Enhancing MML Clustering Using Context Data with Climate Applications

Estimating the number of components (the order) in a mixture model is often addressed using criteria such as the Bayesian information criterion (BIC) and minimum message length. However, when the space is very large, use of these criteria may grossly underestimate the order. Here, it is suggested that this failure is not mainly attributable to the criterion (e.g., BIC), but rather to the lack of structure in standard mixtures-these models trade off data fitness and model complexity only by varying the order. The authors of the present paper propose mixtures with a richer set of tradeoffs. The proposed model allows each component its own informative subset, with all other features explained by a common model (shared by all components). Parameter sharing greatly reduces complexity at a given order. Since the space of these parsimonious modeling solutions is vast, this space is searched in an efficient manner, integrating the component and selection within the generalized expectation-maximization (GEM) learning for the mixture parameters. The quality of the proposed (unsupervised) solutions is evaluated using both classification error and test set data likelihood. On text data, the proposed multinomial version-learned without labeled examples, without knowing the true number of topics, and without preprocessing-compares quite favorably with both alternative unsupervised methods and with a supervised naive Bayes classifier. A Gaussian version compares favorably with a recent method introducing feature saliency in mixtures.

Latent profile analysis with nonnormal mixtures: A Monte Carlo examination of model selection using fit indices

In this paper, we are interested in investigating the causal relationships among futures sugar prices in the Zhengzhou futures exchange market (ZF), the spot sugar prices in Zhengzhou (ZS) and the futures sugar prices in New York futures exchange market (NF). A useful tool called Bayesian network is introduced to analyze the problem. Since there are only three variables in our Bayesian network, the algorithm is straightforward: we display all the 25 possible network structures and adopt certain scoring metrics to evaluate them. We applied five different scoring metrics in total. Firstly, for each metric, we obtained 24 scores, each calculated from one of the 24 possible structures i.e. a Directed Acyclic Graph (DAG). Then we eliminated the network structure which represents the independence of the three variables according to our prior knowledge concerning the futures sugar market. After that, the optimal network structure which implies the causal relationships was selected according to the corresponding scoring metric. Finally, after comparing the results from different scoring metrics, we obtained the relatively affirmative conclusion that ZS causes ZF from both the Bayesian Dirichlet (BD) metric, Bayesian Dirichlet-Akaike Information Criterion (BD-AIC) metric, Bayesian Dirichlet-Bayesian Information Criterion (BD-BIC) metric and Bayesian Information Criterion (BIC) metric. The conclusions that NF causes ZF and ZF causes ZS from the Akaike Information Criterion (AIC) metric and ZF causes ZS from the BIC metric were useful and significant to our investigation.

Time series study is of paramount importance especially in developing countries such as India. The objective of this study is to forecast the number of dengue cases by applying time series models. Furthermore, this study also aims to uncover the correlation of ecological variables with dengue cases using a p value test. The ecological variables considered are the rainfall (with a 2-month lag period) and average relative humidity. An evaluation of host factors such as age and gender is done with the number of cases to determine the most affected strata. Monthly data on dengue cases from 2014 to 2017 are taken from the integrated disease surveillance programme, Government of India, and data on ecological variables, humidity and rainfall are taken from www.Indiastat.com . A 2-month lag period is considered for rainfall. These data were analysed by the autoregressive integrated moving average (ARIMA) and exponential smoothing model (ES). Predictive performance of these techniques was assessed by evaluation parameters such as the Akaike information criterion (AIC), Bayesian information criterion (BIC), mean absolute error and mean absolute scaled error. Applying time series models was useful in the prediction. There were many more males than females according to the data for 2014–2017. The Akaike information criterion (AIC), Bayesian information criterion (BIC) and mean absolute scaled error for ARIMA are 48.6526, 448.333333, 449.30008, 453.08 and 0.507826, respectively. Based on model indices such as the Akaike information criterion (AIC), Bayesian information criterion (BIC), mean absolute error and mean absolute scaled error, the ARIMA performed better than the ES model. Rainfall at the 2-month lag was correlated with the number of cases.

