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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Is BIC asymptotically efficient for minimizing prediction error if the true model is being considered?

If a set of models is being compared using BIC and AIC, given the fact that the true model (the one which generated the data) is in this set (and given the other assumptions that guarantee BIC ...
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Problems with training a discriminative model with generative methods

I'm reading Friedman, Geiger and Goldszmidt's 1997 paper "Bayesian Network Classifiers". On page 7, they discuss the problems with using methods for learning generative models (specifically ...
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Calculating AIC & BIC

I have an output from two LMER-models and I'd like to calculate AIC & BIC. I believe I've understood the tables correctly, but I'm uncertain regarding the k parameter; have I understood it ...
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Log Likelihood for Two Stage Least Squares (for AIC or BIC)

I'm looking to use a number of information criteria (BIC, AIC, etc.) for Two Stage Least Squares. Of course all information criteria need a log likelihood - and I'm also aware that for a Log-...
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BIC for combined model selection on independent data sets (BIC not additive)

I have two statistically independent data sets, $x_1$ and $x_2$, both of size $n$, and I would like to select a model $m$ out of the same candidate set $\{1 \ldots M\}$ for each of them, i.e. I select ...
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Selecting a model for linear regression: adjusted metrics (BIC, AIC, adjusted R2 etc…) on training set or validation/crossvalidation using test set?

Linear regression has model hyperparameters such as number of predictors. For example in a autoregressive time series model AR(p), p is the number of predictors. To find which value of p to find we ...
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23 views

Application of BIC when using data to estimate hyperparameters

I plan on using the following equation to calculate the Bayesian information criterion of various linear models applied to the same dataset: $n\ln(RSS/n) + k\ln(n)$ (I believe this equation applies ...
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51 views

negative values for AIC and BIC

I am trying to fit a gumbel distribution using MLE for the following 10 data points. DATA=(3.62,3.76,3.57,3.56,3.61,3.77,3.46,3.6,3.39,3.74) The problem is that the ...
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Picking a suitable performance metric when comparing the same model but using different sets of training data (Causal inference model)

I am comparing the same models prediction accuracy (Causal Impact) using different control variables as predictors and looking for a metric to decide which set of controls to use. Reading into AIC and ...
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BIC and RMSE are Contradict each other for ARIMA Model Selection using R: Do I Err in Theory or in Practice?

I was surprised to see that RMSE and BIC have contradictory trends for the same time-series data. EDITED The procedures in my code are: simulate a 15 AR series of ...
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Bayes Information Criterion — what does log mean?

Super basic question about the BIC — is it defined in terms of log base ten or the natural logarithm? I see the latter on Wikipedia; but see ‘log’ not ‘ln’ in the original paper (though am aware that ...
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How to calculate AIC and BIC?

I should find formula of BIC and AIC which is used in statsmodels. I have array with values: ...
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How can I determine what value of k to use for an AIC/BIC of a fractional power equation?

I have two equations of which I am trying to determine which is the better fit using AIC and BIC: a quadratic equation of the formula $$\ y = β_{1}x^2+β_{2}x+β_{0}$$ and a fractional power equation ...
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79 views

Validity of BIC for Dirichlet process mixture models

I am implementing clustering using Dirichlet process mixture models via scikit learn's Variational Bayesian Gaussian Mixture model. I arrived at the appropriate priors iteratively, and I am able to ...
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75 views

LASSO Regression with AIC or BIC as Model Selection Criterion

I am fitting a linear model using LASSO and exploring BIC (or AIC) as the selection criterion. The most useful resource I have stumbled upon is this earlier question here on CrossValidated: Is it ...
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AIC and BIC for wrong models! [closed]

If the models we consider for the data are wrong, what happens to the model selection with AIC or BIC as the data increases? Any hint?
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How do I find Schwartz criterion (or Bayesian Information Criterion) for these three models?

