Likelihood Principle is a statistical principle which states that the best estimate of a parameter is the value that maximizes the likelihood function. This principle is commonly used to estimate parameters for statistical models such as logistic regression, linear regression, and Poisson regression. The likelihood principle is a fundamental tool in the fields of statistics, probability theory, and machine learning.

The Likelihood Principle can be stated as follows: “Given a set of data, the best estimates for the parameters of a model should be those that maximize the likelihood function”. The likelihood function is a function of the parameters that describes the probability of the observed data given the model. The likelihood principle states that the parameters which maximize the likelihood function should be the ones used to estimate the values of the parameters.

The Likelihood Principle is a useful tool in many areas of statistics and machine learning. It can be used to estimate parameters for models such as logistic regression, linear regression, and Poisson regression. It can also be used to compare different models to determine which one best fits the data. The principle is also used in Bayesian inference to calculate the posterior probability distribution.

The Likelihood Principle is an important tool in statistics and machine learning because it allows us to estimate parameters with a minimum amount of data. It is also a useful tool for comparing different models and determining which one best fits the data.

References

Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference and Prediction. New York, NY: Springer.

Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2014). Bayesian Data Analysis (3rd ed.). Boca Raton, FL: Chapman & Hall/CRC.

Gourieroux, C., & Monfort, A. (1995). Statistics and Econometric Models (Vol. 1). Cambridge, MA: Cambridge University Press.

Murphy, K. P. (2012). Machine Learning: A Probabilistic Perspective. Cambridge, MA: MIT Press.