Optimizing spatio-temporal correlation structures for modeling food security in Africa: a simulation-based investigation.

This study investigates the impact of spatio- temporal correlation using four spatio-temporal models: Spatio-Temporal Poisson Linear Trend Model (SPLTM), Poisson Temporal Model (TMS), Spatio-Temporal Poisson Anova Model (SPAM), and Spatio-Temporal Poisson Separable Model (STSM) concerning food security and nutrition in Africa. Evaluating model goodness of fit using the Watanabe Akaike Information Criterion (WAIC) and assessing bias through root mean square error and mean absolute error values revealed a consistent monotonic pattern. SPLTM consistently demonstrates a propensity for overestimating food security, while TMS exhibits a diverse bias profile, shifting between overestimation and underestimation based on varying correlation settings. SPAM emerges as a beacon of reliability, showcasing minimal bias and WAIC across diverse scenarios, while STSM consistently underestimates food security, particularly in regions marked by low to moderate spatio-temporal correlation. SPAM consistently outperforms other models, making it a top choice for modeling food security and nutrition dynamics in Africa. This research highlights the impact of spatial and temporal correlations on food security and nutrition patterns and provides guidance for model selection and refinement. Researchers are encouraged to meticulously evaluate the biases and goodness of fit characteristics of models, ensuring their alignment with the specific attributes of their data and research goals. This knowledge empowers researchers to select models that offer reliability and consistency, enhancing the applicability of their findings.

Multimodel Approaches Are Not the Best Way to Understand Multifactorial Systems.

Information-theoretic (IT) and multi-model averaging (MMA) statistical approaches are widely used but suboptimal tools for pursuing a multifactorial approach (also known as the method of multiple working hypotheses) in ecology. (1) Conceptually, IT encourages ecologists to perform tests on sets of artificially simplified models. (2) MMA improves on IT model selection by implementing a simple form of shrinkage estimation (a way to make accurate predictions from a model with many parameters relative to the amount of data, by "shrinking" parameter estimates toward zero). However, other shrinkage estimators such as penalized regression or Bayesian hierarchical models with regularizing priors are more computationally efficient and better supported theoretically. (3) In general, the procedures for extracting confidence intervals from MMA are overconfident, providing overly narrow intervals. If researchers want to use limited data sets to accurately estimate the strength of multiple competing ecological processes along with reliable confidence intervals, the current best approach is to use full (maximal) statistical models (possibly with Bayesian priors) after making principled, a priori decisions about model complexity.

Bootstrap Approximation of Model Selection Probabilities for Multimodel Inference Frameworks.

Most statistical modeling applications involve the consideration of a candidate collection of models based on various sets of explanatory variables. The candidate models may also differ in terms of the structural formulations for the systematic component and the posited probability distributions for the random component. A common practice is to use an information criterion to select a model from the collection that provides an optimal balance between fidelity to the data and parsimony. The analyst then typically proceeds as if the chosen model was the only model ever considered. However, such a practice fails to account for the variability inherent in the model selection process, which can lead to inappropriate inferential results and conclusions. In recent years, inferential methods have been proposed for multimodel frameworks that attempt to provide an appropriate accounting of modeling uncertainty. In the frequentist paradigm, such methods should ideally involve model selection probabilities, i.e., the relative frequencies of selection for each candidate model based on repeated sampling. Model selection probabilities can be conveniently approximated through bootstrapping. When the Akaike information criterion is employed, Akaike weights are also commonly used as a surrogate for selection probabilities. In this work, we show that the conventional bootstrap approach for approximating model selection probabilities is impacted by bias. We propose a simple correction to adjust for this bias. We also argue that Akaike weights do not provide adequate approximations for selection probabilities, although they do provide a crude gauge of model plausibility.

A Selective Review on Information Criteria in Multiple Change Point Detection.

Change points indicate significant shifts in the statistical properties in data streams at some time points. Detecting change points efficiently and effectively are essential for us to understand the underlying data-generating mechanism in modern data streams with versatile parameter-varying patterns. However, it becomes a highly challenging problem to locate multiple change points in the noisy data. Although the Bayesian information criterion has been proven to be an effective way of selecting multiple change points in an asymptotical sense, its finite sample performance could be deficient. In this article, we have reviewed a list of information criterion-based methods for multiple change point detection, including Akaike information criterion, Bayesian information criterion, minimum description length, and their variants, with the emphasis on their practical applications. Simulation studies are conducted to investigate the actual performance of different information criteria in detecting multiple change points with possible model mis-specification for the practitioners. A case study on the SCADA signals of wind turbines is conducted to demonstrate the actual change point detection power of different information criteria. Finally, some key challenges in the development and application of multiple change point detection are presented for future research work.

