# Difference Between AIC and BIC

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## Introduction

AIC and BIC are related to statistics. They are two separate approaches to selecting a model. The full form of AIC is Akaike Information Criteria. It is a mathematical method used in statistics where different possible models are brought in, and AIC is used to find out which one of the models fits well with the data from where it has been generated. The relative quality of a statistical model is measured by AIC for a given data set. The full form of BIC is Bayesian Information Criteria. BIC is also like AIC, a model selection criterion, but it is used to select from among a finite set of models. BIC is closely related to AIC, but they also have significant differences.

## AIC vs BIC

AIC and BIC are both related to statistics. They are separate approaches or criteria for model selection in statistics. The full form of AIC is Akaike Information Criteria. In 1971, a statistician, named Hirotugu Akaike first announced this model after which it came to be known after his last name. He published the first formal paper in the year 1974 which was cited more than 14,000 times. AIC is used to find out how well an estimated statistical model fits with the data from where it has been generated. The full form of BIC is Bayesian Information Criteria. It is also a criterion for model selection but it is used to select from among a finite set of models. Partially, it is based on the function of likelihood. In 1978, Gideon E. Schwarz developed this theory of BIC. It is also called Schwarz Information Criterion and is shortly known as SIC, SBC, or SBIC.

## What is AIC?

The full form of AIC is Akaike Information Criteria. It is a criterion for model selection like BIC. This criterion was first developed by a statistician named Hirotugu Akaike in the year 1971. In 1974, he published his first formal on this, which was cited for more than 14,000 times. It is a mathematical method used for evaluation in the field of statistics. There are different models present before a statistician, and he uses AIC to evaluate and find out from all these models which model perfectly fits with the data and how perfectly it fits with the data from where it was generated. The AIC scores of multiple possible models are calculated and compared, and then one can find out which model fits well with the data.

• The AIC is a model's integrated probability purpose. When a model has a lower AIC, statisticians estimate that it is more similar with accuracy. AIC is useful when the conclusion is a false negative. In AIC, if one wants to select a true model, then the probability has to be less than 1. AIC provides unpredictable and complex results, and the main reason for this is because AIC’s dimension is infinite and much higher in number. The most optimal coverage can be calculated in AIC with the help of assumptions. The terms of penalty in the case of AIC are very few. While presuming in AIC, many researchers believe that it has the minimum number of risks. The reason for this is because n here is much larger than k2. The formula for AIC calculation is AIC =2k-2ln(lá´§). When a statistician is testing a particular hypothesis, he might gather data on variables he is uncertain about. This happens especially while exploring a novel idea. He wants to find out from among his measured independent variables which one explains the dependent variable's variation. It can be found by creating a set of models where each one of them will contain a different combination of the measured independent variables.
• The different combinations should be based on the statistician's knowledge of the study system and his experimental design. Parameters that are not logically connected should not be used here. When the various models are created, AIC can be used to compare them. Models having lower AIC scores are better and are more likely to fit with the data, after which the model that most perfectly fits with the data is chosen. Models using more parameters are penalized by AIC. However, if a situation arises when the same amount of variation is explained by two models then the model having the lower AIC score due to less use of parameters will perfectly fit with the data.

## What is BIC?

The full form of BIC is Bayesian Information Criteria. Like AIC, it is also a model selection criterion, but here the model is selected from among a finite set of models. Partially, it is based on the likelihood function, and it is to some extent related to AIC, but still, it has its purposes. After finding out the accuracy of the model, BIC is used to evaluate the purpose of the possibility based on a specific Bayesian structure. A model is acknowledged and is further expected to be the precise model when there is a lower BIC.

This theory of BIC was founded by a man named Gideon E. Schwarz in the year 1978. It is also called Schwarz Information Criterion, and shortly it is known as SIC, SBIC, and SBC. In the case of BIC, the probability has to be exactly 1 to select a true model. BIC is chosen as the model selection criteria when the outcome needs to be a false positive. There are larger penalty terms in the case of BIC. BIC has a finite and lower dimension than that of AIC, which enables it to give easy and consistent results. The optimal coverage that is calculated in BIC through assumptions is less than AIC, according to scientists. This is the reason why there are more risks in BIC than in AIC because n here can be defined. The formula for calculating BIC is BIC = k ln(n)-2ln(Lá´§). A fact to be remembered about BIC is that it gives more penalties than AIC when the model is complex. Simpler and easier models have a maximum probability of fitting well with the new data so, simplicity is preferred in the field of model selection.

