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Questions tagged [bic]

BIC is an acronym for Bayesian Information Criterion. BIC is one method of model comparison. See also AIC

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26 views

AIC and BIC values by auto.arima and manual ARIMA

A time series of yearly data, I want to compare the AIC and BIC values by auto.arima and manual ARIMA. ...
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BIC of regression with cutoff

Assume we are fitting a linear regression (or poisson regression) on Y ~ X, and the BIC of this model can be obtained as follow: ...
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23 views

AIC / BIC for Model Seleciton in Copula Model

I'm trying to select the distributional model of 30 marginals (which are restricted to have the same distributional family) in a copula model. However, I therefore get 30 Likelihood/AIC/BIC values for ...
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16 views

Interpretation of likelihood function of a continuous random variable in the context of Bayesian Information Criterion

I am confused about the interpretation of the likelihood function of continuously distributed random variable. It's my understanding that the likelihood function is defined to be $L(\theta|x) = f_\...
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28 views

what is wrong with my Gaussian Mixture density estimation fitting (Python)?

I have a data set (1D) link: dataset, which has values ranging from 21,000 to 8,000,000. When i plot histogram of the log values, i can see there are two peaks, roughly. I tried to fit Gaussian ...
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41 views

What is the correct implementation of BIC with residual sum of squares?

BIC is most often calculated by maximizing the log likelihood function. However, it is also possible to calculate BIC with residual sums of squares. This is pretty easy to find online and not an issue ...
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60 views

Calculating the AIC based on histograms for selection of stochastic models

I am modelling a nonlinear stochastic process and have data to compare model output against. My aim is to obtain an evolution equation of the form, $$\frac{du}{dt} = f(u,\theta_f)+\alpha(u,\theta_\...
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25 views

Clarification on Akaike's IC (AIC) and BIC for Expectation Maximization with time-changing parameters

I apologize in advance for the trivial question, but I need a clarification on the following issue. Suppose I have a generic model in state-space form described as $$x_{t+1}=\phi_{t} x_{t}+w_{t+1}$$ $...
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Calculating BIC based on number of parameters in neural network and loss

I have implemented a variational autoencoder. Now, I would like to calculate the Bayesian Information Criterion (BIC) based on the number of parameters in the network and the loss. For example, let's ...
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41 views

Test all models possibles is a good manner to choose the “best” model?

I have programmed a function in python to test all possibles linear regression models that I can do with 5 variables. I choose the "best" model in base its AIC and BIC. These models are ...
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35 views

Comparing BIC values from variations of a data set

I have a data set of 10000 obs of insurance claims. I've fitted it to a Gamma distribution after dividing my values by 10^8; to a Log-Normal distribution, without changing anything in my data set; and ...
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6 views

MLE with higher order markov chain model

I am trying to estimate my Markov chain model. I understand that in a standard model, a higher order will lead to overfitting and higher likelihood. Hence, one can use AIC/BIC to find the order of the ...
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586 views

On George Box, Galit Shmueli and the scientific method?

(This question might seem like it is better suited for the Philosophy SE. I am hoping that statisticians can clarify my misconceptions about Box's and Shmueli's statements, hence I am posting it here)....
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Can the BIC be used in neural nets despite its large no. of parameters?

I wonder if I can calculate a BIC value ($BIC=-2\log L(\hat{\theta}) + \log n \cdot d$) for a neural net. The number of parameters is large, $d \approx 20,000$ and I only have $n=700$ samples. Here, ...
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41 views

Determining the optimal number of clusters using plots of Bayesian Information Criterion

I am having trouble interpreting the results from an Expectation Maximization clustering using mclust and the Iris flower data, Using R. Reproducible example If ...
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105 views

Why is the bayesian information criterion called that way?

