carbonetto	2025-12-29	Created pdf version of bayes_multiclass vignette.
html	b705a3f	Peter Carbonetto	2025-12-29	Created pdf version of bayes_multiclass vignette.
Rmd	4b35829	Peter Carbonetto	2025-12-29	Created pdf version of bayes_multiclass vignette.
html	4b35829	Peter Carbonetto	2025-12-29	Created pdf version of bayes_multiclass vignette.
Rmd	7a8ffe4	Peter Carbonetto	2025-12-29	Created pdf version of LR_and_BF vignette.
html	7a8ffe4	Peter Carbonetto	2025-12-29	Created pdf version of LR_and_BF vignette.
html	abfebce	Peter Carbonetto	2025-12-29	Added link to overview page.
Rmd	8d76ae3	Peter Carbonetto	2025-12-29	workflowr::wflow_publish("analysis/index.Rmd")
html	e8ef030	Peter Carbonetto	2025-03-05	Added a link to the home page.
Rmd	e1a2bea	Peter Carbonetto	2025-03-05	workflowr::wflow_publish("index.Rmd")
html	af9b387	Matthew Stephens	2022-04-26	Build site.
Rmd	c8e7b30	Matthew Stephens	2022-04-26	workflowr::wflow_publish("index.Rmd")
html	0d7365c	Matthew Stephens	2022-03-01	Build site.
Rmd	a0212b9	Matthew Stephens	2022-03-01	workflowr::wflow_publish("index.Rmd")
html	e9a48b8	Matthew Stephens	2021-04-20	Build site.
Rmd	14b5c3e	Matthew Stephens	2021-04-20	workflowr::wflow_publish("analysis/index.Rmd")
html	387cf13	Matthew Stephens	2021-03-01	Build site.
Rmd	ce7c149	Matthew Stephens	2021-03-01	workflowr::wflow_publish("index.Rmd")
html	f4d1736	Matthew Stephens	2021-01-26	Build site.
Rmd	a40ff17	Matthew Stephens	2021-01-26	workflowr::wflow_publish("index.Rmd")
html	fe66b94	Matthew Stephens	2021-01-26	Build site.
Rmd	c2b0a96	Matthew Stephens	2021-01-26	workflowr::wflow_publish("index.Rmd")
html	e4dabb4	Matthew Stephens	2021-01-25	Build site.
Rmd	f74014b	Matthew Stephens	2021-01-25	workflowr::wflow_publish("index.Rmd")
html	aebdb28	Matthew Stephens	2020-09-23	Build site.
Rmd	1cb6337	Matthew Stephens	2020-09-23	workflowr::wflow_publish("index.Rmd")
html	38e0138	Matthew Stephens	2020-07-22	Build site.
Rmd	daa57b1	Matthew Stephens	2020-07-22	workflowr::wflow_publish("index.Rmd")
html	a5a03a1	Matthew Stephens	2020-03-01	Build site.
Rmd	66fc13f	Matthew Stephens	2020-03-01	gaussian_process.Rmd
html	5f62ee6	Matthew Stephens	2019-03-31	Build site.
Rmd	0cd28bd	Matthew Stephens	2019-03-31	workflowr::wflow_publish(all = TRUE)
html	dbcff1f	stephens999	2019-01-23	Build site.
Rmd	7a0ba80	stephens999	2019-01-23	workflowr::wflow_publish("analysis/index.Rmd")
html	3c642ff	stephens999	2018-05-17	Build site.
Rmd	e8e0399	stephens999	2018-05-17	wflow_publish("analysis/index.Rmd")
html	ccb9962	stephens999	2018-05-03	Build site.
Rmd	5530e01	stephens999	2018-05-03	workflowr::wflow_publish("analysis/index.Rmd")
html	6053d26	stephens999	2018-04-23	Build site.
Rmd	1077c97	stephens999	2018-04-23	workflowr::wflow_publish(c("analysis/index.Rmd", "analysis/MH_intro.Rmd",
html	30630b2	stephens999	2018-04-23	Build site.
Rmd	5c310c2	stephens999	2018-04-23	MH_intro.Rmd
html	f995d0a	stephens999	2018-04-23	Build site.
Rmd	a7ec7b7	stephens999	2018-04-23	workflowr::wflow_publish(c("analysis/index.Rmd",
html	d251967	stephens999	2018-04-23	Build site.
Rmd	9e15ba0	stephens999	2018-04-23	workflowr::wflow_publish(c("analysis/index.Rmd",
html	d41d022	stephens999	2017-04-24	Build site.
Rmd	f012c1d	stephens999	2017-04-24	Files commited by wflow_commit.
html	c1d0c3f	stephens999	2017-04-17	update index
Rmd	72ef4ea	stephens999	2017-04-17	Files commited by wflow_commit.
