From 0ecb5565900ea6d788e9071fd443815ea92fdec8 Mon Sep 17 00:00:00 2001 From: GitHub Actions Date: Mon, 8 Jul 2024 08:57:04 +0000 Subject: [PATCH] Built site for vibass@0.0.48: f7e9be1 --- articles/like_surf.html | 2 +- articles/p2count.html | 16 +-- articles/p2normal.html | 52 ++++--- articles/p5.html | 127 ++++++++++++++---- .../figure-html/unnamed-chunk-17-1.png | Bin 0 -> 53989 bytes ...-chunk-20-1.png => unnamed-chunk-21-1.png} | Bin .../figure-html/unnamed-chunk-23-1.png | Bin 67840 -> 0 bytes .../figure-html/unnamed-chunk-24-1.png | Bin 49422 -> 67840 bytes .../figure-html/unnamed-chunk-25-1.png | Bin 0 -> 49422 bytes .../figure-html/unnamed-chunk-27-1.png | Bin 68314 -> 0 bytes .../figure-html/unnamed-chunk-28-1.png | Bin 59831 -> 68314 bytes .../figure-html/unnamed-chunk-29-1.png | Bin 0 -> 59831 bytes articles/p6.html | 50 ++++--- articles/p8.html | 14 +- .../figure-html/unnamed-chunk-36-1.png | Bin 20427 -> 20425 bytes pkgdown.yml | 2 +- 16 files changed, 164 insertions(+), 99 deletions(-) create mode 100644 articles/p5_files/figure-html/unnamed-chunk-17-1.png rename articles/p5_files/figure-html/{unnamed-chunk-20-1.png => unnamed-chunk-21-1.png} (100%) delete mode 100644 articles/p5_files/figure-html/unnamed-chunk-23-1.png create mode 100644 articles/p5_files/figure-html/unnamed-chunk-25-1.png delete mode 100644 articles/p5_files/figure-html/unnamed-chunk-27-1.png create mode 100644 articles/p5_files/figure-html/unnamed-chunk-29-1.png diff --git a/articles/like_surf.html b/articles/like_surf.html index f3d4a02..dbecd83 100644 --- a/articles/like_surf.html +++ b/articles/like_surf.html @@ -1955,7 +1955,7 @@
- + diff --git a/articles/p2count.html b/articles/p2count.html index d550007..0f6446c 100644 --- a/articles/p2count.html +++ b/articles/p2count.html @@ -347,19 +347,17 @@

The posterior distribution of
 setNames(nm = c(0.025, 0.975)) |> qgamma(643.5, 25) |> round(1)
 #> 0.025 0.975 
-#>  23.8  27.8
-
-setNames(nm = c(0.025, 0.975)) |> qgamma(748.8, 29.6) |> round(1)
+#>  23.8  27.8
+setNames(nm = c(0.025, 0.975)) |> qgamma(748.8, 29.6) |> round(1)
 #> 0.025 0.975 
 #>  23.5  27.1

and the subsequent posterior probabilities that the mean number of letters u’s in a page of A Game of Thrones is between 24 and 26 letters are

-
+
 round(pgamma(27, 643.5, 25) - pgamma(24, 643.5, 25), 3)
-#> [1] 0.851
-
-round(pgamma(27, 748.8, 29.6) - pgamma(24, 748.8, 29.6), 3)
+#> [1] 0.851
+round(pgamma(27, 748.8, 29.6) - pgamma(24, 748.8, 29.6), 3)
 #> [1] 0.887
@@ -386,7 +384,7 @@

GaPo(748.8,29.6,1)\text{GaPo}(748.8,\, 29.6, 1) if we work in the framework of the posterior 2. Now we represent both predictive distributions

-
+
 library(extraDistr)
 x <- c(10:40)
 pred1 <- dgpois(10:40, 643.5, 25)
@@ -399,7 +397,7 @@ 

= "probability" )

-
+
 plot(
   x, pred2,
   type = "h", lwd = 2, col = "purple",
diff --git a/articles/p2normal.html b/articles/p2normal.html
index 13085f8..c085ac8 100644
--- a/articles/p2normal.html
+++ b/articles/p2normal.html
@@ -251,9 +251,8 @@ 

