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

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How to calculate BIC for K-Means to get best K

I'm really new to K-Means clustering technique. I'd like to calculate BIC for K-Means to find best K (number of clusters). I looked around on the web to find a solution in python but there is no ...
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Find best K value for K-Means clustering

I'm doing the K-Means clustering for my data. Following python script does K-Means for 2 clusters. ...
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Negative BIC in k-means

Probably a simple question but I'm trying to interpret BIC for k-means. I have some k-means clustering and calculating BIC gives me a negative value, with a plot something like this: ...
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Can BIC be Used for Hypothesis Testing

Define the Bayesian information criterion as $$ \mathrm{BIC} = {-2 \cdot \ln{\hat L} + k \cdot (\ln(n) - \ln(2 \pi))} $$ (I do not drop the constant, $ - \ln(2 \pi)$, to avoid issues when equating to ...
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Post Model Selection Inference problems - which remedies exist?

Recently, Hannes Leeb from Yale University and Benedikt Pötscher from the University of Vienna have published a series of papers dealing with what they call Post Model Selection Inference problems.* ...
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AIC/BIC and data transformation

Can you use AIC/BIC to compare models on untransformed data with models on transformed data (such as log, inverse hyperbolic sine, etc.)? I.e. if a model using logged data gives an AIC = 53.62 and a ...
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AIC / BIC alternative in random effect model

I am looking at at panel data set. Hausmann recommends using random effects modeling, I have 3 nested models and Wald believes each step to add information. However, since some of the parameters had ...
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33 views

Linear Discriminant Analysis for dimensionality reduction - choosing the dimension

I'm using Linear Discriminant Analysis to do dimensionality reduction of a multi-class data. What is the best method to determine the "correct" number of dimensions? Can I use a method similar to PCA, ...
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Specify order of ARIMA model using autocorrelogram

How can I, using the correlograms above, specify the orders of the ARIMA model? These are the pac an ac of the differenced time series. Using AIC and BIC, I can't seem te find a proper model. ...
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Model comparison with different predictors

I have a conducted a series of experiments and manipulated a variable (X) that - from the literature - I know is relevant in this context. For theoretical reasons, I am now convinced that the ...
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39 views

Selecting best ARIMA model with regressors and dummy variable

I have data on GDP, employment rate, inflation and production on two countries and I like to make some ARIMA models. I have done this before, but not with including regressors. Also, the time period ...
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How does one decide the most suitable GARCH model?

I am trying to model financial data using GARCH($p$,$q$). My question is, what information criteria do I use to determine which orders for $p$ and $q$ are most suitable? For instance, for ARIMA ...
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Match model selection strategies with modelling objectives

I am confused trying to match different model selection strategies with different modelling objectives. (Unfortunately, my confusion is reflected in the length of the post. Please be patient.) Model ...
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Zero-inflated Poisson regression Vuong test: Raw, AIC- or BIC-corrected results

I'm analyzing count data for a set of ten species and found that for the five species with highest detection rate, the zero-inflated poisson (ZIP) regression fits the data significantly better than ...
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31 views

Criterion for model selection in an AR model?

I would like to smooth some financial time series data under the assumption that the data consists of variable trend and cyclic components plus white noise. I am thinking of applying an AR model to ...
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Calculating 'k' for k-Means and Expectation Maximization

This question inspired my question. I've read a lot of articles on the Internet, and it seems like most people use sums of squares to find 'k' for k-Means and they use BIC to find 'k' for Expectation ...
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F-test vs. BIC for forward stepwise nested linear model selection

I'm an astronomer trying to choose an appropriate linear model for some time series data. The models I'm choosing between are successively higher-order polynomials in the independent variable $t$ ($y ...
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53 views

Choose model by BIC in a stepwise algorithm after choosing model from glmnet

I have data where number of observation n is smaller than number of variables p. The answer variable is binary. For example: ...
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39 views

Can we apply BIC to select between models in which the parameters are estimated by MCMC

I never considered this problem before. Assume we have two models, $A$ and $B$, we estimate the parameter in $A$ and $B$ respectively by sample mean. Two questions: We can always use the means of ...
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152 views

Paradox in model selection (AIC, BIC, to explain or to predict?)

