diff --git a/BayesBasics.bib b/BayesBasics.bib index 49c56dc..3f2ad9b 100644 --- a/BayesBasics.bib +++ b/BayesBasics.bib @@ -11,12 +11,20 @@ @book{kruschke_doing_2010 keywords = {Mathematics / Applied, Mathematics / General} } +@book{kruschke2014doing, + title={Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan}, + author={Kruschke, John}, + year={2014}, + publisher={Academic Press} +} + @book{gelman_bda, edition = {3rd}, title = {Bayesian Data Analysis}, isbn = {9781439840955}, abstract = {Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.}, language = {en}, + url = {http://www.stat.columbia.edu/~gelman/book/}, author = {Gelman, Andrew and Carlin, John B. and Stern, Hal S. and Dunson, David B. and Vehtari, Aki and Rubin, Donald B.}, month = nov, year = {2013}, @@ -137,11 +145,7 @@ @article{gelmanHwangVehtari publisher={Springer} } -@article{gelmanVehtariWAIC, - title={WAIC and cross-validation in Stan}, - author={Vehtari, Aki and Gelman, Andrew}, - year={2014} -} + @book{mcelreath2016, title={Statistical Rethinking: A Bayesian Course with Examples in R and Stan}, @@ -149,4 +153,53 @@ @book{mcelreath2016 volume={122}, year={2016}, publisher={CRC Press} +} + +@book{mcelreath2020, + title={Statistical rethinking: A Bayesian course with examples in R and Stan}, + author={McElreath, Richard}, + year={2020}, + publisher={Chapman and Hall/CRC} +} + +@book{mcelreath2020statistical, + title={Statistical rethinking: A Bayesian course with examples in R and Stan}, + author={McElreath, Richard}, + year={2020}, + publisher={Chapman and Hall/CRC} +} + + +@article{gelmanVehtariWAIC, + title={WAIC and cross-validation in Stan}, + author={Vehtari, Aki and Gelman, Andrew}, + year={2014} +} + +@article{vehtari2017practical, + title={Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC}, + author={Vehtari, Aki and Gelman, Andrew and Gabry, Jonah}, + journal={Statistics and computing}, + volume={27}, + number={5}, + pages={1413--1432}, + year={2017}, + publisher={Springer} +} + +@article{vehtari2015pareto, + title={Pareto smoothed importance sampling}, + author={Vehtari, Aki and Simpson, Daniel and Gelman, Andrew and Yao, Yuling and Gabry, Jonah}, + journal={arXiv preprint arXiv:1507.02646}, + year={2015} +} + +@article{carpenter2017stan, + title={Stan: A probabilistic programming language}, + author={Carpenter, Bob and Gelman, Andrew and Hoffman, Matthew D and Lee, Daniel and Goodrich, Ben and Betancourt, Michael and Brubaker, Marcus and Guo, Jiqiang and Li, Peter and Riddell, Allen}, + journal={Journal of statistical software}, + volume={76}, + number={1}, + year={2017}, + publisher={Columbia Univ., New York, NY (United States); Harvard Univ., Cambridge, MA~…} } \ No newline at end of file diff --git a/Bayesian-Basics.log b/Bayesian-Basics.log deleted file mode 100644 index 73ecf68..0000000 --- a/Bayesian-Basics.log +++ /dev/null @@ -1,348 +0,0 @@ -This is XeTeX, Version 3.1415926-2.5-0.9999.3 (MiKTeX 2.9 64-bit) (preloaded format=xelatex 2014.8.17) 22 JUL 2017 10:24 -entering extended mode -**Bayesian-Basics.tex -(D:\Documents\Stats\Repositories\Docs\bayesian-basics\Bayesian-Basics.tex -LaTeX2e <2014/05/01> -Babel <3.9k> and hyphenation patterns for 68 languages loaded. -(D:\Programs\MiKTeX\tex\latex\base\book.cls -Document Class: book 2007/10/19 v1.4h Standard LaTeX document class 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Package graphics Error: No driver specified. - -See the graphics package documentation for explanation. -Type H for immediate help. - ... - -l.89 } - -Here is how much of TeX's memory you used: - 10272 strings out of 428791 - 178158 string characters out of 3166350 - 205259 words of memory out of 3000000 - 13561 