### Install brms Development Version from GitHub

Source: https://github.com/paul-buerkner/brms/blob/master/README.md

Install the latest developmental version of brms directly from GitHub. Ensure the 'remotes' package is installed first if you don't have it.

```r
if (!requireNamespace("remotes")) {
  install.packages("remotes")
}
remotes::install_github("paul-buerkner/brms")
```

--------------------------------

### Basic BRMS Phylogenetic Model Setup

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_phylogenetics.html

This snippet shows the basic setup for a phylogenetic generalized linear mixed-effects model using BRMS. It requires the 'brms' and 'ape' packages and a phylogenetic tree object.

```R
library(brms)
library(ape)

# Load your phylogenetic tree (e.g., from a Nexus file)
tree <- read.nexus("path/to/your/tree.nex")

# Define your model formula (replace with your actual model)
# Example: a simple linear model with a phylogenetic random effect
formula <- bf(trait ~ 1 + predictor + (1 | gr(phylo, cov = V)),
                sigma ~ 1 + predictor,
                family = gaussian())

# Fit the model
fit <- brm(formula, data = your_data, data2 = list(V = vcv(tree)),
           prior = c(prior("normal(0, 1)", class = "b"),
                     prior("cauchy(0, 1)", class = "sd"),
                     prior("normal(0, 1)", class = "Intercept"),
                     prior("normal(0, 1)", class = "sigma")))

```

--------------------------------

### BRMS Threading Example

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_threading.html

This is a general example related to BRMS threading. It might demonstrate a specific pattern or utility function used for managing threads.

```java
public class BrmsThreading {

    public static void main(String[] args) {
        // Example of creating and starting a thread
        Thread thread = new Thread(() -> {
            System.out.println("Thread is running...");
            // Thread logic here
        });
        thread.start();

        try {
            // Wait for the thread to finish
            thread.join();
            System.out.println("Thread finished.");
        } catch (InterruptedException e) {
            Thread.currentThread().interrupt();
            System.err.println("Thread interrupted: " + e.getMessage());
        }
    }
}
```

--------------------------------

### BRMS Synchronization Example

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_threading.html

Demonstrates synchronization mechanisms used in BRMS to prevent race conditions and ensure data consistency between threads.

```java
public class BrmsSynchronization {
    private int counter = 0;

    public synchronized void incrementCounter() {
        counter++;
        System.out.println(Thread.currentThread().getName() + " incremented counter to " + counter);
    }

    public static void main(String[] args) {
        BrmsSynchronization sync = new BrmsSynchronization();

        Thread t1 = new Thread(() -> {
            for (int i = 0; i < 5; i++) {
                sync.incrementCounter();
            }
        }, "Thread-1");

        Thread t2 = new Thread(() -> {
            for (int i = 0; i < 5; i++) {
                sync.incrementCounter();
            }
        }, "Thread-2");

        t1.start();
        t2.start();
    }
}
```

--------------------------------

### Nonlinear Model Example (Gompertz Growth)

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_nonlinear.html

Example of fitting a Gompertz growth model. This model is also used for growth curves but has a different shape compared to logistic growth.

```R
fit_gompertz <- brm(
  bf(y ~ a * exp(-b * exp(-c * x))),
  data = df_gompertz,
  family = gaussian(),
  prior = c(
    prior("normal", nlpar = "a"),
    prior("normal", nlpar = "b"),
    prior("normal", nlpar = "c")
  ),
  chains = 4,
  iter = 2000,
  cores = 4
)
```

--------------------------------

### Nonlinear Model Example (Michaelis-Menten Kinetics)

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_nonlinear.html

Example of fitting a Michaelis-Menten model, commonly used in enzyme kinetics. It describes the rate of enzymatic reactions.

```R
fit_michaelis_menten <- brm(
  bf(y ~ (Vmax * x) / (Km + x)),
  data = df_mm,
  family = gaussian(),
  prior = c(
    prior("normal", nlpar = "Vmax"),
    prior("normal", nlpar = "Km")
  ),
  chains = 4,
  iter = 2000,
  cores = 4
)
```

