Question

Consider the GLM for the Poisson exponential family. Assume for simplicity that n=1. What is the log-likelihood function \ell (\mathbf Y,\mathbb {X},{\boldsymbol \beta }) with the canonical link function?

Use X for X_1, Y for Y_1, and + c for the constant term. Do not use \phi and instead use the actual value of \phi for the Poisson exponential family. To input a dot product a^ T b, write it as a*b.

\ell (\mathbf Y,\mathbb {X},{\boldsymbol \beta })=
GPT 3.5
Y*log(X*beta)-X*beta-log(Y!)+Y*log(1)-log(1)

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