This paper discusses the unsupervised learning problem for a mixture of gamma distributions. An important pan of the unsupervised problem is determining the number of components which best describes some data. We apply the minimum message length (MML) criterion to the unsupervised learning problem in the case of a mixture of gamma distributions. We give a comparison of criteria in the literature for estimating the number of components in a data set. The comparison concerns synthetic and RADARSAT SAR images.

This paper introduces a SAS/IML program to select among the multivariate model candidates based on a few well-known multivariate model selection criteria. Stepwise regression and all-possible-regression are considered. The program is user friendly and requires the user to paste or read the data at the beginning of the module, include the names of the dependent and independent variables (the y's and the x's), and then run the module. The program produces the multivariate candidate models based on the following criteria: Forward Selection, Forward Stepwise Regression, Backward Elimination, Mean Square Error, Coefficient of Multiple Determination, Adjusted Coefficient of Multiple Determination, Akaike's Information Criterion, the Corrected Form of Akaike's Information Criterion, Hannan and Quinn Information Criterion, the Corrected Form of Hannan and Quinn (HQc) Information Criterion, Schwarz's Criterion, and Mallow's PC. The output also constitutes detailed as well as summarized results.

The age and growth information of fish is important for assessment of the dynamics, planning, and management in fisheries. In this study, the mean size at age data of 10 fish species collected from literature were fitted by the five growth models and the growth parameters were estimated by the maximum likelihood method. The best model was selected using the Akaike information criterion (AIC) and Bayesian information criterion (BIC). The growth of most species can be best described by the von Bertalanffy and allometric growth models. The results showed that both AIC and BIC have their advantages in the testing of significance of the difference between the functions of models. As for the demersal fishes (snappers and groupers), BIC is better than AIC in selecting the best growth model.

This study compared the performance of Poisson regression, negative binomial regression and generalized negative binomial regression models using road traffic crashes data collected from Ekiti state command of Federal Road Safety Commission (FRSC). The method of maximum likelihood estimation was employed to determine the parameter estimate for each models, the significance of each variable consider were examined. The criteria used in selecting the best model fitted are Akaike information criterion (AIC), Bayesian information criterion and Deviance. R software package was used in analysing the data. Firstly multicollinearity was tested to determine if there is high correlation between the predictor variables. Data were analysed and the result from the three model were compared using Akaike information criterion (AIC) and Bayesian information criterion (BIC) and the deviance.The result from the three models were compared using AIC, BIC and Deviance, AIC values for the models are (414.79, 476.8 and 587.312), BIC values (490.8873, 495.59 and 589.321) and Deviance value (61.93, 66.927 and 69.927) respectively. Generalized negative binomial regression (GNBR) had the least value of AIC and BIC, thus consider as the best model for analyzing road traffic crashes data in Ekiti state, Nigeria. Having shown a smaller AIC, BIC and deviance values, the generalized negative binomial was consider a better fit model when analysing road traffic crashes in Ekiti state, Nigeria.

The purpose of using the criteria for selecting models is to determine an appropriate model that leads to estimates that we can use in making future predictions. In this study, we presented a number of information criteria that help to choose the best model in the time series, such as Akaike information criterion (AIC), Bayesian information criterion ( BIC), Akaike corrected information criterion (AICC) and Pham information criterion (PIC). We aim to obtain a appropriate model for a time series used to predict the lowest temperatures in Erbil governorate for the next three years depending on the Box-Jenkins methodology for the purpose of building time series models. The best model was chosen from among the estimated models based on the value of the aforementioned statistical criteria. The model was used to predict the lowest temperatures for the next three years in Erbil governorate, as the predictive values ​​were consistent with the real values ​​of temperature ranges.