--------------------------------

### Nonlinear Model Example (Logistic Growth)

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_nonlinear.html

Example of fitting a logistic growth model. This model is suitable for data that exhibits an S-shaped growth curve.

```R
fit_logistic <- brm(
  bf(y ~ a / (1 + exp(-(b * (x - c))))),
  data = df_logistic,
  family = gaussian(),
  prior = c(
    prior("normal", nlpar = "a"),
    prior("normal", nlpar = "b"),
    prior("normal", nlpar = "c")
  ),
  chains = 4,
  iter = 2000,
  cores = 4
)
```

--------------------------------

### Model Comparison with Different Phylogenetic Structures

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_phylogenetics.html

This example shows how to compare models with different phylogenetic structures (e.g., Brownian motion vs. Pagel's lambda) using information criteria like LOO or WAIC.

```R
# Fit a model with Brownian motion (default if V is provided)
fit_bm <- brm(bf(trait ~ 1 + predictor + (1 | gr(phylo, cov = V))), 
                data = your_data, data2 = list(V = vcv(tree)),
                family = gaussian())

# Fit a model with Pagel's lambda
fit_lambda <- brm(bf(trait ~ 1 + predictor + (1 | pagel(phylo, cov = V))), 
                  data = your_data, data2 = list(V = vcv(tree)),
                  family = gaussian())

# Compare models using LOO cross-validation
loo_bm <- loo(fit_bm)
loo_lambda <- loo(fit_lambda)

# Print comparison
print(loo_bm)
print(loo_lambda)

# Or use a comparison function
# compare(fit_bm, fit_lambda)

```

--------------------------------

### Fit a Simple BRMS Model

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_phylogenetics.html

This snippet demonstrates how to fit a basic Bayesian regression model using the brms package. Ensure the 'brms' package is installed and loaded.

```R
library(brms)
simple_model <- brm(Y ~ X + (1|group), data = data)

```

--------------------------------

### Multilevel Poisson Model with BRMS

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_threading.html

Example of fitting a multilevel Poisson model using brms. This snippet demonstrates setting up priors, specifying the family, and configuring threading for parallel execution.

```R
model_poisson <- brm(
  y ~ 1 + x1 + x2 + (1 | g),
  data = fake,
  family = poisson(),
  iter = 500, # short sampling to speedup example
  chains = 2,
  prior = prior(normal(0,1), class = b) +
    prior(constant(1), class = sd, group = g),
  backend = "cmdstanr",
  threads = threading(4)
)
```

--------------------------------

### Load Phylogenetic Data and Prepare Covariance Matrix

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_phylogenetics.html

Loads a phylogenetic tree and associated data, then computes the phylogenetic covariance matrix. Ensure the 'ape' package is installed.

```r
phylo <- ape::read.nexus("https://paul-buerkner.github.io/data/phylo.nex")
data_simple <- read.table(
  "https://paul-buerkner.github.io/data/data_simple.txt",
  header = TRUE
)
head(data_simple)
A <- ape::vcv.phylo(phylo)
```

--------------------------------

### Fit a nonlinear model with a logistic growth function

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_nonlinear.html

Example of fitting a nonlinear model using the logistic growth function. This is useful for modeling processes that exhibit saturation.

```R
brms_nl_logistic <- brm(
  Y ~ nlf(a / (1 + exp(-(b + c * X))), nlpars = c(a, b, c)),
  data = data_nl,
  family = gaussian()
)
```

--------------------------------

### Fit a nonlinear model with a power law function

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_nonlinear.html

Example of fitting a nonlinear model using a power law function. This is suitable for relationships where one variable scales with a power of another.

```R
brms_nl_power_law <- brm(
  Y ~ nl(a * X^b, nlpars = c(a, b)),
  data = data_nl,
  family = gaussian()
)
```

--------------------------------

### Install brms from CRAN

Source: https://github.com/paul-buerkner/brms/blob/master/README.md

Use this command to install the latest stable release of the brms package from the Comprehensive R Archive Network (CRAN).

```r
install.packages("brms")
```

--------------------------------

### Load and Inspect BTdata

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_multivariate.html

Loads the BTdata dataset and displays the first few rows to show its structure.

```r
data("BTdata", package = "MCMCglmm")
head(BTdata)
```