A prior distribution for probabilities

 qnorm(c(0.005, 0.995), 1.70, 0.07)
-#> [1] 1.519692 1.880308
-
-pnorm(c(1.50, 1.60, 1.70, 1.80, 1.90), 1.70, 0.07)
+#> [1] 1.519692 1.880308
+pnorm(c(1.50, 1.60, 1.70, 1.80, 1.90), 1.70, 0.07)
 #> [1] 0.002137367 0.076563726 0.500000000 0.923436274 0.997862633

Consequently, a 99%\% @@ -267,7 +266,7 @@

A prior distribution for is between 1.60 and 1.80 is 0.9234-0.0766= 0.8468 or the probability that is taller than 1.80 is 1-0.9234=0.0766. Next we show the graphic of the density of this prior distribution.

-
+
 cap <- "Prior distribution for the mean height."
 m0 <- 1.7; s0 <- 0.07
 curve(
@@ -313,7 +312,7 @@ 

The likelihood function of the likelihood function of μ\mu is

-
+
 cap <- "Likelihood function."
 Lnorm <- function(mu, y, sigma) {
   # Essentially:
@@ -359,7 +358,7 @@ 

The posterior distribution of \pi(\mu &)=\mathcal{N}(\mu_0=1.70, \sigma_0=0.07)\\ \pi(\mu &\mid \mathcal D)=\mathcal{N}(\mu_n=1.6648, \sigma_n=0.0242) \end{align*}

-
+
 m0 <- 1.7; s0 <- 0.07
 m1 <- 1.6648; s1 <- 0.0242
 curve(
@@ -394,11 +393,10 @@ 

The posterior distribution of σn\sigma_n metres. According to it, we can compute the following percentiles and probabilities

-
+
 qnorm(c(0.005, 0.995), m1, s1)
-#> [1] 1.602465 1.727135
-
-pnorm(c(1.50, 1.60, 1.70, 1.80, 1.90), m1, s1)
+#> [1] 1.602465 1.727135
+pnorm(c(1.50, 1.60, 1.70, 1.80, 1.90), m1, s1)
 #> [1] 4.882741e-12 3.706635e-03 9.271024e-01 1.000000e+00 1.000000e+00

Consequently, a 99% credible interval for μ\mu @@ -435,7 +433,7 @@

μ\mu and the posterior predictive distribution (in purple) for Aninè’s height illustrating the previous comments.

-
+
 mp <- m1; sp <- sqrt(s1^2 + 0.1^2)
 curve(
   dnorm(x, m1, s1),
@@ -454,7 +452,7 @@ 

+
 qnorm(c(0.025, 0.975), 1.6642, 0.1029)
 #> [1] 1.46252 1.86588

This indicates that the probability that Aninè’s height is between @@ -604,7 +602,7 @@

The posterior distribution of are 0.0000,0.0006,0.9916,1.0000,and 1.00000.0000, 0.0006, 0.9916, 1.0000, \text{and } 1.0000, respectively.

-
+
 ny <- length(hwomen$height)
 ybar <- mean(hwomen$height)
 s2 <- sum((hwomen$height - ybar) ** 2) / (ny - 1)
@@ -614,12 +612,11 @@ 

The posterior distribution of scale = sqrt(s2 / ny) ) post_mu$scale * qt(c(0.005, 0.995), ny - 1) + post_mu$mean -#> [1] 1.616134 1.703866

-
-pt((c(1.50, 1.60, 1.70, 1.80, 1.90) - post_mu$mean) / post_mu$scale, ny - 1)
+#> [1] 1.616134 1.703866
+pt((c(1.50, 1.60, 1.70, 1.80, 1.90) - post_mu$mean) / post_mu$scale, ny - 1)
 #> [1] 1.669533e-08 5.718022e-04 9.916131e-01 9.999999e-01 1.000000e+00

The graphics of that posterior density is

-
+
 curve(
   dt((x - post_mu$mean) / post_mu$scale, ny - 1) / post_mu$scale,
   xlab = expression(paste(mu)), ylab = "density",
@@ -653,7 +650,7 @@ 

The posterior distribution of

Next we show the approximate graph and some posterior characteristics of the posterior π(σ2𝒟)\pi(\sigma^2 \mid \mathcal D).