Lawson, DJ, Olmos, AA, Mosiman, SJ, Sontag, SA, Goodin, JR, and Dawes, JJ. Velocity Variables: Determining Predictive Metrics during the Back Squat and Bench Press to Failure at Different Relative Loads. J Strength Cond Res XX(X): 000-000, 2025-This study aimed to determine a best velocity variable and prediction model for estimating repetitions to failure (RTF) across 3 relative loads (%1RM) comparing the average concentric velocity (ACV) of a single repetition set (ACVSingle), ACV from the first repetition (ACVFirst), ACV across all repetitions (ACVMean), and the fastest repetition velocity (FRV) achieved during the back squat and bench press exercises. Twenty-six (n = 26; males = 18, females = 8) resistance-trained individuals performed 3 sets to failure at 90, 80, and 70% of their 1RM on both exercises for 2 testing sessions. Repeated measures mixed effects models were constructed for univariate, adjusted (corrected for sex), and interaction (velocity*sex) models from Visit 2 data. Model selection criteria were determined by the smallest residual mean error (RME) and standard deviation (SD), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) serving as fit indicators. Best fit models were cross-validated by applying fixed-effects coefficients from Visit 2 to Visit 3 velocity variables, estimating RTF and calculating error as the predicted versus observed variable delta. The ACVSingle adjusted model demonstrated the best fit for the squat (RME = 0.0056, SD = 3.7731, AIC = 360.88, BIC = 363.24). The FRV interaction model demonstrated the best fit for the bench press (RME = 0.0303, SD = 2.4011, AIC = 300.71, and BIC = 303.07). Although no single predictor exhibited superiority across all intensities, ACVSingle and FRV provide lower prediction error variability under specific conditions, with the best predictor determined by both intensity and exercise.

This report documents the Multi-Model Analysis (MMA) computer code. MMA can be used to evaluate results from alternative models of a single system using the same set of observations for all models. As long as the observations, the observation weighting, and system being represented are the same, the models can differ in nearly any way imaginable. For example, they may include different processes, different simulation software, different temporal definitions (for example, steady-state and transient models could be considered), and so on. The multiple models need to be calibrated by nonlinear regression. Calibration of the individual models needs to be completed before application of MMA. MMA can be used to rank models and calculate posterior model probabilities. These can be used to (1) determine the relative importance of the characteristics embodied in the alternative models, (2) calculate model-averaged parameter estimates and predictions, and (3) quantify the uncertainty of parameter estimates and predictions in a way that integrates the variations represented by the alternative models. There is a lack of consensus on what model analysis methods are best, so MMA provides four default methods. Two are based on Kullback-Leibler information, and use the AIC (Akaike Information Criterion) or AICc (second-order-bias-corrected AIC) model discrimination criteria. The other two default methods are the BIC (Bayesian Information Criterion) and the KIC (Kashyap Information Criterion) model discrimination criteria. Use of the KIC criterion is equivalent to using the maximum-likelihood Bayesian model averaging (MLBMA) method. AIC, AICc, and BIC can be derived from Frequentist or Bayesian arguments. The default methods based on Kullback-Leibler information have a number of theoretical advantages, including that they tend to favor more complicated models as more data become available than do the other methods, which makes sense in many situations. Many applications of MMA will be well served by the default methods provided. To use the default methods, the only required input for MMA is a list of directories where the files for the alternate models are located. Evaluation and development of model-analysis methods are active areas of research. To facilitate exploration and innovation, MMA allows the user broad discretion to define alternatives to the default procedures. For example, MMA allows the user to (a) rank models based on model criteria defined using a wide range of provided and user-defined statistics in addition to the default AIC, AICc, BIC, and KIC criteria, (b) create their own criteria using model measures available from the code, and (c) define how each model criterion is used to calculate related posterior model probabilities. The default model criteria rate models are based on model fit to observations, the number of observations and estimated parameters, and, for KIC, the Fisher information matrix. In addition, MMA allows the analysis to include an evaluation of estimated parameter values. This is accomplished by allowing the user to define unreasonable estimated parameter values or relative estimated parameter values. An example of the latter is that it may be expected that one parameter value will be less than another, as might be the case if two parameters represented the hydraulic conductivity of distinct materials such as fine and coarse sand. Models with parameter values that violate the user-defined conditions are excluded from further consideration by MMA. Ground-water models are used as examples in this report, but MMA can be used to evaluate any set of models for which the required files have been produced. MMA needs to read files from a separate directory for each alternative model considered. The needed files are produced when using the Sensitivity-Analysis or Parameter-Estimation mode of UCODE_2005, or, possibly, the equivalent capability of another program. MMA is constructed using