Integrated intravoxel incoherent motion tensor and diffusion tensor brain MRI in a single fast acquisition.

The acquisition of intravoxel incoherent motion (IVIM) data and diffusion tensor imaging (DTI) data from the brain can be integrated into a single measurement, which offers the possibility to determine orientation-dependent (tensorial) perfusion parameters in addition to established IVIM and DTI parameters. The purpose of this study was to evaluate the feasibility of such a protocol with a clinically feasible scan time below 6 min and to use a model-selection approach to find a set of DTI and IVIM tensor parameters that most adequately describes the acquired data. Diffusion-weighted images of the brain were acquired at 3 T in 20 elderly participants with cerebral small vessel disease using a multiband echoplanar imaging sequence with 15 b-values between 0 and 1000 s/mm2 and six non-collinear diffusion gradient directions for each b-value. Seven different IVIM-diffusion models with 4 to 14 parameters were implemented, which modeled diffusion and pseudo-diffusion as scalar or tensor quantities. The models were compared with respect to their fitting performance based on the goodness of fit (sum of squared fit residuals, chi2 ) and their Akaike weights (calculated from the corrected Akaike information criterion). Lowest chi2 values were found using the model with the largest number of model parameters. However, significantly highest Akaike weights indicating the most appropriate models for the acquired data were found with a nine-parameter IVIM-DTI model (with isotropic perfusion modeling) in normal-appearing white matter (NAWM), and with an 11-parameter model (IVIM-DTI with additional pseudo-diffusion anisotropy) in white matter with hyperintensities (WMH) and in gray matter (GM). The latter model allowed for the additional calculation of the fractional anisotropy of the pseudo-diffusion tensor (with a median value of 0.45 in NAWM, 0.23 in WMH, and 0.36 in GM), which is not accessible with the usually performed IVIM acquisitions based on three orthogonal diffusion-gradient directions.

A two-level copula joint model for joint analysis of longitudinal and competing risks data.

In this article, we propose a two-level copula joint model to analyze clinical data with multiple disparate continuous longitudinal outcomes and multiple event-times in the presence of competing risks. At the first level, we use a copula to model the dependence between competing latent event-times, in the process constructing the submodel for the observed event-time, and employ the Gaussian copula to construct the submodel for the longitudinal outcomes that accounts for their conditional dependence; these submodels are glued together at the second level via the Gaussian copula to construct a joint model that incorporates conditional dependence between the observed event-time and the longitudinal outcomes. To have the flexibility to accommodate skewed data and examine possibly different covariate effects on quantiles of a non-Gaussian outcome, we propose linear quantile mixed models for the continuous longitudinal data. We adopt a Bayesian framework for model estimation and inference via Markov Chain Monte Carlo sampling. We examine the performance of the copula joint model through a simulation study and show that our proposed method outperforms the conventional approach assuming conditional independence with smaller biases and better coverage probabilities of the Bayesian credible intervals. Finally, we carry out an analysis of clinical data on renal transplantation for illustration.

Acoustic Emission and Artificial Intelligence Procedure for Crack Source Localization.

The acoustic emission (AE) technique is one of the most widely used in the field of structural monitoring. Its popularity mainly stems from the fact that it belongs to the category of non-destructive techniques (NDT) and allows the passive monitoring of structures. The technique employs piezoelectric sensors to measure the elastic ultrasonic wave that propagates in the material as a result of the crack formation's abrupt release of energy. The recorded signal can be investigated to obtain information about the source crack, its position, and its typology (Mode I, Mode II). Over the years, many techniques have been developed for the localization, characterization, and quantification of damage from the study of acoustic emission. The onset time of the signal is an essential information item to be derived from waveform analysis. This information combined with the use of the triangulation technique allows for the identification of the crack location. In the literature, it is possible to find many methods to identify, with increasing accuracy, the onset time of the P-wave. Indeed, the precision of the onset time detection affects the accuracy of identifying the location of the crack. In this paper, two techniques for the definition of the onset time of acoustic emission signals are presented. The first method is based on the Akaike Information Criterion (AIC) while the second one relies on the use of artificial intelligence (AI). A recurrent convolutional neural network (R-CNN) designed for sound event detection (SED) is trained on three different datasets composed of seismic signals and acoustic emission signals to be tested on a real-world acoustic emission dataset. The new method allows taking advantage of the similarities between acoustic emissions, seismic signals, and sound signals, enhancing the accuracy in determining the onset time.