I have to find the schwarz criterion for each of the models in this maths question using RStudio but I don't know where to start. I know I need to find the free parameters but don't know how to find ...
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Can I use AIC/BIC to compare a Poisson model to a negative Binomial model?

I would please like to enquire if it's appropriate for me to compare the fit of a Poisson vs. a negative Binomial model for my data, given that the two models are nested, i.e. the negative Binomial ...
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Model fit across methods

I have one dataset and I would like to compare analytic methods. The data have to do with risk factors predicting functioning in multiple domains (multiple IVs, multiple DVs). All variables are ...
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18 views

BIC for mixed continuous and discrete parameters?

I am interested in doing a BIC analysis for models which have mixed continuous and discrete variables. To give a minimalistic example which captures the relevant structure, let $\theta\in\mathbb{R}^2$ ...
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46 views

Conjectures regarding EM approximations of mixtures of multivariate normal distributions

Consider $X\in\mathbb{R}^{N\times d}$ containing data for $N$ points in $d$ dimensions drawn from a bimodal multivariate normal distribution, where any row $x$ of $X$ follows the mixed multivariate ...
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24 views

How to use BIC (Bayesian Information Criterion) if the data are not identically distributed but rely on other covariate?

I'm now constructing some models and would like to compare and select the models. I read the wikipedia and some slides about BIC, then I found the ML(maximum likelihood) part in BIC seems to be based ...
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93 views

How to get log-likelihood from squared deviance in Scikit Learn

The score() function computes D^2, the percentage of deviance explained, but I'd like to get the log-likelihood to calculate BIC. What's the formula to go from deviance to log-likelihood? Score ...
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32 views

Test to select best models in production

I've got four models in production and using the average of them as the served prediction. We get ground truth data immediately. I've optimized them and found the best models during my training/...
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AIC/BIC vs the rule of “must include lower order interaction”

I am running a series of mixed effect models, which include both linear and quadratic term of a variable T (continuous) and the main IV I (categorical), and facing a dilemma. Model 2 include ...
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AIC/BIC formula wrong in James/Witten?

Reading "An Introduction to Statistical Learning" (by James, Witten, Hastie and Tibshirani), on p.211 I came across the following formula for BIC in case of linear regression: $ BIC = \frac{...
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336 views

ARIMA grid search for best $p$, $d$, $q$ orders based on BIC metric

i am new to R, and i was hoping to get some answers to some questions i have is there a function to loop through a range of ARIMA model to get the best order/seasonal based on BIC/AIC ? do i have ...
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87 views

Calculate AIC value from a given BIC value?

Is it valid, given a certain BIC value (an output from an R package) with known n and k, to transform the BIC value via mathematical manipulation of the formulae for BIC and AIC to get the "...
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The Ambiguity in Schwarz Information Criterion Definition

Suppose there are 100 countries, $i = 1, 2, ..., 100$. Let $b_i$ be the median birth weight of all new born boys in country #i in 2019. Let $g_i$ be the median birth weight of all new born girls in ...
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96 views

Differences between formulas for AIC and BIC

I have a question regarding the information criteria AIC and BIC: I found different formulas for the AIC/BIC, the common ones including the likelihood $\mathcal{L}$ are $$AIC = 2K - 2 ln(\mathcal{L})\...
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304 views

Log-Likelihood Computation for AIC & BIC

Considering $n$ observations that an be modelled by a Gaussian error model and two nested motion models with $p = 4$ and $p = 7$ parameters, I want to compute the log likelihoods $L$ given the Maximum ...
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How to compare count data to determine

I am performing an experiment to check which information criterion performs best, better and least among Akaike Information Criterion (aic), Bayesian Information Criterion (bic) and aicc. I am ...
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details in X-means algorithm running and Bic

I want to run x-means and needs to make sure I understand fully . I want to simulate X-means algorithm based on [1] in MATLAB. I have some questions about this algorithm. X-means Algorithm Steps: (1) ...
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Why doesn't the formula for the BIC include $\frac{\lambda}{\pi}$ in it?