Effectiveness of maintenance programs of existing concrete bridges is highly dependent on the accuracy of the deterioration parameters utilised in the asset management models of the bridge assets. In this paper, bridge deterioration is modelled using non-homogenous Poisson processes, since deterioration of reinforced concrete bridges involves multiple processes. Minimum Message Length (MML) is used to infer the parameters for the model. MML is a statistically invariant Bayesian point estimation technique that is statistically consistent and efficient. In this paper, a method is demonstrated estimate the decay-rates in non-homogeneous Poisson processes using MML inference. The application of methodology is illustrated using bridge inspection data from road authorities. Bridge inspection data are well known for their high level of scatter. An effective and rational MML-based methodology to weed out the outliers is presented as part of the inference.

One of the most difficult aspects of spike sorting is choosing the number of neurons in extracellular recording. The paper proposes a methodology for estimating the number of neurons based on the Gaussian mixture model. The following criteria have been examined: Bayesian selection method, Akaikes information criteria, minimum description length, minimum message length, fuzzy hyper volume, evidence density and partition coefficient. In order to validate the procedure, an experimental comparative study was carried out, comparing the proposed methodology with three spike sorting algorithms. The proposed methodology has an advantage of setting the minimum number of parameters and is very robust to background noise. We conclude that only fuzzy hyper volume and evidence density criteria are able to identify the correct number of neurons across different noise levels.

Comparison of random regression and repeatability models to predict breeding values from test-day records of Norwegian goats

Different imaging paradigms have been used to select patients for endovascular therapy in stroke. We sought to determine whether computed tomographic perfusion (CTP) selection improves endovascular therapy outcomes compared with noncontrast computed tomography alone. Review of a prospectively collected registry of anterior circulation stroke patients undergoing stent-retriever thrombectomy at a tertiary care center between September 2010 and March 2016. Patients undergoing CTP were compared with those with noncontrast computed tomography alone. The primary outcome was the shift in the 90-day modified Rankin scale (mRS). A total of 602 patients were included. CTP-selected patients (n=365, 61%) were younger (P=0.02) and had fewer comorbidities. CTP selection (n=365, 61%) was associated with a favorable 90-day mRS shift (adjusted odds ratio [aOR]=1.49; 95% confidence interval [CI], 1.06-2.09; P=0.02), higher rates of good outcomes (90-day mRS score 0-2: 52.9% versus 40.4%; P=0.005), modified Thrombolysis in Cerebral Infarction-3 reperfusion (54.8% versus 40.1%; P<0.001), smaller final infarct volumes (24.7 mL [9.8-63.1 mL] versus 34.6 mL [13.1-88 mL]; P=0.017), and lower mortality (16.6% versus 26.8%; P=0.005). When matched on age, National Institutes of Health Stroke Scale (NIHSS) score, and glucose (n=424), CTP remained associated with a favorable 90-day mRS shift (P=0.016), lower mortality (P=0.02), and higher rates of reperfusion (P<0.001). CTP better predicted functional outcomes in patients presenting after 6 hours (as assessed by comparison of logistic regression models: Akaike information criterion: 199.35 versus 287.49 and Bayesian information criterion: 196.71 versus 283.27) and those with an Alberta Stroke Program Early Computed Tomography Score ≤7 (Akaike information criterion: 216.69 versus 334.96 and Bayesian information criterion: 213.6 versus 329.94). CTP selection is associated with a favorable mRS shift in patients undergoing stent-retriever thrombectomy. Future prospective studies are warranted.