-
+
 y <- seq(0, 40, 0.001)
 simuchi <- rchisq(y, ny - 1)
 simu.sigma <- 0.045598 / simuchi 
@@ -664,19 +661,16 @@ 

The posterior distribution of main = NULL, ylab = "density", xlab = expression(paste(sigma2)) )

-
+
 
 summary(simu.sigma)
 #>     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
-#> 0.000904 0.002667 0.003413 0.003789 0.004466 0.026238
-
-var(simu.sigma)
-#> [1] 2.768883e-06
-
-sqrt(var(simu.sigma))
-#> [1] 0.001663996
-
-quantile(simu.sigma, probs = c(0.005,0.995))
+#> 0.000904 0.002667 0.003413 0.003789 0.004466 0.026238
+var(simu.sigma)
+#> [1] 2.768883e-06
+sqrt(var(simu.sigma))
+#> [1] 0.001663996
+quantile(simu.sigma, probs = c(0.005,0.995))
 #>        0.5%       99.5% 
 #> 0.001468482 0.010937895

We observe that @@ -697,7 +691,7 @@

Time to individual work

Exercice

We focus now on the height of the VIBASS men participants.

-
+
 hmen <- data.frame(height = c(1.92, 1.82, 1.69, 1.75, 1.72, 1.71, 1.73, 1.69, 1.70, 1.78, 1.88, 1.82, 1.86, 1.65))
  1. diff --git a/articles/p5.html b/articles/p5.html index 37e3938..955a2d6 100644 --- a/articles/p5.html +++ b/articles/p5.html @@ -451,10 +451,16 @@

    Performance of the proposal di
    ## [1] 10000

  2. + +
+
+

Changing the proposal distribution - Importance Sampling +

+
  • Use a different proposal distribution and check how sampling weights, ESS and point estimates differ from those in the current -example. For example, a +example when using Importance Sampling. For example, a Ga(5,0.1)\text{Ga}(5,\, 0.1) will put a higher mass on values around 40, unlike the actual posterior distribution. What differences do you find with the example presented @@ -496,6 +502,77 @@

    Performance of the proposal di

+
+

Changing the prior distribution - Metropolis-Hastings +

+
    +
  • +

    We can also try using a different prior distribution on +λ\lambda, +and analyse the data using the Metropolis-Hastings algorithm. Run the +example for a prior distribution on +λ\lambda +which is a Gamma distribution with parameters +1.01.0 +and +1.01.0, +which is centred at 1 and has a larger precision (i.e., smaller +variance) than before. How does the different prior distribution change +the estimate of +λ\lambda, +and why?

    +

    Solution

    +
    +# Prior distribution: Ga(1.0, 1.0)
    +logprior <- function(lambda) {
    +  dgamma(lambda, 1.0, 1.0, log = TRUE)
    +}
    +# Number of iterations
    +n.iter <- 40500
    +
    +# Simulations of the parameter
    +lambda <- rep(NA, n.iter)
    +
    +# Initial value
    +lambda[1] <- 30
    +
    +for(i in 2:n.iter) {
    +  new.lambda <- rq(lambda[i - 1])
    +
    +  # Log-Acceptance probability
    +  logacc.prob <- loglik(y, new.lambda) + logprior(new.lambda) +
    +    logdq(lambda[i - 1], new.lambda)
    +  logacc.prob <- logacc.prob - loglik(y, lambda[i - 1]) - logprior(lambda[i - 1]) - 
    +    logdq(new.lambda, lambda[i - 1])
    +  logacc.prob <- min(0, logacc.prob)#0 = log(1)
    +
    +  if(log(runif(1)) < logacc.prob) {
    +    # Accept
    +    lambda[i] <- new.lambda
    +  } else {
    +    # Reject
    +    lambda[i] <- lambda[i - 1]
    +  }
    +}
    +# Remove burn-in
    +lambda <- lambda[-c(1:500)]
    +
    +# Thinning
    +lambda <- lambda[seq(1, length(lambda), by = 10)]
    +
    +# Summary statistics
    +summary(lambda)
    +
    ##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    +##   21.69   24.12   24.76   24.77   25.42   28.48
    +
    +par(mfrow = c(1, 2))
    +plot(lambda, type = "l", main = "MCMC samples", ylab = expression(lambda))
    +plot(density(lambda), main = "Posterior density", xlab = expression(lambda))
    +