Comparing DIC and WAIC for multilevel models with missing data.

In Bayesian statistics, the most widely used criteria of Bayesian model assessment and comparison are Deviance Information Criterion (DIC) and Watanabe-Akaike Information Criterion (WAIC). We use a multilevel mediation model as an illustrative example to compare different types of DIC and WAIC. More specifically, we aim to compare the performance of conditional and marginal DICs and WAICs, and investigate their performance with missing data. We focus on two versions of DIC ([Formula: see text] and [Formula: see text]) and one version of WAIC. In addition, we explore whether it is necessary to include the nuisance models of incomplete exogenous variables in likelihood. Based on the simulation results, whether [Formula: see text] is better than [Formula: see text] and WAIC and whether we should include the nuisance models of exogenous variables in likelihood functions depend on whether we use marginal or conditional likelihoods. Overall, we find that the marginal likelihood based-[Formula: see text] that excludes the likelihood of covariate models generally had the highest true model selection rates.

An improved sparse identification of nonlinear dynamics with Akaike information criterion and group sparsity.

A crucial challenge encountered in diverse areas of engineering applications involves speculating the governing equations based upon partial observations. On this basis, a variant of the sparse identification of nonlinear dynamics (SINDy) algorithm is developed. First, the Akaike information criterion (AIC) is integrated to enforce model selection by hierarchically ranking the most informative model from several manageable candidate models. This integration avoids restricting the number of candidate models, which is a disadvantage of the traditional methods for model selection. The subsequent procedure expands the structure of dynamics from ordinary differential equations (ODEs) to partial differential equations (PDEs), while group sparsity is employed to identify the nonconstant coefficients of partial differential equations. Of practical consideration within an integrated frame is data processing, which tends to treat noise separate from signals and tends to parametrize the noise probability distribution. In particular, the coefficients of a species of canonical ODEs and PDEs, such as the Van der Pol, Rössler, Burgers' and Kuramoto-Sivashinsky equations, can be identified correctly with the introduction of noise. Furthermore, except for normal noise, the proposed approach is able to capture the distribution of uniform noise. In accordance with the results of the experiments, the computational speed is markedly advanced and possesses robustness.

[The Validity of the Poisson Distribution to Analyze Microbial Colony Counts on Agar Plates for Food Samples].

Microbial colony counts of food samples in microbiological examinations are one of the most important items. The probability distributions for the colony counts per agar plate at the dilution of counting had not been intensively studied so far. Recently we analyzed the colony counts of food samples with several probability distributions using the Pearson's chi-square value by the "traditional" statistics as the index of fit [Fujikawa and Tsubaki, Food Hyg.Saf.Sc., 60, 88-95 (2019)]. As a result, the selected probability distributions depended on the samples. In this study we newly selected a probability distribution, namely a statistical model, suitable for the above data with the method of maximum likelihood from the probabilistic point of view. The Akaike's Information Criterion (AIC) was used as the index of fit. Consequently, the Poisson model were better than the negative binomial model for all of four food samples. The Poisson model was also better than the binomial for three of four microbial culture samples. With Baysian Information Criterion (BIC), the Poisson model was also better than these two models for all the samples. These results suggested that the Poisson distribution would be the best model to estimate the colony counts of food samples. The present study would be the first report on the statistical model selection for the colony counts of food samples with AIC and BIC.

Multilayer Perceptron Network Optimization for Chaotic Time Series Modeling.

Chaotic time series are widely present in practice, but due to their characteristics-such as internal randomness, nonlinearity, and long-term unpredictability-it is difficult to achieve high-precision intermediate or long-term predictions. Multi-layer perceptron (MLP) networks are an effective tool for chaotic time series modeling. Focusing on chaotic time series modeling, this paper presents a generalized degree of freedom approximation method of MLP. We then obtain its Akachi information criterion, which is designed as the loss function for training, hence developing an overall framework for chaotic time series analysis, including phase space reconstruction, model training, and model selection. To verify the effectiveness of the proposed method, it is applied to two artificial chaotic time series and two real-world chaotic time series. The numerical results show that the proposed optimized method is effective to obtain the best model from a group of candidates. Moreover, the optimized models perform very well in multi-step prediction tasks.