The word "Bayes" suggests that we are updating a distribution using data, to get a posterior distribution. The fact that the Bayesian information criterion (BIC) is used to select a model from a set ...
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28 views

BIC in practice with gaussian distribution

I am considering a gaussian distribution: \begin{equation} y \sim N(net(x,w), \sigma^2). \end{equation} $net()$ is just the output of some neural net with weights $w$ and input $x$. The log-...
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AIC criteria for a matrix decomposition problem

I am trying to decompose a matrix such that $$A \approx UV_1 \approx UV_2V_1 \approx UV_3V_2V_1V_2$$ where $A \in R^{n \times l}$, $U \in R^{n \times k_1}$, $V_1 \in R^{k_1 \times l}$, $V_2 \in R^{k_2 ...
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Does a high Chi square p-value for a whole model mean it is insignificant if likelihood ratio tests indicated variables should be added?

I've been estimating lots of versions of the same model by incrementally adding variables. With some variables, if I add them to the model, the likelihood ratio test indicates that they are ...
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28 views

Bayesian Information Criterion Formula Proof

while I was digging arima model I saw that BIC value is given as $k*log(n)-2*log(L)$ where $L$ is the maximized value of likelihood function whereas $k$ is number of parameters. I wonder how it is ...
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247 views

AIC, BIC values keep changing with lag.max in VAR model

I'm using a VARselect function from vars package in R to select order for my model. My data set has 2 time series with 21 data points. When I give ...
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19 views

eviews augmented dickey fuller lag selection

Can someone tell me how does eviews calculate teh optimal Schwarz lag selection? I did a quick search this https://en.wikipedia.org/wiki/Bayesian_information_criterion is this the same method that ...
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285 views

3D plot of Akaike Information Criterion (AIC) for suitable ranges of Lˆ and k

Giving that Akaike Information Criterion (AIC) is as follow: How can I Produce a 3D plot of AIC for suitable ranges of Lˆ and k. In other words what could be a suitable ranges of L to try? Moreover,...
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Is it possible that AIC = BIC?

Two well-known (and related) measures of model complexity from statistics are the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). When might AIC = BIC?
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Logistic regression BIC: what's the right N?

TL;DR: Which $N$ is correct for BIC in logistic regression, the aggregated binomial or Bernoulli $N$? UPDATES AT BOTTOM Suppose I have a data set to which I'd like to apply logistic regression. For ...
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336 views

Find (or calculate) log-likelihood value, AIC, and BIC for SUR model (for each equation) with systemfit

I have estimated SUR model with systemfit (R package). With the estimated results, I am trying to get logLik, AIC and BIC for ...
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26 views

Inestability of BIC when selecting nested models

Currently I am working with spline regression and a method for selecting knots adaptively. My method gives me a set of potential knots that generally has a large number of elements. Following He et al....
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13 views

What is the prerequisites “the same dataset” for AIC/BIC?

Let make a example. Suppose I'm doing model selection and my observation data is $Y_{N\times 1}$ and $X_{N\times K}$.(More specify, K=6) Now I have two model, M1 and M2. M1 includes the first ...
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102 views

Comparing AIC, BIC and HQC for selection of nested model

I am working with spline regression and in this step what I want to do is to somehow reduce the number of knots by applying backward selection. Technically what I am doing is to delete sequentially ...
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15 views

How can I choose correct variant of ADF test?

Sorry for this question, but I am not sure in this problem. Can I make decision according to AIC, BIC and so on?
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42 views

A simulation study of linear mixed model

I am reading this paper, a note on BIC in mixed effects models, and I was trying to repeat their simulation study. And I will paste part of the experiment settings here to clarify my question. Now, I ...
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30 views

Asymptotic equivalence between cross validation and bayesian information criteria

I heard that Bayesian information criteria and cross validation are asymptotically equivalent when the size of validation set is large enough similar to the relationship between Akaike information ...
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1answer
100 views

Understanding Intuition for ETS Damping Selection via AIC/BIC

I'm trying to understand how ETS selects whether to use a damped model via information criteria (I'm not sure which of AIC, AICc or BIC are used). I have a time series and I'm comparing two ETS ...
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1answer
117 views

Selecting between OLS regression and ARIMA for time series, why AIC or BIC for ARIMA is much larger in my data?

