human
Write me a code to and the other steps required given the following:

A two-layer bayesian neural network with computational flow
given by D_X => D_H => D_H => D_Y where D_H is the number of
hidden units.
"""

def bnn(X, Y, layer_sizes):
    D_X, D_Y = X.shape[1], 1

    z = X
    for i, (D_in, D_out) in enumerate(zip(layer_sizes[:-1], layer_sizes[1:])):
        w = numpyro.sample(f"w{i}", dist.Normal(jnp.zeros((D_in, D_out)), jnp.ones((D_in, D_out))))  # D_X D_H
        z = jnp.tanh(jnp.matmul(z, w))  # N D_H  <= first layer of activations

    # sample final layer of weights and neural network output
    w_final = numpyro.sample(f"w_final", dist.Normal(jnp.zeros((D_out, D_Y)), jnp.ones((D_out, D_Y))))  # D_H D_Y
    z_final = jnp.matmul(z, w_final).squeeze(-1)  # N D_Y  <= output of the neural network

    # Bernoulli likelihood <= Binary classification
    Y = numpyro.sample("Y", dist.Bernoulli(logits=z_final), obs=Y)

def run_inference(model, rng_key, num_warmup=100, num_samples=100, num_chains=1, **kwargs):
    kernel = NUTS(model)
    mcmc = MCMC(kernel, num_warmup=num_warmup, num_samples=num_samples, num_chains=num_chains, progress_bar=False)
    mcmc.run(rng_key, **kwargs)
    return mcmc

def get_predictions(
    model, rng_key, samples, X, layer_sizes, num_warmup=100, num_samples=100, num_chains=1, **bnn_kwargs
):
    # helper function for prediction
    @jit
    def predict(samples, rng_key):
        model_ = handlers.substitute(handlers.seed(model, rng_key), samples)
        # note that Y will be sampled in the model because we pass Y=None here
        model_trace = (
            handlers.trace(model_).get_trace(X=X, Y=None, layer_sizes=layer_sizes, **bnn_kwargs)
            if bnn_kwargs
            else handlers.trace(model_).get_trace(X=X, Y=None, layer_sizes=layer_sizes)
        )
        return model_trace["Y"]["value"]

    # predict Y at inputs X
    keys = random.split(rng_key, num_samples * num_chains)
    predictions = vmap(predict, in_axes=(0, 0))(samples, keys)
    return predictions

def get_mean_predictions(predictions, threshold=0.5):
    #...
Given the above code, generate some markdown instructions for it.
assistant
#Here is code to and the other steps required.

As you can see, we have 4 categories in default that share a higher-order structure (the half-moons). However, in the pure data space, no single classifier will be able to do a good job here. Also, because we only have 50 data points in each class, a NN will likely have a hard time producing robust results. But let's actually test this.
Fit separate MLPs, one per task
First we fit one MLP per task/dataset. For details, see Thomas's blob post 
 on Bayesian Deep Learning.