Having read Galit Shmueli's "To Explain or to Predict" (2010) I am puzzled by an apparent contradiction. There are three starting points, AIC- versus BIC-based model choice (end of p. 300 - start of ...
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42 views

Bayesian Information Criterion and Basic Marginal likelihood identity

Given the basic marginal likelihood identity: $$ ln \; m(y)=ln \; p(y|\theta^*)+ln\; \pi(\theta^*)-ln \pi(\theta^*|y) $$ is there a way to derive from this the Bayesian Information Criterion? ...
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Effective sample size: does it depend on the model?

When applying the Bayesian information criterion, one has to use an "effective sample size" in the penalty term. E.g. if observing longitudinal data (e.g. changes in the blood pressure of an ...
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How do you derive AIC and BIC for discrete-valued observables?

Let's say I have an experiment which yields discrete results between 1 and $N$. I am modelling the results using a number of statistical models and want to use Akaike (corrected) or Bayesian ...
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422 views

X-means algorithm and BIC

I want to simulate X-means algorithm based on [1] in MATLAB. I have some questions about this algorithm. X-means Algorithm Steps: (1) Initialize K = Kmin. (2) Run K-means algorithm. (3) FOR k = ...
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BIC difference for model selection when models have different (and correlated) predictors

I have a binomial dependent variable Y and two main IVs: A is categorical (5 non ordered levels) and B is continuous. A and B are collinear (I tested the effect of A on B with a linear model, and it ...
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X-Means Likelihood for BIC

I have recently been trying to understand the X-means method for deciding on K, using BIC. However I have become stuck on one particular equation in the original paper. On the 4th page, when ...
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172 views

Using BIC,AIC for estimating number of clusters in document clustering using Kmeans

In my approach I am trying to find the optimal value of 'k' for clustering a set of documents using KMEANS algorithm. I wanted to use 'AIC' and 'BIC' information criterion function for finding the ...
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46 views

Best candidate model using AIC or BIC equal to initial model used to generate simulated data?

For a given ARMA model (order and coefficients are known) we generate simulated data. Model is stationary and invertible. Then using this data, I want to find the best model by trying all combinations ...
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42 views

comparing ARIMA and AR with external regressor

Consider the following models fitted to the same time series: ARIMA(0,1,1) ARIMA(1,0,0) (that is, AR(1)) with an external regressor Can I use the AIC (or any other information criteria) to decide ...
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64 views

Calculating BIC for a HMM without any training data

I need to evaluate my HMM models, that are trained using EM algorithm, since I don't have any training data. In order to evaluate with BIC or with most of the other criterions I need the log ...
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158 views

BIC selection yields much smaller model than AIC - can I use the likelihood ratio test to compare?

I'm trying to model the data (not make predictions) and am NOT using lasso for this, just want to know if my plan is somewhat reasonable here: I'm modelling for a "yes/no" response variable, so I ...
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104 views

X-Means Calculation of BIC

I am trying to calculate the BIC for the X-Means algorithm as described in the paper by Pelleg and Moore (https://www.cs.cmu.edu/~dpelleg/download/xmeans.pdf). The paper describes the calculation of ...
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215 views

Implementing the Bayesian Information Criterion (BIC) Using PyKalman

I'm trying to use pykalman to do a Kalman filter on financial data and it seems to be generally working very well. However, when I attempt to extend the code using BIC $\mathrm{BIC} = {-2 \cdot ...
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Integrated Classification Likelihood computation for R package HDclassif

