Maximum Likelihood Estimation for Gaussian Distribution
Statistical Inference DS practice problem on Onlearn.
Difficulty: easy.
Topics: Maximum Likelihood Estimation for Gaussian Distribution, Log-Likelihood Function, Partial Derivatives, Fisher Information, Hessian Matrix, Stationary Points, Probability Theory, Statistical Inference, Calculus, Optimization Theory, Linear Algebra, Probability Density Functions, Parameter Estimation, Multivariate Calculus, Iterative Numerical Methods, Matrix Decompositions.
Implement Maximum Likelihood Estimation (MLE) to estimate the parameters of a Gaussian (Normal) distribution from observed data. Given a 1D numpy array of observations assumed to come from a Gaussian distribution, compute the MLE estimates for the distribution's mean and variance parameters. Your function should take a numpy array of data points and return a tuple containing the estimated mean and variance. The MLE approach finds parameter values that maximize the probability of observing the given data. Note: The MLE estimate for variance differs from the commonly used unbiased sample variance estimator. Your implementation should return the true MLE estimates.