add assignments2023 folder

_quarto.yml

@@ -5,6 +5,7 @@ project:
   post-render:
     - quarto render --profile public assignments
     - cp -r assignments/assignments _site
+    - cp -r assignments2023 _site
 
 website:
   title: "Bayesian Data Analysis course"

assignments2023/additional_files/assignment6/linear_model.stan

@@ -0,0 +1,34 @@
+data {
+    // number of data points
+    int<lower=0> N; 
+    // covariate / predictor
+    vector[N] x; 
+    // observations
+    vector[N] y; 
+    // number of covariate values to make predictions at
+    int<lower=0> no_predictions;
+    // covariate values to make predictions at
+    vector[no_predictions] x_predictions; 
+}
+parameters {
+    // intercept
+    real alpha; 
+    // slope
+    real beta; 
+    // the standard deviation should be constrained to be positive
+    real<upper=0> sigma; 
+}
+transformed parameters {
+    // deterministic transformation of parameters and data
+    vector[N] mu = alpha + beta * x // linear model
+}
+model {
+    // observation model / likelihood
+    y ~ normal(mu, sigma); 
+}
+generated quantities {
+    // compute the means for the covariate values at which to make predictions
+    vector[no_predictions] mu_pred = alpha + beta * x_predictions;
+    // sample from the predictive distribution, a normal(mu_pred, sigma).
+    array[no_predictions] real y_pred = normal_rng(to_array_1d(mu), sigma);
+}

assignments2023/additional_files/assignment7/chickens_separate.stan

@@ -0,0 +1,46 @@
+data {
+  int<lower=0> N_observations;
+  int<lower=0> N_diets;
+  array[N_observations] int diet_idx; // Pair observations to their diets.
+  vector[N_observations] weight;
+}
+
+parameters {
+  // Average weight of chicks with a given diet.
+  vector[N_diets] mean_diet;
+
+  // Standard deviation of weights observed among chicks sharing a diet.
+  vector<lower=0>[N_diets] sd_diet;
+}
+
+model {
+  // Priors
+  // These look bad. I need to think about these again.
+
+  for (diet in 1:N_diets) {
+    mean_diet[diet] ~ normal(0, 10);
+    sd_diet[diet] ~ exponential(.02);
+  }
+
+  // Likelihood
+  for (obs in 1:N_observations) {
+    weight[obs] ~ normal(mean_diet[diet_idx[obs]], sd_diet[diet_idx[obs]]);
+  }
+
+  // Best practice would be to write the likelihood without the for loop as:
+  // weight ~ normal(mean_diet[diet_idx], sd_diet[diet_idx]);
+}
+
+generated quantities {
+  real weight_pred;
+  real mean_five;
+  // The below is just there to make the plotting in the template work with the "wrong model". 
+  real sd_diets = sd_diet[4];
+
+  // Sample from the (posterior) predictive distribution of the fourth diet.
+  weight_pred = normal_rng(mean_diet[4], sd_diet[4]);
+
+  // Construct samples of the mean of the fifth diet.
+  // We only have the prior...
+  mean_five = normal_rng(0, 10);
+}