China 
Africa 
Explore chapters and articles related to this topic
Model Selection
Published in Julian J. Faraway, Linear Models with Python, 2021
Many other criteria have been proposed. One well-known alternative is the Bayes information criterion (BIC) which replaces the 2p term in the AIC with plogn. BIC penalizes larger models more heavily and so will tend to prefer smaller models in comparison to AIC. AIC and BIC are often used as selection criteria for other types of models too. If we believe that there is a true model and we aim to choose it from a finite set of alternative models, BIC will choose the true model with probability approaching one as the sample size grows. On the other hand, suppose we do not believe in the true model but are willing to consider an increasing number of alternatives as our sample size grows. In this situation the AIC-selected model will tend to do as well as the best choice from those available. Unfortunately, these theories do not help much in deciding what to use in practice but there is some evidence to suggest that AIC is better for prediction problems.
A Single Time Series Model
Published in Yu Ding, Data Science for Wind Energy, 2019
uses the BIC for model selection. The default setting in auto.arima is AICc. We want to note that certain software packages, like these in R, count the variance estimate, σ^ε2, as a parameter estimated. Hence, the number of parameters in an ARMA(p, q) model becomes p + q + 2. Using this parameter number does change the AIC and BIC values but they do not change the model selection outcome, as all AIC’s or BIC’s are basically offset by a constant. When this new number of parameters is used with AICc, however, it could end up choosing a different model.
Machine learning for radiation oncology
Published in Jun Deng, Lei Xing, Big Data in Radiation Oncology, 2019
The Bayesian information criterion (BIC) is also a criterion for model selection among a finite set of models, and the model with the lowest BIC is preferred. The BIC is closely related to the AIC and is intended to resolve overfitting by introducing a penalty term for the number of parameters in the model. They have a different penalty for the number of parameters. Although the penalty of AIC is related to the number of estimated parameters, the penalty of BIC is related to its product with the log function of the sample size. It is assumed that a “true model” is in the set of candidates and that BIC will select the “true model” with the probability of 1, as n → ∞, but the probability of the selection via AIC is less than 1. [25,27,28] However, a simulation study demonstrates that the risk of selecting a very bad model is minimized with AIC under such an assumption. [27] If the “true model” is not in the candidate set, AIC is appropriate for finding the best approximating model when the approximation is done with regard to information loss. [25,27,28]
General power laws of the causalities in the causal Bayesian networks
Published in International Journal of General Systems, 2023
Boyuan Li, Xiaoyang Li, Zhaoxing Tian, Xia Lu, Rui Kang
Once the hypothesized passes the test, it should be concerned whether other confusing distributions may provide better fits. In this case, three typical fat-tailed distributions: the lognormal distribution, the Weibull distribution, and the exponential distribution are also selected to describe the EI. To compare the fitting results of the distributions, the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) are commonly used. BIC penalizes the increase of model parameters rigorously to prevent the overfitting when the sample size is large. However, there is an elevated risk of underfitting for BIC when the sample size is modest (Dziak et al. 2020). Compared with BIC, AIC is usually inferior to BIC for the large-size samples, but it generally performs better when the sample size is finite (Lin, Hsiang, and Dayton 1997). Since the EIs studied in this work is relatively finite, a corrected version of AIC, AICc (Hurvich and Tsai 1989), is adopted and calculated as: where: m is the number of model parameters; is the likelihood function and is the number of EIs larger than EImin. The smaller the calculated AICc is, the better fit the corresponding distribution is.
Detection of latent heteroscedasticity and group-based regression effects in linear models via Bayesian model selection
Published in Technometrics, 2021
Thomas A. Metzger, Christopher T. Franck
We compare the FBF approach described in Section 2.2.3 with posterior class probabilities approximated using the Bayesian information criterion (BIC, Schwarz, 1978). This is a computationally simpler approach which obviates the need for the user to specify a Bayesian model. The BIC approximation to a Bayes factor comparing models m1 and m2 is , where and are the BIC values for models 1 and 2, respectively (Kass and Raftery, 1995). BIC is appealing as an automatic approximate technique for model selection that can be obtained by maximizing the likelihood and applying a simple penalty based on the number of parameters in a given model. Our usage of BIC is based on an optimization of the likelihood as a function of the regression effects and error variances, while our FBF approach considers the log-variance scale. Further explanation for this can be found in Section 6.
Regret minimization based joint econometric model of mode choice and departure time: a case study of university students in Toronto, Canada
Published in Transportmetrica A: Transport Science, 2019
Sabreena Anowar, Ahmadreza Faghih-Imani, Eric J. Miller, Naveen Eluru
In estimating the models, independent sequential models (MD sequence and DM sequence) assuming the two alternative interrelationship structures from the two choice paradigms are used as a starting point for estimating the latent segmentation based model. Please note that these models are non-nested; hence, their performance is compared based on the Bayesian Information Criterion (BIC). The empirical equation for BIC is: where denotes the log likelihood value at convergence, denotes the number of parameters, and represents the number of observations. The advantage of using BIC over other information criterion is that it imposes a substantially higher penalty on over-fitting in terms of the number of parameters. The computed BIC values for the final specifications of all the models are presented in Table 4. The model with the lowest value is the preferred model.