--------------------------------

### Benchmark Threading Configuration

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_threading.html

Configures chunking for benchmarking threading performance by calculating grainsize based on the number of chunks. Uses a small number of iterations for quick testing.

```r
chunking_bench <- transform(
    data.frame(chunks = 4^(0:3)),
    grainsize = ceiling(N / chunks)
)

iter_test <- c(10, 20, 40)  # very short test runs
scaling_chunking <- benchmark_threading(
  model_poisson,
  cores = 1,
  grainsize = chunking_bench$grainsize,  # test various grainsizes
  iter = iter_test,
  static = TRUE  # with static partitioner
)

# run as reference the model *without* reduce_sum
ref <- benchmark_reference(model_poisson, iter_test)

# for additional data munging please refer to the appendix
```

--------------------------------

### Plotting Model Fit with Regex

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_missings.html

Use this snippet to visualize the convergence of model parameters, specifically focusing on parameters matching a regular expression. This is useful for diagnosing potential convergence issues.

```R
plot(fit_imp1, variable = "^b", regex = TRUE)
```

--------------------------------

### Multivariate Normal Distribution

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_multivariate.html

Example of defining and sampling from a multivariate normal distribution.

```R
library(brms)

# Define a multivariate normal distribution
# mu: mean vector
# Sigma: covariance matrix
mu <- c(0, 0)
Sigma <- matrix(c(1, 0.5, 0.5, 1), nrow = 2)

# Sample from the distribution
set.seed(123)
nsamples <- 1000
posterior_samples <- rmvnorm(n = nsamples, mean = mu, sigma = Sigma)

# Plot the samples (optional)
plot(posterior_samples, pch = '.', xlab = 'X1', ylab = 'X2')

```

--------------------------------

### Fit a nonlinear model with a log-logistic function

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_nonlinear.html

Example of fitting a nonlinear model using the log-logistic function. This is a common choice for dose-response curves.

```R
brms_nl_log_logistic <- brm(
  Y ~ nl(a / (1 + exp(-(b + c * log(X)))), nlpars = c(a, b, c)),
  data = data_nl,
  family = gaussian()
)
```

--------------------------------

### Add City Identifier and City-Related Variation

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_monotonic.html

Adds a 'city' identifier to the data and introduces city-specific variation to the 'ls' variable. This setup is for multilevel modeling.

```R
dat$city <- rep(1:10, each = 10)
var_city <- rnorm(10, sd = 10)
dat$ls <- dat$ls + var_city[dat$city]
```

--------------------------------

### Running a BRMS model serially

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_threading.html

This snippet shows how to run a BRMS model serially using the cmdstanr backend. It serves as a baseline for comparison when implementing parallelization.

```R
fit_serial <- brm(
  count ~ zAge + zBase * Trt + (1|patient),
  data = epilepsy,
  family = poisson(),
  chains = 4, cores = 4, backend = "cmdstanr"
)
```

--------------------------------

### Fit a nonlinear model with a von Bertalanffy growth function

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_nonlinear.html

Demonstrates fitting a nonlinear model using the von Bertalanffy growth function, commonly used in fisheries science to model fish growth.

```R
brms_nl_von_bertalanffy <- brm(
  Y ~ nl(a * (1 - exp(-b * (X - c))), nlpars = c(a, b, c)),
  data = data_nl,
  family = gaussian()
)
```

--------------------------------

### Fit a nonlinear model with a linear function

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_nonlinear.html

Example of fitting a nonlinear model using a simple linear function. This can be used as a baseline or when the relationship is approximately linear.

```R
brms_nl_linear <- brm(
  Y ~ nl(a + b * X, nlpars = c(a, b)),
  data = data_nl,
  family = gaussian()
)
```

--------------------------------

### Load and Prepare Fisher's z Data for Meta-Analysis

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_phylogenetics.html

Loads Fisher's z-transformed correlation coefficients and sample sizes from a URL and prepares the data for a meta-analytic model. It adds an observation index and calculates the sampling variance.

```R
data_fisher <- read.table(
  "https://paul-buerkner.github.io/data/data_effect.txt",
  header = TRUE
)
data_fisher$obs <- 1:nrow(data_fisher)
head(data_fisher)
```

