Exact gradient of the beta-binomial log-likelihood function for theta using sums.

grad_theta_old calculates the value of the gradient of the beta-binomial log-likelihood function to theta at given data points via a number of sums, which is slow for high-value data but fast for low-value data. This function is called by grad_theta if necessary, and should not be called outside of this.

grad_theta_old(ms, ns, pi, theta)

Arguments

ms

Numeric vector. Vector of number of successes

ns

Numeric vector. Vector of number of trials

pi

Number. Probability of success; 0 >= pi >= 1

theta

Number. Dispersion parameter; 0 >= theta > +Inf

Value

A numeric vector of the same length as ms and ns, containing the gradient to theta in the give data points