html	c7e182b	stephens999	2017-04-17	Build site.
Rmd	9f09eca	stephens999	2017-04-17	Files commited by wflow_commit.
html	34bcc51	John Blischak	2017-03-06	Build site.
Rmd	2aa70fe	John Blischak	2017-03-06	Manually udpate some Rmd files.
html	8e61683	Marcus Davy	2017-03-03	rendered html using wflow_build(all=TRUE)
html	fffe50c	stephens999	2017-02-20	Build site.
Rmd	92d7daa	stephens999	2017-02-20	Files commited by wflow_commit.
html	20c6639	stephens999	2017-02-19	Build site.
Rmd	d20b048	stephens999	2017-02-19	Files commited by wflow_commit.
html	9778b49	stephens999	2017-02-19	Build site.
Rmd	592db57	stephens999	2017-02-19	Files commited by wflow_commit.
html	48bf85f	stephens999	2017-01-28	Build site.
Rmd	ca3b3b6	stephens999	2017-01-28	Files commited by wflow_commit.
html	fbfa018	stephens999	2017-01-28	Build site.
Rmd	2c4f22e	stephens999	2017-01-28	Files commited by wflow_commit.
html	a19b65a	stephens999	2017-01-24	Build site.
Rmd	fc0336e	stephens999	2017-01-24	Files commited by wflow_commit.
html	c3b365a	John Blischak	2017-01-02	Build site.
Rmd	ae24830	stephens999	2016-09-04	add example of computing LR on different data
Rmd	966d6f6	stephens999	2016-05-17	Merge branch ‘gh-pages’ of https://github.com/jhmarcus/fiveMinuteStats into jhmarcus-gh-pages
Rmd	6bb4560	stephens999	2016-05-12	add gibbs sampling example
Rmd	a72861e	stephens999	2016-05-02	add integral
Rmd	153e684	stephens999	2016-05-02	add IS
Rmd	8466ce3	stephens999	2016-05-02	add gibbs sampling example
Rmd	47f75ca	stephens999	2016-04-20	add BF and p value comparison
Rmd	c5e07f5	Xiao Nan	2016-04-13	add shiny conjugate normal app link to index
Rmd	ed83285	jhmarcus	2016-04-07	added popgen section to index and wright_fisher tutorials
Rmd	f1dd5fc	stephens999	2016-04-04	update index
Rmd	106d322	mbonakda	2016-02-24	add new notes to index
Rmd	294d219	stephens999	2016-02-16	add normal markov chain example
Rmd	be2da01	stephens999	2016-02-15	add multivariate normal
Rmd	0ba385e	mbonakda	2016-02-06	update index
Rmd	d1b8aae	jnovembre	2016-02-05	Changed sub-headings
Rmd	dce7ece	jnovembre	2016-02-05	modified index.html to add Poisson process and fix typo
Rmd	1187afb	mbonakda	2016-02-02	fix typos
Rmd	ac0ba21	mbonakda	2016-02-02	add to index
Rmd	313901b	jnovembre	2016-01-31	Modified index and added html
Rmd	ad8b7b5	mbonakda	2016-01-30	update names
Rmd	4e0c4fd	mbonakda	2016-01-30	update index
Rmd	4335247	mbonakda	2016-01-23	fix index typo
Rmd	9d4269b	mbonakda	2016-01-23	add simulating discrete chains to index
Rmd	b0339a9	stephens999	2016-01-19	update index
Rmd	9156677	stephens999	2016-01-19	add multiclass example
Rmd	ff6b857	mbonakda	2016-01-12	add asymptotic normality of MLE and wilks
Rmd	3ee2cf4	stephens999	2016-01-12	add likelihood function
Rmd	d6f4bea	stephens999	2016-01-12	add examples
Rmd	6feeb2e	stephens999	2016-01-11	update index
Rmd	8b7278d	stephens999	2016-01-11	add LR for continuous data
Rmd	93476ef	stephens999	2016-01-07	update LR to make clear it is for discrete data
Rmd	8f61232	stephens999	2016-01-07	add simple LR example
Rmd	f1b8c7c	stephens999	2016-01-05	add likelihood and loglikelihood
Rmd	90df5f8	stephens999	2016-01-05	tidy up material related to ashlar by removing much of it
Rmd	d3c8f4e	jhsiao999	2015-12-12	fix typo
Rmd	10bba89	jhsiao999	2015-12-12	add tutorial
Rmd	99f4499	jhsiao999	2015-12-12	add a Rmarkdown example
Rmd	1b891a0	jhsiao999	2015-12-12	first commit