The problems with complex models are that there is the risk of capturing noise in the data and of overfitting. So, models having a greater number of parameters are penalized by BIC, making it very similar to AIC, but still, they are not the same. Some of their characteristics may match, but still, they are different. Large sample sizes give more information regarding the underlying population, but this means complexity in models increases and hence increases in penalty by BIC. This makes sure that the chosen model is absolutely simple so that there is no chance of overcomplicating the representation of data. This is the reason why subjects, where there is extensive data to be collected, BIC is beneficial. Moreover, BIC is a very versatile approach to model selection and consists of a wide variety of models including both linear and nonlinear models.

## Major Differences Between AIC and BIC (In Points)

• AIC and BIC are both related to statistics. They are both different criteria or approaches to model selection. The full form of AIC is Akaike Information Criteria. This theory was introduced by a statistician named Hirotugu Akaike in the year 1971. AIC is a mathematical method used in statistics. There are multiple models present before a data, and AIC is used to find out which one of the models fits perfectly with the data from where it came from. The AIC scores of multiple possible models are calculated and compared, and then one can find out which model fits well with the data. The full form of BIC is Bayesian Information Criteria. This theory was developed by a man named Gideon E. Schwarz. It is also known as the Schwarz Information Criterion and is shortly called SIC, SBIC, and SBC. BIC is also a model selection criterion like AIC, but it selects from a finite number of models and finds out which model perfectly fits with the data.
•  AIC, developed by Hirotugu Akaike, has a relatively high and infinite dimension. This leads to unpredictable and complex results in AIC. BIC, on the other hand, which Gideon E. Schwarz develops, has a finite and lower dimension than that of AIC, which is the reason why BIC can give easy and consistent results. Moreover, AIC can calculate the most optimal coverage with the help of assumptions, whereas the optimal coverage is less in the case of BIC, which is calculated through assumptions.
• AIC is chosen as the criteria for model selection when the outcome is in false negative but when the outcome is in false positive then BIC is chosen as the model selection criteria. Moreover, in AIC, the terms of the penalty are not much, but in BIC, there are larger penalty terms. Models having lower AIC scores are better and are more likely to fit with the data, but models using more parameters are penalized by AIC even if the probability of penalty is much less here. So, models having less use of parameters have lower AIC scores and are more likely to fit with the data. BIC, on the other hand, penalizes the model when the model is complex. Simpler and easier models have a maximum probability of fitting well with the data so, simplicity is preferred in the field of model selection in BIC. Complex models lead to the risk of capturing noise in the data and of overfitting.
• In the case of AIC, the probability has to be less than 1 if one wants to select the true model but in the case of BIC, the probability has to be exactly 1 if one wants to select the true model. It is also to be remembered that the risk is minimal in the case of AIC, but there are maximum risks in the case of BIC. This is because there are fewer terms of penalty in AIC than in BIC. The formula for calculating AIC is AIC=2k-2ln(lá´§), and the formula for calculating BIC is BIC= k ln(n)-2ln(L).

## Conclusion

Hence, AIC and BIC are two separate criteria for model selection in statistics. AIC stands for Akaike Information Criteria, and BIC stands for Bayesian Information Criteria. AIC is a criterion used for model selection. When there are multiple models AIC is used to find out which model perfectly fits with the data from where it is generated. BIC is also closely related to AIC but is still significantly different. BIC is also a criterion like AIC used for model selection, but the difference is that it selects from a finite number of models and finds out which model fits best with the data.

• https://www.scribbr.com/statistics/akaike-information-criterion/
• https://medium.com/@analyttica/what-is-bayesian-information-criterion-bic-b3396a894be6