My data set is quarterly time seires data (around 140 data points). Method 1: simple OLS regression with 5-6 exogenous variables, which are drivers of the dependent variable. None of the explanatory ...
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1answer
105 views

AIC calculated in lm(y~1) and stepwise selection in R

http://www.stat.wisc.edu/courses/st333-larget/aic.pdf The AIC calculated with the model lm(SAT~1) was 560.4736, but the AIC calculated with stepwise selection starting with lm(SAT~1) was 419.42. May ...
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21 views

How to implement Bayesian Information Criterion (BIC) in a practical problem?

I found a lot of theoretical literature about BIC online, but I had a difficult time when I was trying to find a real case. So I was wondering how do we implement the BIC in a practical problem? Do ...
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15 views

Information criterion when model could be mis-specified and data is dependent

Common information criteria (AIC, BIC, etc) require the user to specify the likelihood function, while in practice rarely the user has the luxury to know the correct likelihood function. In the case ...
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1answer
230 views

How can we calculate AIC from a negative binomial GLMM?

Our problem here described is to calculate AIC from a GLMM negbin. Our data compose by 2 Categorical variables (Yes/Not), 3 Numerical variables and our random factor, all without any NA. We want to ...
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2answers
953 views

Best BIC value for K-means clusters

I am using code from Using BIC to estimate the number of k in KMEANS (answer by Prabhath Nanisetty) to find BIC values for K-means using different number of components. However, using iris dataset, I ...
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How to use a previously calculated set of clusters to start EM Clustering in R?

I have performed Hierarchical Clustering on a data set. I would now like to compare the BIC of the clustering methods. The process involves using the clusters you have determined to act as your ...
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AIC and BIC and number of quantization level

I want to test how many quantization levels (discretizing levels) are the best for the given data(time series) set I have. Therefore I am applying different levels of binning (like discretisize data ...
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194 views

Time series analysis VAR model: AIC and BIC test criteria

Consider two variables. Imagine you want to analyse the effects of the lags of variable A on variable B. The possiblity you see an effect of variable A on B is reasonable, but there is absolutely no ...
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391 views

What is the actual significance of a difference in AIC or BIC values?

Usually, when a difference of a statistic is discussed, that discussion is presented in the context of a significance of that difference. When self-entropy, i.e., information content, is examined, ...
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954 views

Elbow Test using AIC/BIC for identifying number of clusters using GMM

How to select number of clusters using GMM when the elbow test (AIC/BIC vs n_components) results in a graph like this?
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1answer
184 views

AIC and BIC in Latent class analysis

I am using the Latent Class Analysis feature available in Stata 15. The two statistical criterions gave me different indications: $AIC$ suggests me to use 6 classes, instead $BIC$ suggests to use 5 ...
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When is the AIC a good model selection criterion for forecasting and when is it not?

I'm trying to wrap my head around why the AIC and other similar ICs work as proxies for out of sample error when trying to perform automated forecast generation. So I performed an experiment on the ...
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78 views

How to choose the number of steps ahead when comparing time series CV to the AIC or the BIC?

I would like to empirically evaluate the performance of the AIC, BIC and Cross Validation as model selection criteria for time series forecasting, i.e. which one of these criteria leads to the best ...
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522 views

Elbow Method or/and Bayesian Information Criterion to select the optimal number of clusters

I am working k-means cluster analysis. I am new in R and even newer with cluster analysis, but happy to learn. I have managed to plot the following two figures to select the optimal number of ...
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1answer
135 views

As you drop variables, can AIC or BIC go up and then down?

I have some potential spline models and I'm trying to use AIC or BIC to choose variables. I'm seeing that AIC is lower when I use all variables than if I exclude any one or two. However, if I exclude ...
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2k views

Is it possible that the AIC and BIC give totally different model selections?

I'm performing a Poisson Regression model with 1 response variable and 6 covariates. Model selection using AIC results in a model with all covariates as well as 6 interaction terms. The BIC however, ...