    +
    +
  • +
+

@@ -621,7 +698,7 @@

Example: Simple Linear Regression

The data can be read into R:

-
+
 # Read in data
 BOD <- c(200,180,135,120,110,120,95,168,180,195,158,145,140,145,165,187,
          190,157,90,235,200,55,87,97,95)
@@ -630,7 +707,7 @@ 

Example: Simple Linear Regression# Create data frame for the analysis Data <- data.frame(BOD=BOD,mayfly.length=mayfly.length)

The package MCMCpack should be loaded into R:

-
+
 
## Loading required package: coda
## Loading required package: MASS
@@ -643,7 +720,7 @@

Example: Simple Linear Regression## ##

For this Bayesian Linear Regression example, we will use the MCMCregress() function; use

-
+
 ?MCMCregress

to see the help page for MCMCregress(). We specify the formula just as we would for a non-Bayesian regression using the lm @@ -694,11 +771,11 @@

Data exploration

Solution

-
+
 # Scatterplot
 plot(BOD,mayfly.length)
-

-
+

+
 # Correlation with hypothesis test
 cor.test(BOD,mayfly.length)
## 
@@ -719,7 +796,7 @@ 

Data explorationlm function in R; this will be useful for comparison with our Bayesian analysis.

Solution

-
+
 # Linear Regression using lm()
 linreg <- lm(mayfly.length ~ BOD, data = Data)
 summary(linreg)
@@ -760,7 +837,7 @@

Running the Gibbs Samplerverbose, where e.g. setting a value of 1000 implies the code will show an update to the screen every 1000 iterations.

Solution

-
+
 # Bayesian Linear Regression using a Gibbs Sampler
 
 # Set the size of the burn-in, the number of iterations of the Gibbs Sampler
@@ -881,7 +958,7 @@ 

Running the Gibbs Sampler## 29.38684 ## -0.06209 ## sigma2 = 3.87291

-
+
 summary(results1)
## 
 ## Iterations = 5001:14991
@@ -911,20 +988,20 @@ 

Running the Gibbs Sampler

Solution

-
+
 par(mfrow=c(2,2))
 traceplot(results1)
-

+

  • Use the function densplot() to view the shape of the posterior densities of each parameter.

    Solution

    -
    +
     par(mfrow=c(2,2))
     densplot(results1)
    -

    +

  • @@ -937,7 +1014,7 @@

    Running the Gibbs Sampler

    Solution

    -
    +
     crosscorr(results1)
    ##             (Intercept)         BOD      sigma2
     ## (Intercept)  1.00000000 -0.96109141 -0.05564442
    @@ -960,7 +1037,7 @@ 

    Reducing t will need to make a correction on the estimate of the regression intercept afterwards.

    Solution

    -
    +
     # Mean-centre the x covariate
     DataC <- Data
     meanBOD <- mean(DataC$BOD)
    @@ -1399,7 +1476,7 @@ 

    Reducing t ## 19.66103 ## -0.05363 ## sigma2 = 2.07754

    -
    +
     summary(results2)
    ## 
     ## Iterations = 50001:59991
    @@ -1421,7 +1498,7 @@ 

    Reducing t ## (Intercept) 18.84960 19.36318 19.63098 19.86544 20.34886 ## BOD -0.07067 -0.06099 -0.05491 -0.04897 -0.03778 ## sigma2 2.01223 2.72506 3.27807 3.98491 6.20298

    -
    +
     # Correct the effect of the mean-centering on the intercept, using the
     # full set of simulated outputs
     results2.simulations <- as.data.frame(results2)
    @@ -1429,10 +1506,10 @@ 

    Reducing t summary(results2.beta.0)

    ##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
     ##   22.78   26.77   27.64   27.61   28.49   31.96
    -
    +
     var(results2.beta.0)
    ## [1] 1.704337
    -
    +
     sd(results2.beta.0)
    ## [1] 1.305503
    @@ -1442,19 +1519,19 @@

    Reducing t before. Are there any notable differences when mean-centering the covariate, especially with regard to the cross-correlations?