multiletter control sequences out of 15000+200000 - 3680 words of font info for 19 fonts, out of 3000000 for 9000 - 1096 hyphenation exceptions out of 8191 - 52i,0n,41p,10424b,109s stack positions out of 5000i,500n,10000p,200000b,50000s - -No pages of output. diff --git a/_output.yml b/_output.yml index b765a6c..1c008a4 100644 --- a/_output.yml +++ b/_output.yml @@ -1,5 +1,5 @@ bookdown::gitbook: - css: [css/book.css, 'https://use.fontawesome.com/releases/v5.0.13/css/all.css'] + css: [css/book.css, 'https://use.fontawesome.com/releases/v5.15.0/css/all.css'] font-import: https://fonts.googleapis.com/css?family=Roboto|Open+Sans|Alex+Brush font-family: 'Roboto' number_sections: false diff --git a/appendix.Rmd b/appendix.Rmd index e8ce356..59dbe2a 100644 --- a/appendix.Rmd +++ b/appendix.Rmd @@ -35,7 +35,7 @@ ggplot(data.frame(mus, L)) + geom_hline(aes(yintercept = max(L)), alpha = .5, lty = 2) + geom_path(aes(x = mus, y = L), color = '#ff5500', alpha = .9, lwd = 2) + labs(x = expression(theta), y = 'Likelihood') + - theme_trueMinimal() + + theme_clean() + theme( axis.ticks.y = element_blank(), axis.text.y = element_blank(), @@ -221,7 +221,7 @@ ggplot(aes(x = mu, y = sigma), data = plotdat) + ) + # geom_path(aes(), col='navy', alpha=.5) + labs(x = expression(mu), y = expression(sigma)) + - theme_trueMinimal() + + theme_clean() + theme( axis.ticks.y = element_blank(), axis.text.y = element_blank(), @@ -299,16 +299,15 @@ colnames(plotdat) = c('sigma', 'Intercept', 'β', 'll') plotdat$nll = -plotdat$ll -# gdat= melt(plotdat, id=c('sigma', 'll', 'nll')) plotdat %>% select(-ll) %>% - gather(key = variable, value = value, -sigma, -nll) %>% + pivot_longer(-c(sigma, nll), names_to = 'variable') %>% ggplot() + geom_point( aes(x = sigma, y = value, size = nll), color = palettes$orange$orange, alpha = .15, - show.legend = F, + show.legend = FALSE, position = position_jitter(w = 0.2, h = 0.2) ) + facet_wrap(~ variable) + #, scales='free_y' @@ -317,7 +316,6 @@ plotdat %>% theme_clean(center_axis_labels = TRUE) + theme( axis.ticks.y = element_blank(), - # axis.text.y = element_blank(), axis.text.x = element_text(color = 'gray25', size = 14), axis.title.x = element_text(color = 'gray25', size = 24), axis.title.y = element_text(color = 'gray25', vjust = 1), @@ -1173,7 +1171,7 @@ dat = list(N = N, # # standard stan # fit = stan(model_code = stanmodelcodeIG, data = dat, iter = nsim, -# warmup=warmup, thin=1, chains = chains, verbose = F) +# warmup=warmup, thin=1, chains = chains, verbose = FALSE) # perhaps closer to above settings? # fitIG = stan(model_code = stanmodelcodeIG, data = dat, iter = nsim, @@ -1182,7 +1180,7 @@ dat = list(N = N, load('data/IGModelData.RData') # print(fitIG, digits_summary=3, probs=c(.025,.5,.975)) -broom::tidy(fitIG, conf.int = TRUE) %>% +broom.mixed::tidy(fitIG, conf.int = TRUE) %>% kable(align = 'lrrrr', digits = 2) %>% kable_styling(full_width = FALSE) # finalest; log_p_th(X, y, finalest) @@ -1219,4 +1217,4 @@ brms, and many others. [^MHmcmc]: This code regards only one chain, though a simple loop or any number of other approaches would easily extend it to two or more. -[^bugswarning]: A word of warning, I haven't even had R2OpenBUGS on my machine in years, so this code for post-processing the model may be a bit iffy depending on how the package works these days. The model code, which is the important part, is fine though. The JAGS section has been recently tested however. \ No newline at end of file +[^bugswarning]: A word of warning, I haven't even had R2OpenBUGS on my machine in years, so this code for post-processing the model may be a bit iffy depending on how the package works these days. The model code, which is the important