Computes the log-likelihood for i.i.d. normal observations.
L(μ,σ²|x) = -n/2 log(2π) - n/2 log(σ²) - Σ(xᵢ-μ)²/(2σ²)
Usage
loglik_normal(mu, sigma, x)
Arguments
- mu
Mean parameter (value object)
- sigma
Standard deviation parameter (value object), must be positive
- x
Numeric vector of observations
Value
A value object representing the log-likelihood
Examples
if (FALSE) { # \dontrun{
x <- rnorm(100, mean = 5, sd = 2)
mu <- val(0)
sigma <- val(1)
ll <- loglik_normal(mu, sigma, x)
backward(ll)
grad(mu) # score for mu
} # }