--------------------------------

### Fit a nonlinear model with a Gompertz growth function

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_nonlinear.html

Demonstrates fitting a nonlinear model using the Gompertz growth function. This function is often used in growth studies.

```R
brms_nl_gompertz <- brm(
  Y ~ nlf(a * exp(-b * exp(c * X)), nlpars = c(a, b, c)),
  data = data_nl,
  family = gaussian()
)
```

--------------------------------

### Bayesian Phylogenetic Tree Inference

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_phylogenetics.html

Example of inferring a phylogenetic tree using BRMS. Requires the 'brms' and 'ape' packages. Ensure your data is in a format compatible with phylogenetic analysis.

```R
library(brms)
library(ape)

# Assuming 'phylo_data' is a phylogenetic tree object (e.g., from ape)
# and 'response_variable' is your trait data

# Define the phylogenetic generalized linear mixed-effects model
# formula: response_variable ~ predictor_variable + (1 | gr(phylo_nodes, cov = phylo_cor))
# where phylo_nodes and phylo_cor are derived from the phylogenetic tree

# Example formula structure (replace with your actual variables and tree structure)
# model_formula <- bf(response_variable ~ predictor_variable, 
#                     sigma ~ gr(phylo_nodes, cov = phylo_cor))

# Fit the model
# fit <- brm(model_formula, data = your_data_frame, family = gaussian(), 
#            data2 = list(phylo_cor = vcv(phylo_data)))

# For demonstration, a placeholder model structure:
fit <- brm(bf(y ~ x + (1 | gr(node, cov = C))), 
           data = data.frame(y = rnorm(10), x = rnorm(10)), 
           data2 = list(C = diag(10)), 
           family = gaussian(), 
           cores = 4)

summary(fit)
plot(fit)
```

--------------------------------

### Fit Custom Beta-Binomial Model

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_customfamilies.html

Fits a brms model using the custom beta-binomial family. This example demonstrates how to specify the custom family and Stan variables when fitting the model.

```R
fit2 <- brm(
  incidence | vint(size) ~ period + (1|herd), data = cbpp,
  family = beta_binomial2, stanvars = stanvars
)
```

--------------------------------

### Fit Non-linear Model

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_nonlinear.html

Fit a non-linear model using brms. This is useful for capturing complex relationships between variables where a linear model is insufficient. Ensure the brms package is installed and loaded.

```R
fit1 <- brm(bf(y ~ x, nl = TRUE), data = dat1)
```

--------------------------------

### MathJax Initialization Script

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_threading.html

This JavaScript snippet dynamically loads the MathJax library, which is used for rendering mathematical formulas in web pages. It appends the script tag to the document's head.

```javascript
(function () { var script = document.createElement("script"); script.type = "text/javascript"; script.src = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"; document.getElementsByTagName("head")[0].appendChild(script); })();
```

--------------------------------

### Update Fitted brms Model Without Recompilation

Source: https://github.com/paul-buerkner/brms/blob/master/README.md

Use the `update` method on an existing fitted brms model object to rerun it, for example with more draws, without recompiling the Stan code.

```r
# Assuming 'fit' is a fitted brms model object
update(fit)
```

--------------------------------

### Fit Multivariate Model and Summarize

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_multivariate.html

Fits the defined multivariate model using brm, adds the 'loo' criterion, and prints a summary of the results.

```r
fit1 <- brm(bform1, data = BTdata, chains = 2, cores = 2)

fit1 <- add_criterion(fit1, "loo")
summary(fit1)
```

--------------------------------

### Load and Inspect NHANES Data

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_missings.html

Loads the NHANES dataset from the 'mice' package and displays the first few rows to show the structure and presence of missing values.

```r
data("nhanes", package = "mice")
head(nhanes)
```

--------------------------------

### Fit Multilevel Model with Monotonic Effects

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_monotonic.html

Fits a multilevel model using brms, allowing the intercept and the monotonic effect of income to vary by city. Ensure the brms package is installed and loaded.

```R
fit6 <- brm(ls ~ mo(income)*age + (mo(income) | city), data = dat)
```

--------------------------------

### Simulate Data for Smooth Term Analysis

Source: https://github.com/paul-buerkner/brms/blob/master/doc/brms_distreg.html

Simulates data suitable for analyzing smooth terms in regression models using the mgcv package.

```r
dat_smooth <- mgcv::gamSim(eg = 6, n = 200, scale = 2, verbose = FALSE)
```