part, is fine though. The JAGS section has been recently tested however. diff --git a/css/book.css b/css/book.css index 488446e..5721aef 100644 --- a/css/book.css +++ b/css/book.css @@ -1,9 +1,9 @@ -@import url("https://fonts.googleapis.com/css?family=Bitter|Roboto|Roboto+Mono|Roboto+Condensed|Open+Sans|Lato|Lora|Fira+Sans|Yellotail"); +@import url("https://fonts.googleapis.com/css?family=Bitter|Alex+Brush|Roboto|Roboto+Mono|Roboto+Condensed|Open+Sans|Lato|Lora|Fira+Sans|Yellotail"); /* title page */ .book .book-body .page-wrapper .page-inner section.normal h1.title { - font-size: 250%; - font-family: Karla, 'Roboto Condensed', 'Fira Sans', Lora, Lato, Roboto, sans; + font-size: 500%; + font-family: 'Alex Brush', Karla, 'Roboto Condensed', 'Fira Sans', Lora, Lato, Roboto, sans; font-style: normal; font-weight: 100; } @@ -75,8 +75,8 @@ https://stackoverflow.com/questions/28623446/hover-effect-expand-bottom-border uri class is for urls */ -.book .book-body .page-wrapper .page-inner section.normal a:active, -.book .book-body .page-wrapper .page-inner section.normal a:focus, +.book .book-body .page-wrapper .page-inner section.normal a:active, +.book .book-body .page-wrapper .page-inner section.normal a:focus, .book .book-body .page-wrapper .page-inner section.normal a:hover { outline: 0; text-decoration: none; @@ -355,6 +355,7 @@ img { } .func { + font-family: 'Roboto Mono', Monaco, Consolas, "Liberation Mono", Menlo, 'Courier New', monospace; color: #007020; /*#007199 #00CBB6; #984ea3; can just use `` instead*/ font-weight: 500; } @@ -412,12 +413,22 @@ div.datatables { text-align: center; line-height: 500px; /* <-- this is what you must define */ vertical-align: bottom; - font-size: 150%; + font-size: 150%; color: hotpink; font-family: yellowtail; height: 300px; background-image: url('../img/mc_sunset_2.png'); background-size: 50%; background-repeat: no-repeat; - background-position: center; + background-position: center; +} + +/* formulas*/ +.MJXc-display { + padding: 10px 0px 10px 0px !important; +} + +/* References */ +div.csl-entry { + padding: 5px; } \ No newline at end of file diff --git a/data/mainModelData.RData b/data/mainModelData.RData deleted file mode 100644 index 25cae2f..0000000 Binary files a/data/mainModelData.RData and /dev/null differ diff --git a/data/mainModels.RData b/data/mainModels.RData index 49fb712..719e7cc 100644 Binary files a/data/mainModels.RData and b/data/mainModels.RData differ diff --git a/diagnostics.Rmd b/diagnostics.Rmd index d39e1db..5046212 100644 --- a/diagnostics.Rmd +++ b/diagnostics.Rmd @@ -57,9 +57,9 @@ ggplot(aes( y = a1, color = factor(.chain) ), data = gdat) + - geom_line(show.legend = F) + + geom_line(show.legend = FALSE) + labs(x = '', y = '') + - theme_trueMinimal() + + theme_clean() + theme( axis.text.y = element_blank(), axis.ticks.y = element_blank(), @@ -76,7 +76,7 @@ ggsave('img/badchains.svg', ### Statistical Measures -To go along with visual inspection, we can examine various statistics that might help our determination of convergence or lack thereof. Gelman and Rubin's potential scale reduction factor, $\hat{R}$, provides an estimate of convergence based on the variance of an estimated parameter $\theta$ between chains, and the variance within a chain. It is interpreted as the factor by which the variance in the estimate might be reduced with longer chains. We are looking for a value near 1 (and at the very least less than 1.1), and it will get there as $N_{sim} \rightarrow \infty$. In the regression model things are looking good in this respect. +To go along with visual inspection, we can examine various statistics that might help our determination of convergence or lack