Akaike's Information Criterion for Stoichiometry Inference of Supramolecular Complexes.

"How do we decide the stoichiometry of host-guest complexes?" This question has long been answered by the Job plot since its first report in 1928. However, as the Job plot was claimed to be misleading in 2016, the question became an open question again and called for renewed investigations. An information-theoretic approach, called Akaike's information criterion, is introduced in this study to select the best model of host-guest complexes, which can rank the models with weight of evidence. A few test cases with unique cylindrical hosts were examined to demonstrate the applicability of the information-theoretic method. Consequently, reasonable views over the thermodynamic behaviors of dumbbell-and-cylinder complexes were obtained. Akaike's information criterion can be a useful and superior alternative to statistical null hypothesis testing, which was proposed as a remedy in place of the Job plot.

Sensitivity and specificity of information criteria.

Information criteria (ICs) based on penalized likelihood, such as Akaike's information criterion (AIC), the Bayesian information criterion (BIC) and sample-size-adjusted versions of them, are widely used for model selection in health and biological research. However, different criteria sometimes support different models, leading to discussions about which is the most trustworthy. Some researchers and fields of study habitually use one or the other, often without a clearly stated justification. They may not realize that the criteria may disagree. Others try to compare models using multiple criteria but encounter ambiguity when different criteria lead to substantively different answers, leading to questions about which criterion is best. In this paper we present an alternative perspective on these criteria that can help in interpreting their practical implications. Specifically, in some cases the comparison of two models using ICs can be viewed as equivalent to a likelihood ratio test, with the different criteria representing different alpha levels and BIC being a more conservative test than AIC. This perspective may lead to insights about how to interpret the ICs in more complex situations. For example, AIC or BIC could be preferable, depending on the relative importance one assigns to sensitivity versus specificity. Understanding the differences and similarities among the ICs can make it easier to compare their results and to use them to make informed decisions.

Exploring the relationship between age and prognosis in glioma: rethinking current age stratification.

BACKGROUND: The age of glioma plays a unique role in prognosis. We hypothesized that age is not positively correlated with survival prognosis and explored its exact relationship. METHODS: Glioma was identified from the SEER database (between 2000 and 2018). A multivariate Cox proportional regression model and restricted cubic spline (RCS) plot were used to assess the relationship between age and prognosis. RESULTS: A total of 66465 patients with glioma were included. Hazard ratios (HR) for ten-year by age: 0-9 years, HR 1.06 (0.93-1.20); 10-19 years: reference; 20-29 years, HR 0.90 (0.82-1.00); 30-39 years, HR 1.14 (1.04-1.25); 40-49 years, HR 2.09 (1.91-2.28); 50-59 years, HR 3.48 (3.19-3.79); 60-69 years, HR 4.91 (4.51-5.35);70-79 years, HR 7.95 (7.29-8.66); 80-84 years, HR 12.85 (11.74-14.06). After adjusting for covariates, the prognosis was not positively correlated with age. The smooth curve of RCS revealed this non-linear relationship: HR increased to 10 years first, decreased to 23 years, reached its lowest point, and became J-shaped. CONCLUSION: The relationship between age and glioma prognosis is non-linear. These results challenge the applicability of current age groupings for gliomas and advocate the consideration of individualized treatment guided by precise age.

Use of information criteria for selecting a correlation structure for longitudinal cluster randomised trials.