I've been going through the derivation of the BIC. In Schwarz's original paper (linked below) he arrives at \begin{align*} nA-\frac{1}{2}k_j\log\left(\frac{n\lambda}{\pi}\right)+\log\alpha_j \end{...
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32 views

Adjusting the number of parameters for AIC / BIC calculation in case of correlated predictors

My current understanding: Both AIC and BIC take the number of parameters as input when comparing nested models with a different number of parameters / predictors. My question: Is it necessary / a good ...
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213 views

Order and interpretation of Gaussian Mixture Model with strong overlap between components

Most examples for Gaussian Mixture Models (GMMs) employ datasets with fairly obvious underlying structure (well-separated clusters). How should one determine the order of a GMM (and interpret the ...
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AIC/BIC parameter

I'm wondering what parameter BIC estimates. It seems that AIC is estimating the cross entropy of the estimated model and the true model, and asymptotically is estimating the out of sample entropy loss....
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k means in python with BIC [duplicate]

I am new to ML. I am trying to implement k-means which uses a BIC function that takes cluster and data points as arguments and returns BIC value. I need a function to find best k value that is ...
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21 views

Generalization Error and Matrix Factorizations?

This is more of a discussion/conceptual idea but: Is the notion of generalization error well-defined for a problem such as matrix factorization? I'm working with tensors/matrices and performing ...
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Which GARCH model to choose if both are showing same AIC/BIC and log-likelihood?

I am doing a GARCH model for returns under different error distributions using the R rugarch package. However, two models, under the generalised error distribution and the skewed generalised error ...
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Bayesian Information Criterion (BIC) Applicability

Question Can you compare BIC results between two models that are the same except for the removal of, say, a block of items from one of the models? Situation I'm still in the process of understanding ...
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How to decide between goodness of fit tests

I have a question on BIC and AIC. I have a data set and I need to test this data set if it fits various distributions (for example, Gamma or Poisson, etc.) I need to use AIC and BIC statistics for ...
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43 views

knowing which predictors are significant in a logistic regression model

I am trying to make a logistic regression model based on 5 predictors: 2 of these are categorical and 3 are numerical. The output is simply 1 or 0, and upon performing the Matlab function glmfit(x,y,'...
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519 views

Function for bayesian information criterion (BIC)

I am writing my own python function for the bayesian information criterion (BIC) calculation. What I want to do is to choose between two models that I fitted with a set of discrete xy data points. I ...
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72 views

Source for BIC with residual sum of squares?

Wikipedia states that under certain circumstances, $\mathrm{BIC} $ can be calculated as: $$\mathrm{BIC} = n \ln(\mathrm{RSS}/n) + k \ln(n),$$ where $\mathrm{RSS}$ is the residual sum of squares. ...
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BIC-Lasso Shrinkage

I am currently reviewing the below paper and was wondering if it was possible to correctly implement the BIC equation for "BIC-LASSO Shrinkage". This doesn't appear to be the same as the typical BIC ...
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260 views

Where is the divide between information criterion (AIC, BIC, etc…) and cross validation?

I've taken a regression class and am now in a machine learning class. In regression, we talk about model selection using adj-R2 and AIC/BIC. In my machine learning class, we primarily select models ...
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87 views

How to perform model selection with the BIC for correlated observations

How is it possible to use the Bayesian Information Criterion (and more generally, to perform model selection) when observations are correlated ? I would like to compare the BIC of different models ...
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BIC/AIC Optimal Values

I was reading this paper (https://dms.umontreal.ca/~augusty/FHMV_paper.pdf) and noticed in their analysis (specifically Tables 2 and 3), the highest AIC and BIC values are highlighted and used as ...
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Should I compare two models using AIC?

I calculated duration (IV) in seconds using two different ranges (0 to 5s and 0 to 10s). The aim was to find out which range contributes to higher word learning outcomes (dichotomous DV). I ...

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