thereof. Gelman and Rubin's *potential scale reduction factor*, $\hat{R}$, provides an estimate of convergence based on the variance of an estimated parameter $\theta$ between chains, and the variance within a chain. It is interpreted as the factor by which the variance in the estimate might be reduced with longer chains. We are looking for a value near 1 (and at the very least less than 1.1), and it will get there as $N_{sim} \rightarrow \infty$. In the regression model things are looking good in this respect. ```{r showRhat, echo=FALSE} broom.mixed::tidyMCMC(fit, rhat = TRUE) %>% @@ -110,10 +110,13 @@ ggplot(data = test, aes(x = Lag, y = AC)) + col = '#ff5500', alpha = .75, lwd = 1.5) + - geom_point(col = palettes$orange$complementary[2], - size = 5) + + geom_point( + col = palettes$orange$complementary[2], + size = 5, + alpha = 1 + ) + labs(x = 'Lag', y = 'Autocorrelation') + - theme_trueMinimal() + + theme_clean() + theme( axis.title.x = element_text(color = 'gray25', size = 15), axis.title.y = element_text(color = 'gray25', size = 15), @@ -128,7 +131,7 @@ for (i in 2:length(pres2)) { } # pdf('img/acfPlotSerial.pdf') -test = tibble(acf = acf(pres2,)$acf[,1,1], lag = 0:(length(acf)-1)) +test = tibble(acf = acf(pres2, plot = FALSE)$acf[,1,1], lag = 0:(length(acf)-1)) ggplot(data = test, aes(x = lag, y = acf)) + geom_hline(aes(yintercept = 0), col = 'gray90') + @@ -137,15 +140,16 @@ ggplot(data = test, aes(x = lag, y = acf)) + col = '#ff5500', lwd = 1.5, alpha = .75, - show.legend = F + show.legend = FALSE ) + geom_point( col = palettes$orange$complementary[2], size = 5, - show.legend = F + alpha = 1, + show.legend = FALSE ) + labs(x = 'Lag', y = 'Autocorrelation') + - theme_trueMinimal() + + theme_clean() + theme( axis.title.x = element_text(color = 'gray25', size = 15), axis.title.y = element_text(color = 'gray25', size = 15), @@ -166,7 +170,7 @@ broom.mixed::tidyMCMC(fit, ess = TRUE) %>% kable_styling(full_width = FALSE) ``` -Monte Carlo error is an estimate of the uncertainty contributed by only having a finite number of posterior draws. We'd typically want roughly less than 5% of the posterior standard deviation (reported right next to it in the Stan output), but might as well go for less than 1%. With no autocorrelation it would equal $\sqrt{\frac{var(\theta)}{n_{\textrm{eff}}}}$[^mcerr]. and $n_{\textrm{eff}}$ would equal the number of simulation draws requested. +*Monte Carlo error* is an estimate of the uncertainty contributed by only having a finite number of posterior draws. We'd typically want roughly less than 5% of the posterior standard deviation (reported right next to it in the Stan output), but might as well go for less than 1%. With no autocorrelation it would equal $\sqrt{\frac{var(\theta)}{n_{\textrm{eff}}}}$[^mcerr]. and $n_{\textrm{eff}}$ would equal the number of simulation draws requested. ```{r showMCerror, echo=FALSE} rstan::summary(fit, pars = c('beta', 'sigma'))$summary[, c('mean', 'se_mean')] %>% @@ -195,9 +199,9 @@ For model comparison of out of sample predictive performance, there are informat ### Posterior Predictive Checking: Statistical -For an overall assessment of model fit, we can examine how well the model can reproduce the data at hand given the $\theta$ draws from the posterior. We discussed earlier the posterior predictive distribution for a future observation $\tilde{y}$[^ppcheck2], and here we'll dive in to using it explicitly. There are two sources of uncertainty in our regression model, the variance in $y$ not explained by the model ($\sigma^2$), and posterior uncertainty in the parameters due to having a finite sample size. As $N\rightarrow\infty$, the latter goes to zero, and so we can simulate