Le diaporama :
Test de student sur groupes indépendants
Loading required package: survival
data ("neuropathy" )library (BayesFactor)
Loading required package: coda
Loading required package: Matrix
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Welcome to BayesFactor 0.9.12-4.7. If you have questions, please contact Richard Morey (richarddmorey@gmail.com).
Type BFManual() to open the manual.
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library (ggplot2)library (dplyr)
Attaching package: 'dplyr'
The following object is masked from 'package:kableExtra':
group_rows
The following objects are masked from 'package:stats':
filter, lag
The following objects are masked from 'package:base':
intersect, setdiff, setequal, union
= neuropathy |> filter (group== "control" ) |> select (pain) |> unlist ()= neuropathy |> filter (group== "treat" ) |> select (pain) |> unlist ()ttestBF (x,y,rscale= 1 )
Bayes factor analysis
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[1] Alt., r=1 : 0.4360155 ±0.02%
Against denominator:
Null, mu1-mu2 = 0
---
Bayes factor type: BFindepSample, JZS
# La loi a posteriori de la différence des moyennes = ttestBF (x,y,posterior = TRUE , iterations = 10000 )plot (samples[,"mu" ])
Un autre exemple :
On s’interesse aux trois questions suivantes :
Le taux de mercure présent dans le sang est-il significativement supérieur chez le groupe exposé ?
La proportion de cellules avec des anomalies structurales est-elle significativement supérieure chez le groupe exposé ?
Test de student sur groupes appariés
L’argument paired=T permet de faire des tests sur groupes appariés :
library (carData)data ("OBrienKaiserLong" )= OBrienKaiserLong |> filter (phase %in% c ("pre" ,"post" )) |> select (score,phase)
Faire le test Bayésien de Student :
Show the code
= data |> filter (phase== "pre" ) |> select (score) |> unlist ()= data |> filter (phase== "post" ) |> select (score) |> unlist ()ttestBF (x,y,paired= T,rscale= 1 )
Bayes factor analysis
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[1] Alt., r=1 : 81325.58 ±0%
Against denominator:
Null, mu = 0
---
Bayes factor type: BFoneSample, JZS
Show the code
# La loi a posteriori de la différence des moyennes = ttestBF (x,y,paired= T,posterior = TRUE , iterations = 10000 )plot (samples[,"mu" ])
Régression linéaire Bayésienne
Pour calculer les facteurs de Bayes :
data ("attitude" )= regressionBF (rating ~ ., data = attitude, progress= TRUE )
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Bayes factor analysis
--------------
[1] complaints : 417938.6 ±0.01%
[2] complaints + learning : 207271.9 ±0%
[3] complaints + learning + advance : 88041.54 ±0%
[4] complaints + raises : 77498.99 ±0%
[5] complaints + privileges : 75015.23 ±0%
[6] complaints + advance : 72759.76 ±0%
Against denominator:
Intercept only
---
Bayes factor type: BFlinearModel, JZS
head (res/ res[length (res)])
Bayes factor analysis
--------------
[1] complaints : 188.949 ±0.01%
[2] complaints + learning : 93.70711 ±0%
[3] complaints + learning + advance : 39.80336 ±0%
[4] complaints + raises : 35.0371 ±0%
[5] complaints + privileges : 33.9142 ±0%
[6] complaints + advance : 32.89451 ±0%
Against denominator:
rating ~ complaints + privileges + learning + raises + critical + advance
---
Bayes factor type: BFlinearModel, JZS
Pour calculer les coefficients du modèle :
Loading required package: Rcpp
This is rstanarm version 2.32.1
- See https://mc-stan.org/rstanarm/articles/priors for changes to default priors!
- Default priors may change, so it's safest to specify priors, even if equivalent to the defaults.
- For execution on a local, multicore CPU with excess RAM we recommend calling
options(mc.cores = parallel::detectCores())
<- stan_glm (rating ~ ., data = attitude, seed= 44 )
SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
Chain 1:
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SAMPLING FOR MODEL 'continuous' NOW (CHAIN 3).
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print (model_bayes, digits = 3 )
stan_glm
family: gaussian [identity]
formula: rating ~ .
observations: 30
predictors: 7
------
Median MAD_SD
(Intercept) 11.029 11.762
complaints 0.615 0.164
privileges -0.069 0.140
learning 0.312 0.173
raises 0.082 0.224
critical 0.037 0.151
advance -0.216 0.185
Auxiliary parameter(s):
Median MAD_SD
sigma 7.231 1.106
------
* For help interpreting the printed output see ?print.stanreg
* For info on the priors used see ?prior_summary.stanreg
This is bayesplot version 1.11.1
- Online documentation and vignettes at mc-stan.org/bayesplot
- bayesplot theme set to bayesplot::theme_default()
* Does _not_ affect other ggplot2 plots
* See ?bayesplot_theme_set for details on theme setting
mcmc_dens (model_bayes, pars = c ("complaints" ))library (bayestestR)hdi (model_bayes)
Highest Density Interval
Parameter | 95% HDI
-----------------------------
(Intercept) | [-13.50, 34.39]
complaints | [ 0.30, 0.95]
privileges | [ -0.34, 0.22]
learning | [ -0.03, 0.67]
raises | [ -0.37, 0.53]
critical | [ -0.26, 0.33]
advance | [ -0.58, 0.16]
describe_posterior (model_bayes)
Summary of Posterior Distribution
Parameter | Median | 95% CI | pd | ROPE | % in ROPE
---------------------------------------------------------------------------
(Intercept) | 11.03 | [-13.49, 34.40] | 82.23% | [-1.22, 1.22] | 6.05%
complaints | 0.61 | [ 0.28, 0.94] | 99.98% | [-1.22, 1.22] | 100%
privileges | -0.07 | [ -0.35, 0.21] | 68.85% | [-1.22, 1.22] | 100%
learning | 0.31 | [ -0.04, 0.66] | 95.80% | [-1.22, 1.22] | 100%
raises | 0.08 | [ -0.36, 0.55] | 64.42% | [-1.22, 1.22] | 100%
critical | 0.04 | [ -0.27, 0.33] | 59.65% | [-1.22, 1.22] | 100%
advance | -0.22 | [ -0.57, 0.17] | 87.30% | [-1.22, 1.22] | 100%
Parameter | Rhat | ESS
-----------------------------
(Intercept) | 0.999 | 4547.00
complaints | 1.001 | 2754.00
privileges | 1.000 | 3788.00
learning | 1.000 | 3323.00
raises | 1.001 | 3102.00
critical | 1.000 | 4329.00
advance | 1.002 | 2800.00