I'm in the process of fitting some mixture models to some data I have. As this data is high-dimensional, I used the subspace clustering package HDclassif. As the package has no option for the Akaike ...
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Reasons for EGARCH(1,1) producing higher/worse AIC/BIC than GARCH(1,1)

I am using the log returns of 3 different stock indices. Two of them show improvements in AIC/BIC critereon when I fit EGARCH(1,1) in comparison to GARCH(1,1). One does not. Assuming that estimation ...
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Comparabilty of BIC, AIC and ICL from Mclust. HDclassif and fem objects

I have a question regarding the way BIC, AIC and ICL are computed in the packages mclust, HDclassif and fisherEM. Both of these packages use the negation of AIC, BIC, ICL (bigger is better). This is ...
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BIC in Item Response Theory Models: Using log(N) vs log(N*I) as a weight

In IRT software packages and in the literature it is common to calculate the BIC as $$ \mathrm{BIC} = -2 \cdot \mathrm{logLik} + \log(N)\mathrm{Npars} $$ where $N$ is the number of rows in wide ...
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Modeling different lag structures

I know there are various information criteria that can be used to compare model specifications, including those with different lag structures. I can easily compare the Akaike Information Criterion ...
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Should information crtieria be applied to training or validation data?

Information criteria for selecting models seem to be applied to training data in general. Could they also be applied to validation data to decide the most predictive and simple model, or is this ...
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BIC for Bayesian ANOVA

I am doing a Bayesian ANOVA as follows: BIC0 = -2 * logLik0 + k0 * log(N) # null hypothesis BIC BIC1 = -2 * logLik1 + k1 * log(N) # alternate hypothesis BIC ...
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Sample size when fitting categorical survey data

I have a model which fits data from repeated surveys: at time $t$, a number $n_t$ respondents is asked a question and can give one of $K$ answers ($k=1, ..., K$). This is repeated $T$ times ($t = 1, ...
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Information criteria for ARIMA model: missing log-likelihood for null model

I am trying to fit an ARIMA model on the time series of exchange rate. I have tried several kinds of ARIMA specifications (MA(1), MA(1,2), ...) and I am evaluating the particular setting according to ...
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Sampling from a set of non-nested models

Consider a collection $\mathcal{M}$ of $m$ different model classes $\mathcal{M} = \{M_1,\dots,M_m\}$, where each model class has a parameter set $\Theta_i$, $i=1,\dots,m$. The model classes are not ...
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100 views

Multiple linear regression: does BIC drop (vaguely) collinear variables?

Say I have the following multiple linear regression: Y ~ X1 + X2 + X3 + X4 All X variables are independent, but X1 and X2 look kind of linearly related when ...
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AIC/BIC values keeps falling as I add more and more lags. How do I select the appropriate lag length?

I am trying to minimize the values of the Akaike and Bayesian Information Criteria to figure out the optimal lag structure for my ARDL error correction model. I am using Stata to run my analysis and ...
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Parameter Estimation vs Inference Error

I am having trouble reconciling (or maybe even understanding properly) the following issues: We have a dataset. We hypothesize a functional form for probability density. Then we estimate the ...
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GLMM with 2 insignificant variables has lower AIC or BIC compared to same model without those variables…?

Background This post has been heavily edited from its previous version (three months ago). I am investigating habitat selection of 35 territorial wolves over several years of denning seasons (41 ...
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How does step function selects best linear Models which includes polynomial effects and interaction effects in R?

I try to find "best" linear models with continuous and categorical covariables with Interaction Effect by BIC. The continuous covariables should have a quadratic effect on the response variable. ...
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255 views

Automatic selection of lowest information criterion comes with warning

I am building a forecasting model (ARMA) and found the very useful code-object arma_order_select_ic(see code below). It all works, however, each calculation comes ...
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Comparing AIC or BIC for constant-only models vs ARIMA models

What if the AIC/BIC is lower (negatively speaking) with the model including just the constant with respect to other ARMA versions? I don't think because k=1 it is lower by construction.