draws of $\tilde{y} \sim N(\tilde{X}\beta, \sigma^2I)$[^conjugate]. If $\tilde{X}$ is the model data as in the following, then we will refer to $y^{\textrm{Rep}}$ instead of $\tilde{y}$. +For an overall assessment of model fit, we can examine how well the model can reproduce the data at hand given the $\theta$ draws from the posterior. We discussed earlier the *posterior predictive distribution* for a future observation $\tilde{y}$[^ppcheck2], and here we'll dive in to using it explicitly. There are two sources of uncertainty in our regression model, the variance in $y$ not explained by the model ($\sigma^2$), and posterior uncertainty in the parameters due to having a finite sample size. As $N\rightarrow\infty$, the latter goes to zero, and so we can simulate draws of $\tilde{y} \sim N(\tilde{X}\beta, \sigma^2I)$[^conjugate]. If $\tilde{X}$ is the model data as in the following, then we will refer to $y^{\textrm{Rep}}$ instead of $\tilde{y}$. -For our model, this entails extracting the simulated values from the model object, and taking a random draw from the normal distribution based on the $\beta$ and $\sigma$ that are drawn to produce our replicated data, $y^{\textrm{Rep}}$ (see @gelman_bda, Appendix C). In what follows, I write out the process explicitly, but bayesplot, rstanarm, and brms make this straightforward, possibly with a single line of code, the latter packages using bayesplot. In addition, it's often simpler to create the $y^{\textrm{Rep}}$ as part of your generated quantities section of the model code if modeling with Stan explicitly. +For our model, this entails extracting the simulated values from the model object, and taking a random draw from the normal distribution based on the $\beta$ and $\sigma$ that are drawn to produce our *replicated data*, $y^{\textrm{Rep}}$ (see @gelman_bda, Appendix C). In what follows, I write out the process explicitly, but bayesplot, rstanarm, and brms make this straightforward, possibly with a single line of code, the latter packages using bayesplot. In addition, it's often simpler to create the $y^{\textrm{Rep}}$ as part of your generated quantities section of the model code if modeling with Stan explicitly. ```{r posteriorPredictiveExample, fig.show='hide', echo=-(1:3)} load('data/mainModels.RData') @@ -221,8 +225,6 @@ As a starting point, we can check our minimum value among the replicated data se ```{r posteriorPredictiveMinComparison, fig.keep='none', fig.show='hide'} min_rep = apply(yRep, 2, min) min_y = min(y) -hist(min_rep, main = '') -abline(v = min_y) c(mean(min_rep), min_y) prop.table(table(min_rep > min_y)) sort(y)[1:5] @@ -233,16 +235,19 @@ sort(y)[1:5] # pdf('img/histofyrepMinimum.pdf', paper='USr') # hist(min_rep, main='', 'FD', yaxt='n', ylab='', border='gray50'); abline(v=min_y, col='gray50') # dev.off() -ggplot(aes(x = min_rep), data = data_frame(min_rep = min_rep)) + +ggplot(aes(x = min_rep), data = tibble(min_rep = min_rep)) + geom_density(fill = scales::alpha('#ff5500', .5), color = 'transparent') + geom_line(color = palettes$orange$complementary[2], stat = 'density') + geom_vline(xintercept = min_y, color = 'gray50', alpha = .75) + - theme_trueMinimal() + + labs(y = '') + + theme_clean() + theme( - axis.title.x = element_text(color = 'gray25', size = 15), - axis.title.y = element_text(color = 'gray25', size = 15), + axis.title.x = element_text(color = 'gray25', size = 15), + axis.title.y = element_text(color = 'gray25', size = 15), + axis.text.y = element_blank(), + axis.ticks.y = element_blank(), plot.background = element_rect(fill = "transparent", colour = NA) ) # ggsave('img/histofyrepMinimum.svg', bg='transparent') @@ -262,10 +267,13 @@ ggplot(aes(x = value), data = q10_rep) + geom_vline(xintercept = quantile(y, .1), color = 'gray50', alpha = .75) + - theme_trueMinimal() + + labs(y = '') + + theme_clean() + theme( - axis.title.x = element_text(color = 'gray25', size = 15), - axis.title.y = element_text(color = 'gray25', size = 15), + axis.title.x = element_text(color = 'gray25', size = 15), + axis.title.y = element_text(color = 'gray25', size = 15), + axis.text.y = element_blank(), + axis.ticks.y = element_blank(), plot.background = element_rect(fill = "transparent", colour = NA) ) # ggsave('img/histofyrepQ10.svg', bg='transparent') @@ -288,7 +296,7 @@ ggplot(aes(x = y, y = avgfits), data = data.frame(y = y, avgfits = avgfits)) + # geom_point(col=palettes$orange$complementary, alpha=.75, size=3) + geom_point(col = '#ff5500', alpha = .5, size = 3) + labs(x = 'Observed y', y = 'Expected y') + - theme_trueMinimal() + + theme_clean() + theme( axis.title.x = element_text(color = 'gray25'), axis.title.y = element_text(color = 'gray25'), @@ -304,58 +312,85 @@ Next, I show density plots for a random sample of 20 of the replicated data sets ```{r posteriorPredictiveIndividually, echo=FALSE, out.width='500px'} -yRepSample = yRep[,sample(1:nsims, 20)] -# gdat = melt(yRepSample); colnames(gdat) = c('n', 'nsim', 'yRep') -gdat = data.frame(yRepSample) %>% - rename_all(stringr::str_replace, pattern='X', replacement='Sim ') %>% - gather(key=nsim, value=yRep) %>% - group_by(nsim) %>% - mutate(N=1:n()) %>% +yRepSample = yRep[, sample(1:nsims, 20)] + +gdat = data.frame(yRepSample) %>% + rename_all(stringr::str_replace, + pattern = 'X', + replacement = 'Sim ') %>% + pivot_longer(everything(), names_to = 'nsim', values_to = 'yRep') %>% + group_by(nsim) %>% + mutate(N = 1:n()) %>% ungroup() -ggplot(aes(x=yRep), data=gdat) + - stat_density(aes(x=y), size=1, fill='gray90', data.frame(y=y)) + - stat_density(aes(group=as.factor(nsim), color=as.factor(nsim)), - alpha=.25, show.legend=F, geom='line', position='dodge') + - # scale_color_discrete() - labs(x='', y='') + - theme_trueMinimal() + - theme(axis.text.y=element_blank(), - axis.ticks.y=element_blank(), - plot.background = element_rect(fill = "transparent",colour = NA)) + +ggplot(aes(x = yRep), data = gdat) + + stat_density(aes(x = y), size = 1, fill = 'gray90', tibble(y = y)) + + stat_density( + aes(group = as.factor(nsim)), + color = alpha('#ff5500', .05), + alpha = .25, + geom = 'line', + show.legend = FALSE, + position = position_dodge() + ) + + labs(x = '', y = '') + + theme_clean() + + theme( + axis.text.y = element_blank(), + axis.ticks.y = element_blank(), + plot.background = element_rect(fill = "transparent", colour = NA) + ) # ggsave('img/yRepDensity.svg', bg='transparent') # marginal distribution check for each y as in BDA 6.5 -# ggplot(aes(x=yRep), data=gdat) + -# # stat_density(aes(x=y), size=1, fill='gray90') + -# stat_density(aes(group=as.factor(N), color=as.factor(N)), -# alpha=.5, show.legend=F, geom='line', position='dodge') + -# geom_vline(aes(xintercept=quantile(y)[3])) + -# labs(x='', y='') + -# theme_trueMinimal() + -# theme(axis.text.y=element_blank(), -# axis.ticks.y=element_blank()) +# ggplot(aes(x = yRep), data = gdat) + +# # stat_density(aes(x=y), size=1, fill='gray90') + +# stat_density( +# aes(group = as.factor(N), color = as.factor(N)), +# alpha = .5, +# show.legend = FALSE, +# geom = 'line', +# position = 'dodge' +# ) + +# geom_vline(aes(xintercept = quantile(y)[3])) + +# labs(x = '', y = '') + +# theme_clean() + +# theme(axis.text.y = element_blank(), +# axis.ticks.y = element_blank()) # yq = round(seq(1,250, length=5)) # rough quantiles # yq = c(50,125,200) -yRepSample = yRep[,sample(1:nsims, 200)] +yRepSample = yRep[, sample(1:nsims, 