    Solution

    -
    +
     par(mfrow=c(2,2))
     traceplot(results2)
    -

    -
    +

    +
     par(mfrow=c(2,2))
     densplot(results2)
     # Need to use the Base R kernel density function to look at the corrected 
     # Intercept
     plot(density(results2.beta.0, bw = 0.3404), xlim=c(22,34),
          main = "Density, corrected Intercept")
    -

    -
    +

    +
     crosscorr(results2)
    ##              (Intercept)         BOD       sigma2
     ## (Intercept)  1.000000000  0.02131006 -0.001004385
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        Exercises#> #> FALSE TRUE #> FALSE 88 44 -#> TRUE 2 16

    -

    -
    +
     boxplot(fakenews$negative ~ fakenews$typeFAKE)

    @@ -301,7 +300,7 @@

    Exercises
    +
    -
    -confint(bayesx.output)
    +#> iterations = 15000  step = 10
    +confint(bayesx.output)
     #>                          2.5%      97.5%
     #> (Intercept)      -4.553338750 -1.3992430
     #> titlehasexclTRUE  1.253023500  5.1184442
    @@ -340,11 +338,11 @@ 

    Exercises
    +
     # Traces can be obtained separately
     plot(bayesx.output,which = "coef-samples")

    -
    +
     # And the density plots one-by-one
     par(mfrow=c(2,2))
     plot(density(samples(bayesx.output)[,"titlehasexclTRUE"]),main="Title Has Excl")
    @@ -357,7 +355,7 @@ 

    Exercisesglm() for comparison. How do the model fits compare?

    Solution

    -
    +
     # Fit model - note similarity with bayesx syntax
     glm.output <- glm(formula = typeFAKE ~ titlehasexcl + title_words + negative,
                       data = fakenews,
    @@ -384,9 +382,8 @@ 

    Exercises#> Residual deviance: 169.36 on 146 degrees of freedom #> AIC: 177.36 #> -#> Number of Fisher Scoring iterations: 4

    -
    -# Perform ANOVA on each variable in turn
    +#> Number of Fisher Scoring iterations: 4
    +# Perform ANOVA on each variable in turn
     drop1(glm.output,test="Chisq")
     #> Single term deletions
     #> 
    @@ -451,7 +448,7 @@ 

    Example: Emergency Room Complaints

    We can use the following code to extract the data we want without having to load the whole package:

    -
    @@ -463,7 +460,7 @@

    Fitting Bayesian Poisson Reg

    In BayesX, the syntax for fitting a Bayesian Poisson Regression Model with one response variable, three explanatory variables and an offset will be like so:

    -
    +
     model1 <- bayesx(formula = y~x1+x2+x3+offset(w),
                      data = data.set,
                      family="poisson")
    @@ -471,7 +468,7 @@

    Fitting Bayesian Poisson Reg for a Poisson GLM we will be using a log() link function by default, we must compute the log of the number of visits and include that in the data set esdcomp:

    -
    +
     esdcomp$log.visits <- log(esdcomp$visits)

    The offset term in the model is then written

    offset(log.visits)

    @@ -489,17 +486,17 @@

    Exercises
    +
     

    -
    +
     # Use boxplots against residency and gender
     boxplot(esdcomp$ratio ~ esdcomp$residency)

    -
    +
     boxplot(esdcomp$ratio ~ esdcomp$gender)

    @@ -511,7 +508,7 @@

    Exercises
    +
     # Fit model - note similarity with bayesx syntax
     esdcomp$log.visits <- log(esdcomp$visits)
     bayesx.output <- bayesx(formula = complaints ~ offset(log.visits) + residency + gender + revenue,
    @@ -541,13 +538,13 @@ 

    Exercises
    +
     

    -
    +
     # And the density plots one-by-one
     par(mfrow =c(2, 2))
     plot(density(samples(bayesx.output)[, "residencyY"]), main = "Residency")
    @@ -560,7 +557,7 @@ 

    Exercisesglm() for comparison. How do the model fits compare?

