# AIC vs BIC: Difference and Comparison

While solving a case study, a researcher encounters many predictors, possibilities, and interactions. That makes it intricate to select a model. With the help of different criteria for model selection, they can resolve those problems and estimate the precision.

The AIC and BIC are the two such criteria processes for evaluating a model. They consist of selective determinants for the aggregation of the considered variables. In 2002, Burnham and Anderson did a research study on both criteria.ย

## Key Takeaways

1. AIC and BIC are both measures used for model selection in statistical analysis.
2. AIC stands for Akaike Information Criterion, and BIC stands for Bayesian Information Criterion.
3. AIC penalizes model complexity less than BIC, which means that AIC may be preferred for smaller sample sizes, while BIC may be preferred for larger sample sizes.

## AIC vs BIC

AIC measures the relative quality of a statistical model for a given set of data. It is based on the likelihood function and the number of parameters in the model. BIC is a similar model based on Bayesian principles on complexity measure but places a greater penalty on models with more parameters.

AIC results in complex traits, whereas BIC has more finite dimensions and consistent attributes. The former is better for negative findings and the latter for positive ones.

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## What is AIC?

The model was first announced by statistician โHirotugu Akaikeโ in 1971. And the first formal paper was published by Akaike in 1974 and received more than 14,000 citations.

Akaike Information Criteria (AIC) evaluates a continual in addition to the corresponding interval among the factsโ undetermined, accurate, and justified probability.

It is the integrated probability purpose of the model. So that a lower AIC means a model is estimated to be more similar to the accuracy. For false-negative conclusions, it is useful.

Reaching a true model requires a probability of less than 1. The dimension of AIC is infinite and relatively high in number, because of which it provides unpredictable and complicated results.

It serves the most optimal coverage of assumptions. Its penalty terms are smaller. Many researchers believe it benefits with the minimum risks while presuming. Because here, n is larger than k2.

The AIC calculation is done with the following formula:ย

• AIC = 2k โ 2ln(L^)

## What is BIC?

Bayesian Information Criteria (BIC) is an evaluation of the purpose of the possibility, following the modelโs accuracy, under a particular Bayesian structure. So a lower BIC means that a model is acknowledged to be further anticipated as the precise model.

The theory was developed and published by Gideon E. Schwarz in 1978. Also, it is known as Schwarz Information Criterion, shortly SIC, SBIC, or SBC. To reach a true model, it requires a probability of exactly 1. For false-positive outcomes, it is helpful.ย

The penalty terms are substantial. Its dimension is finite that gives consistent and easy results. Scientists say that its optimal coverage is less than AIC for assumptions. That even sequences into maximum risk-taking. Because here, n is definable.

The BIC calculation is doneย  with the following formula:ย

• BIC = k ln(n) โ 2ln(L^)

The โBridge Criterionโ, BC, was developed by Jie Ding, Vahid Tarokh, and Yuhong Yang. The criterion was published on 20th June 2017 in IEEE Transactions on Information Theory. Its motive was to bridge the fundamental gap between AIC and BIC modules.

## Main Differences Between AIC and BIC

1. AIC is used in model selection for false-negative outcomes, whereas BIC is for false-positive.
2. The former has an infinite and relatively high dimension. On the contrary, the latter has finite.
3. The penalty term for the first is smaller. At the same time, the second one is substantial.
4. Akaike information criteria have complicated and unpredictable results. Conversely, the Bayesian information criterion has easy results with consistency.
5. AIC provides optimistic assumptions. At the same time, BIC coverages are less optimal assumptions.
6. Risk is minimized in AIC and is maximum in BIC.
7. The Akaike theory requires a probability of less than 1, and Bayesian needs exactly 1 to reach the true model.
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