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Inference

Likelihood Ratio and Likelihood

• Likelihood Ratio for fully specified models, discrete data (PDF)
• Likelihood Ratio for fully specified models, continuous data (PDF)
• Likelihood Ratios: Examples and Pitfalls
  • Examples and Pitfalls
  • Example: LRs must be computed on same data
• Likelihood Ratios: how big is convincing? (PDF)
• Likelihood Ratios: Wilks’s Theorem
• The Likelihood Function (PDF)
• Asymptotic Normality of MLE

Bayesian Inference

• Bayesian inference for comparing two fully-specified models
• Bayesian inference for comparing multiple fully-specified models (PDF)
• Bayesian inference for a continuous parameter: analytic calculation (PDF)
• Bayesian inference for a continuous parameter: summarizing the posterior (PDF)
• Bayesian inference for a continuous parameter: conjugacy (PDF)
• Bayesian inference for a normal mean (PDF)
• Bayesian inference for a normal mean (shiny app illustration)
• Bayesian inference for multiple independent parameters

Empirical Bayes

• The Empirical Bayes Normal Means problem

Frequentist vs Bayesian Inference

• The difficulty calibrating p values
• Relationship between Bayes Factor and p value
• Conditional coverage of a standard normal CI

Decision Theory

• Making a decision under uncertainty: the two class problem
• Brief introduction to decision theory for prediction problems

Mixture Models

• Introduction to Mixture Models (PDF)
• Introduction to the EM algorithm (PDF)
• A variational view of the EM algorithm (PDF)
• EM for Gaussian Mixture Models
• Archive: Alternative Introduction to Mixture Models

Bayesian Computation

• Every Bayesian computation is an integral (or a sum) (PDF)
• Importance sampling (PDF)

Markov Chain Monte Carlo

• The Metropolis-Hastings algorithm, Part 1 (PDF)
• The Metropolis-Hastings algorithm, Part 2 (PDF)
• Simple examples of Metropolis-Hastings algorithm (PDF)
• Introduction to Gibbs sampling (PDF)
• Gibbs sampling for a univariate normal mixture (PDF)
• Gibbs sampling for a mixture of product-Bernoullis (PDF)

Variational inference

• Variational inference: approximations, objectives and algorithms

Hidden Markov Models

• Forwards Backwards calculation example (PDF)

Distributions

• The Beta Distribution
• The Dirichlet Distribution
• The Pólya–Gamma Distribution

Stochastic Processes

Discrete-Time Markov Chains

• Discrete-Time Markov Chains: Introduction (PDF)
• Discrete-Time Markov Chains: Finding the Stationary Distribution via solution of the global balance equations (PDF)
• Discrete-Time Markov Chains: Finding the Stationary Distribution via eigendecomposition
• Simulating Discrete-Time Markov Chains: An Introduction (PDF)
• Simulating Discrete-Time Markov Chains: Limiting Distributions (PDF)

Poisson Processes

• Poisson Processes: Thinning with time-dependent probabilities
• Poisson Process: The Limiting Case of the Bernoulli Process (PDF)

Methods for sampling non-standard distributions

• Inverse transform sampling (PDF)

Multivariate Normal

• A key property of univariate normal
• Bivariate normal distribution
• Multivariate Normal
• The precision matrix
• Interpreting \(N(\mu,\Sigma)\) via eigen-decomposition of \(\Sigma\)

Gaussian Process

• Introduction to Gaussian Processes

Population Genetics

• Simulating from a simple genetic mixture model (PDF)
• Wright-Fisher Model
• Wright-Fisher Model Approximations