    Solution

    -
    +
     # Fit model - note similarity with bayesx syntax
     esdcomp$log.visits <- log(esdcomp$visits)
     glm.output <- glm(formula = complaints ~ offset(log.visits) + residency + gender + revenue,
    @@ -588,9 +585,8 @@ 

    Exercises#> Residual deviance: 58.698 on 40 degrees of freedom #> AIC: 189.48 #> -#> Number of Fisher Scoring iterations: 5

    -
    -# Perform ANOVA on each variable in turn
    +#> Number of Fisher Scoring iterations: 5
    +# Perform ANOVA on each variable in turn
     drop1(glm.output, test = "Chisq")
     #> Single term deletions
     #> 
    diff --git a/articles/p8.html b/articles/p8.html
    index d9da503..14525de 100644
    --- a/articles/p8.html
    +++ b/articles/p8.html
    @@ -684,7 +684,7 @@ 

    Exercises# Summarise output summary(inla.output)

    ## Time used:
    -##     Pre = 0.888, Running = 0.542, Post = 0.0136, Total = 1.44 
    +##     Pre = 0.838, Running = 0.433, Post = 0.00914, Total = 1.28 
     ## Fixed effects:
     ##                    mean    sd 0.025quant 0.5quant 0.975quant   mode kld
     ## (Intercept)      -3.016 0.761     -4.507   -3.016     -1.525 -3.016   0
    @@ -836,7 +836,7 @@ 

    Exercises# Summarise output summary(inla.output)

    ## Time used:
    -##     Pre = 0.849, Running = 0.182, Post = 0.00445, Total = 1.04 
    +##     Pre = 0.806, Running = 0.189, Post = 0.00424, Total = 0.999 
     ## Fixed effects:
     ##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
     ## (Intercept) -7.171 0.688     -8.520   -7.171     -5.822 -7.171   0
    @@ -982,7 +982,7 @@ 

    Multilevel Modellingsummary(m1)

    ## Time used:
    -##     Pre = 0.77, Running = 0.246, Post = 0.0112, Total = 1.03 
    +##     Pre = 0.824, Running = 0.22, Post = 0.00967, Total = 1.05 
     ## Fixed effects:
     ##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
     ## (Intercept)  9.685 1.070      7.586    9.685     11.784  9.685   0
    @@ -1029,7 +1029,7 @@ 

    Multilevel Modellingsummary(m2)

    ## Time used:
    -##     Pre = 0.895, Running = 0.282, Post = 0.0133, Total = 1.19 
    +##     Pre = 0.815, Running = 0.294, Post = 0.0139, Total = 1.12 
     ## Fixed effects:
     ##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
     ## (Intercept) 10.626 1.495      7.698   10.624     13.565 10.624   0
    @@ -1201,7 +1201,7 @@ 

    Poisson regression) summary(m1nc)

    ## Time used:
    -##     Pre = 0.814, Running = 0.166, Post = 0.00375, Total = 0.984 
    +##     Pre = 0.778, Running = 0.159, Post = 0.00401, Total = 0.941 
     ## Fixed effects:
     ##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
     ## (Intercept) -0.647 0.090     -0.824   -0.647     -0.471 -0.647   0
    @@ -1227,7 +1227,7 @@ 

    Poisson regressionsummary(m2nc)

    ## Time used:
    -##     Pre = 0.88, Running = 0.21, Post = 0.00774, Total = 1.1 
    +##     Pre = 0.94, Running = 0.216, Post = 0.00805, Total = 1.16 
     ## Fixed effects:
     ##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
     ## (Intercept) -0.650 0.104     -0.857   -0.649     -0.446 -0.649   0
    @@ -1258,7 +1258,7 @@ 

    Poisson regressionsummary(m3nc)

    ## Time used:
    -##     Pre = 0.749, Running = 0.207, Post = 0.00725, Total = 0.964 
    +##     Pre = 0.87, Running = 0.195, Post = 0.00722, Total = 1.07 
     ## Fixed effects:
     ##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
     ## (Intercept) -0.029 0.063     -0.156   -0.028      0.091 -0.028   0
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    diff --git a/pkgdown.yml b/pkgdown.yml
    index dd36bbd..884d9d8 100644
    --- a/pkgdown.yml
    +++ b/pkgdown.yml
    @@ -11,7 +11,7 @@ articles:
       p6: p6.html
       p7: p7.html
       p8: p8.html
    -last_built: 2024-07-07T22:01Z
    +last_built: 2024-07-08T08:55Z
     urls:
       reference: http://vabar.es/vibass/reference
       article: http://vabar.es/vibass/articles