BACKGROUND: When designing and analysing longitudinal cluster randomised trials, such as the stepped wedge, the similarity of outcomes from the same cluster must be accounted for through the choice of a form for the within-cluster correlation structure. Several choices for this structure are commonly considered for application within the linear mixed model paradigm. The first assumes a constant intra-cluster correlation for all pairs of outcomes from the same cluster (the exchangeable/Hussey and Hughes model); the second assumes that correlations of outcomes measured in the same period are higher than outcomes measured in different periods (the block exchangeable model) and the third is the discrete-time decay model, which allows the correlation between pairs of outcomes to decay over time. Currently, there is limited guidance on how to select the most appropriate within-cluster correlation structure. METHODS: We simulated continuous outcomes under each of the three considered within-cluster correlation structures for a range of design and parameter choices, and, using the ASReml-R package, fit each linear mixed model to each simulated dataset. We evaluated the performance of the Akaike and Bayesian information criteria for selecting the correct within-cluster correlation structure for each dataset. RESULTS: For smaller total sample sizes, neither criteria performs particularly well in selecting the correct within-cluster correlation structure, with the simpler exchangeable model being favoured. Furthermore, in general, the Bayesian information criterion favours the exchangeable model. When the cluster auto-correlation (which defines the degree of dependence between observations in adjacent time periods) is large and number of periods is small, neither criteria is able to distinguish between the block exchangeable and discrete time decay models. However, for increasing numbers of clusters, periods, and subjects per cluster period, both the Akaike and Bayesian information criteria perform increasingly well in the detection of the correct within-cluster correlation structure. CONCLUSIONS: With increasing amounts of data, be they number of clusters, periods or subjects per cluster period, both the Akaike and Bayesian information criteria are increasingly likely to select the correct correlation structure. We recommend that if there are sufficient data available when planning a trial, that the Akaike or Bayesian information criterion is used to guide the choice of within-cluster correlation structure in the absence of other compelling justifications for a specific correlation structure. We also suggest that researchers conduct supplementary analyses under alternate correlation structures to gauge sensitivity to the initial choice.

Analysis of steady-state carbon tracer experiments using akaike information criteria.

INTRODUCTION: Carbon isotope tracers have been used to determine relative rates of tricarboxylic acid cycle (TCA) cycle pathways since the 1950s. Steady-state experimental data are typically fit to a single mathematical model of metabolism to determine metabolic fluxes. Whether the chosen model is appropriate for the biological system has generally not been evaluated systematically. An overly-simple model omits known pathways while an overly-complex model may produce incorrect results due to overfitting. OBJECTIVES: The objectives were to develop and study a method that systematically evaluates multiple TCA cycle mathematical models as part of the fitting process. METHODS: The problem of choosing overly-simple or overly-complex models was approached by developing software that automatically explores all possible combinations of flux through pyruvate dehydrogenase, pyruvate kinase, pyruvate carboxylase and anaplerosis at propionyl-CoA carboxylase, and equivalent pathways, all relative to TCA cycle flux. Typical TCA cycle metabolic tracer experiments that use 13C nuclear magnetic resonance for detection and quantification of 13C-enriched glutamate products were simulated and analyzed. By evaluating the multiple model fits with both the conventional sum-of-squares residual error (SSRE) and the Akaike Information Criterion (AIC), the software helps the investigator understand the interaction between model complexity and goodness of fit. RESULTS: When fitting alternative models of the TCA cycle metabolism, the SSRE may identify more than one model that fits the data well. Among those models, the AIC provides guidance as to which is the simplest of the candidate models is sufficient to describe the observed data. However under some conditions, AIC used alone inappropriately discriminates against necessary metabolic complexity. CONCLUSION: In combination, the SSRE and AIC help the investigator identify the model that best describes the metabolism of a biological system.

Comparisons of zero-augmented continuous regression models from a Bayesian perspective.

The two-part model and the Tweedie model are two essential methods to analyze the positive continuous and zero-augmented responses. Compared with other continuous zero-augmented models, the zero-augmented gamma model (ZAG) demonstrates its performance on the mass zeros data. In this article, we compare the Bayesian model for continuous data of excess zeros by considering the ZAG and Tweedie model. We model the mean of both models in a logarithmic scale and the probability of zero within the zero-augmented model in a logit scale. As previous researchers employed different priors in Bayesian settings for the Tweedie model, by conducting a sensitivity analysis, we select the optimal priors for Tweedie model. Furthermore, we present a simulation study to evaluate the performance of two models in the comparison and apply them to a dataset about the daily fish intake and blood mercury levels from National Health and Nutrition Examination Survey. According to the Watanabe-Akaike information criterion and leave-one-out cross-validation criterion, the Tweedie model provides higher predictive accuracy for the positive continuous and zero-augmented data.

A hierarchical procedure to select intrauterine and extrauterine factors for methodological validation of preterm birth risk estimation.