200)] yq = 100 -gdat = data.frame(yRepSample) %>% - rename_all(stringr::str_replace, pattern='X', replacement='Sim ') %>% - gather(key=nsim, value=yRep) %>% - group_by(nsim) %>% - mutate(N=1:n()) %>% + +gdat = data.frame(yRepSample) %>% + rename_all(stringr::str_replace, + pattern = 'X', + replacement = 'Sim ') %>% + pivot_longer(everything(), names_to = 'nsim', values_to = 'yRep') %>% + group_by(nsim) %>% + mutate(N = 1:n()) %>% ungroup() %>% filter(N %in% yq) -ggplot(aes(x=yRep), data=gdat) + - geom_vline(aes(xintercept=sort(y)[yq]), alpha=.5) + - stat_density(aes(group=as.factor(N)), color='#ff5500', - alpha=.85, show.legend=F, geom='line', position='dodge') + - labs(x='', y='') + - theme_trueMinimal() + - theme(axis.text.y=element_blank(), - axis.ticks.y=element_blank(), - plot.background = element_rect(fill = "transparent",colour = NA)) + +ggplot(aes(x = yRep), data = gdat) + + geom_vline(aes(xintercept = sort(y)[yq]), alpha = .5) + + stat_density( + aes(group = as.factor(N)), + color = '#ff5500', + alpha = .85, + show.legend = FALSE, + geom = 'line', + position = 'dodge' + ) + + labs(x = '', y = '') + + theme_clean() + + theme( + axis.text.y = element_blank(), + axis.ticks.y = element_blank(), + plot.background = element_rect(fill = "transparent", colour = NA) + ) # ggsave('img/posteriorPredictiveFittedY.svg', bg='transparent') ``` @@ -372,7 +407,7 @@ fits = sapply(1:nsims, \(s) X %*% betas[s,]) realizedResids = sapply(1:nsims, \(s) rnorm(250, fits[,s], sigmas[s]) - fits[,s]) -# gdat = melt(realizedResids); colnames(gdat) = c('n', 'nsim', 'residual') + gdat = data.frame(realizedResids) %>% rename_all(stringr::str_replace, pattern = 'X', @@ -387,20 +422,20 @@ gdat$minres = rep(apply(realizedResids, 1, min), 1000) gdat$maxres = rep(apply(realizedResids, 1, max), 1000) # plot 6.11a -ggplot(aes(x = fit, y = residual), data = gdat %>% slice(1:250)) + +ggplot(aes(x = fit, y = residual), data = gdat %>% dplyr::slice(1:250)) + # geom_linerange(aes(ymin = minres, ymax = maxres), alpha = .1)+ - geom_hline(aes(yintercept = 0), col = 'darkred', alpha = .25) + + geom_hline(aes(yintercept = 0), alpha = .25) + geom_point(aes(ymin = minres, ymax = maxres), color = '#FF5500', alpha = .85) + scale_x_continuous(breaks = c(-3, 0, 3, 6, 9, 12)) + labs(x = 'Expected y', y = 'Realized Residual') + - theme_trueMinimal() + + theme_clean() + theme( - axis.title.x = element_text(size = 15), - axis.title.y = element_text(size = 15), - axis.text.y = element_blank(), - axis.ticks.y = element_blank(), + axis.title.x = element_text(size = 15), + axis.title.y = element_text(size = 15), + axis.text.y = element_blank(), + axis.ticks.y = element_blank(), plot.background = element_rect(fill = "transparent", colour = NA) ) @@ -415,12 +450,12 @@ avgresidRep = rowMeans(yRep - fits) ggplot(aes(x = avgfits, y = avgresidRep), data = data.frame(avgfits, avgresidRep)) + geom_point(alpha = .85, color = '#FF5500') + labs(x = 'Average Expected y', y = 'Average Realized Residual') + - theme_trueMinimal() + + theme_clean() + theme( - axis.title.x = element_text(size = 15), - axis.title.y = element_text(size = 15), - axis.text.y = element_blank(), - axis.ticks.y = element_blank(), + axis.title.x = element_text(size = 15), + axis.title.y = element_text(size = 15), + axis.text.y = element_blank(), + axis.ticks.y = element_blank(), plot.background = element_rect(fill = "transparent", colour = NA) ) diff --git a/docs/404.html b/docs/404.html new file mode 100644 index 0000000..eb07774 --- /dev/null +++ b/docs/404.html @@ -0,0 +1,410 @@ + + + + + + + Page not found | Bayesian Basics + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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