Develop an MH algorithm for the dichotomous probit model.

1. Develop an MH algorithm for the dichotomous probit model.

2. Develop a rejection sampler for simulating from a truncated normal distribution using a triangular density, rather than a uniform density, as discussed in Section 8.1.3.

3. Starting with the Gibbs sampler shown earlier for the dichotomous probit model, modify it to make it a hybridized Gibbs-MH algorithm. That is, continue to sample the latent data at each iteration (a Gibbs sampling step), but update the parameters using MH steps.

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