BACKGROUND: Etiopathogenesis of preterm birth (PTB) is multifactorial, with a universe of risk factors interplaying between the mother and the environment. It is of utmost importance to identify the most informative factors in order to estimate the degree of PTB risk and trace an individualized profile. The aims of the present study were: 1) to identify all acknowledged risk factors for PTB and to select the most informative ones for defining an accurate model of risk prediction; 2) to verify predictive accuracy of the model and 3) to identify group profiles according to the degree of PTB risk based on the most informative factors. METHODS: The Maternal Frailty Inventory (MaFra) was created based on a systematic review of the literature including 174 identified intrauterine (IU) and extrauterine (EU) factors. A sample of 111 pregnant women previously categorized in low or high risk for PTB below 37 weeks, according to ACOG guidelines, underwent the MaFra Inventory. First, univariate logistic regression enabled p-value ordering and the Akaike Information Criterion (AIC) selected the model including the most informative MaFra factors. Second, random forest classifier verified the overall predictive accuracy of the model. Third, fuzzy c-means clustering assigned group membership based on the most informative MaFra factors. RESULTS: The most informative and parsimonious model selected through AIC included Placenta Previa, Pregnancy Induced Hypertension, Antibiotics, Cervix Length, Physical Exercise, Fetal Growth, Maternal Anxiety, Preeclampsia, Antihypertensives. The random forest classifier including only the most informative IU and EU factors achieved an overall accuracy of 81.08% and an AUC of 0.8122. The cluster analysis identified three groups of typical pregnant women, profiled on the basis of the most informative IU and EU risk factors from a lower to a higher degree of PTB risk, which paralleled time of birth delivery. CONCLUSIONS: This study establishes a generalized methodology for building-up an evidence-based holistic risk assessment for PTB to be used in clinical practice. Relevant and essential factors were selected and were able to provide an accurate estimation of degree of PTB risk based on the most informative constellation of IU and EU factors.

Associations between curve severity and revised Scoliosis Research Society-22 and scoliosis Japanese Questionnaire-27 scores in female patients with adolescent idiopathic scoliosis: a multicenter, cross-sectional study.

BACKGROUND: Patient-reported outcome measures are widely utilized to assess health-related quality of life (HRQOL) in patients with adolescent idiopathic scoliosis (AIS). However, the association between HRQOL and curve severity is mostly unknown. The aim of this study is to clarify the association between HRQOL and curve severity, and to determine the optimal cutoff values of patient-reported outcomes for major curve severity in female patients with AIS. METHODS: Female patients with AIS treated conservatively were recruited. The patients' HRQOL outcomes were examined using the revised Scoliosis Research Society-22 (SRS-22r) and the Scoliosis Japanese Questionnaire-27 (SJ-27). The correlations of the SRS-22r and SJ-27 scores with the major Cobb angle were assessed using Spearman's correlation coefficient analysis. The association between HRQOL issues in the SJ-27 and the major Cobb angle was evaluated by calculating Akaike's Information Criterion (AIC). Furthermore, the optimal cutoff values of the SRS-22r and SJ-27 scores for the major Cobb angle were determined by AIC analysis. RESULTS: The study cohort comprised 306 female patients with AIS. The SRS-22r and SJ-27 scores were significantly correlated with the major Cobb angle. Questions in the SJ-27 regarding discomfort when wearing clothes showed a lower AIC value in patients with severe scoliosis. The optimal cutoff values were a SRS-22r score of 3.2 for the discrimination of severe scoliosis (Cobb angle ≥48°), and a SJ-27 score of 32 for the discrimination of moderate scoliosis (Cobb angle ≥33°). CONCLUSION: Discomfort when wearing clothes was the most important HRQOL problem caused by severe scoliosis. The SRS-22r and SJ-27 scores are useful for the discrimination of clinical status in female patients with severe scoliosis or moderate scoliosis.

A close look at 2019 novel coronavirus (COVID 19) infections in Turkey using time series analysis & efficiency analysis.

2019 novel coronavirus (COVID 19) infections detected as the first official records of the disease in Wuhan, China, affected almost all countries worldwide, including Turkey. Due to the number of infected cases, Turkey is one of the most affected countries in the world. Thus, an examination of the pandemic data of Turkey is a critical issue to understand the shape of the spread of the virus and its effects. In this study, we have a close look at the data of Turkey in terms of the variables commonly used during the pandemic to set an example for possible future pandemics. Both time series modeling and popular efficiency measurement methods are used to evaluate the data and enrich the results. It is believed that the results and discussions are useful and can contribute to the language of numbers for pandemic researchers working on the elimination of possible future pandemics.