The correct answer is D. computationally intense.
Maximum likelihood methods are a powerful tool for statistical inference, but they can be computationally expensive. This is because they require the calculation of the likelihood function, which can be a complex function of the parameters. In some cases, the likelihood function may not even be able to be calculated analytically, and numerical methods must be used. This can make maximum likelihood methods impractical for large datasets.
The other options are incorrect. Option A is incorrect because maximum likelihood methods are often quite complex. Option B is incorrect because maximum likelihood methods are not necessarily less complex than other statistical methods. Option C is incorrect because maximum likelihood methods are not necessarily less complex than other statistical methods.
Here is a brief explanation of each option:
- Option A: Mathematically less folded. This is incorrect because maximum likelihood methods are often quite complex. For example, the likelihood function for a Gaussian distribution is given by
$$L(\theta|x) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp \left( -\frac{(x-\mu)^2}{2\sigma^2} \right)$$
This is a complex function of the parameters $\mu$ and $\sigma^2$.
Option B: Mathematically less complex. This is incorrect because maximum likelihood methods are not necessarily less complex than other statistical methods. For example, the method of moments is a simpler statistical method than maximum likelihood.
Option C: Mathematically less complex. This is incorrect because maximum likelihood methods are not necessarily less complex than other statistical methods. For example, the method of moments is a simpler statistical method than maximum likelihood.
Option D: Computationally intense. This is the correct answer because maximum likelihood methods require the calculation of the likelihood function, which can be a complex function of the parameters. In some cases, the likelihood function may not even be able to be calculated analytically, and numerical methods must be used. This can make maximum likelihood methods impractical for large datasets.