Fakultet primijenjene matematike i informatike

Mirta Benšić


AVM6252 1 200x300 2 Professor
Department of Mathematics
Josip Juraj Strossmayer University of Osijek
Trg Ljudevita Gaja 6
Osijek, HR-31000, Croatia¸
phone: +385-31-224-800
fax: +385-31-224-801
email:  mirta @ mathos.hr
office:  25 (first floor)

Google Scholar profil


Research Interests

Statistical theory (estimators - asymptotic properties)
Statistical applications (medical statistics, econometrics)


PhD in  Mathematics,  University of Zagreb , 1997.
MSc in Mathematics,  University of Zagreb , 1990.
BSc in Mathematics and Physics, University of Osijek, Croatia, 1985.


Journal Publications

  1. S. Guljaš, M. Benšić, Z. Krivdić Dupan, O. Pavlović, V. Krajina, D. Pavoković, P. Šmit Takač, M. Hranić, T. Salha, Dynamic Contrast Enhanced Study in Multiparametric Examination of the Prostate—Can We Make Better Use of It?, Tomography 8/3 (2022), 1509-1521
    We sought to investigate whether quantitative parameters from a dynamic contrast-enhanced study can be used to differentiate cancer from normal tissue and to determine a cut-off value of specific parameters that can predict malignancy more accurately, compared to the obturator internus muscle as a reference tissue. This retrospective study included 56 patients with biopsy proven prostate cancer (PCa) after multiparametric magnetic resonance imaging (mpMRI), with a total of 70 lesions; 39 were located in the peripheral zone, and 31 in the transition zone. The quantitative parameters for all patients were calculated in the detected lesion, morphologically normal prostate tissue and the obturator internus muscle. Increase in the Ktrans value was determined in lesion-to-muscle ratio by 3.974368, which is a cut-off value to differentiate between prostate cancer and normal prostate tissue, with specificity of 72.86% and sensitivity of 91.43%. We introduced a model to detect prostate cancer that combines Ktrans lesion-to-muscle ratio value and iAUC lesion-to-muscle ratio value, which is of higher accuracy compared to individual variables. Based on this model, we identified the optimal cut-off value with 100% sensitivity and 64.28% specificity. The use of quantitative DCE pharmacokinetic parameters compared to the obturator internus muscle as reference tissue leads to higher diagnostic accuracy for prostate cancer detection.
  2. I. Netinger-Grubeša, M. Benšić, M. Vračević, New methods for assessing brick resistance to freeze-thaw cycles, Materiales De Construcción 71 (2021)
    The aim of this research is to analyse the reliability of the existing methods, and find new ones, for assessing brick resistance to freeze-thaw cycles. A series of bricks were tested against a range of properties; compressive strength ratios pre- to post-freezing and Maage’s factor, were calculated. Using a database created in this way, an analysis of existing classifiers was carried out and new ones were established based on which bricks could be classified into resistant and non-resistant to freeze-thaw cycles. The median pore radius, the ratio of compressive strengths pre- to post-freezing and the water desorption coefficient at 180-360 minutes proved to be good classifiers with a clearly specified cut-off for the distinction between resistant and non-resistant bricks with an acceptable risk of a wrong decision. The ratio of compressive strengths pre to post freezing and the water desorption coefficient at 180-360 minutes were described using the pore system in the brick.
  3. V. Barišić, I. Flanjak, A. Tot, M. Budeč, M. Benšić, A. Jozinović, J. Babić, D. Šubarić, B. Miličević, Đ. Ačkar, 5-hydroxymethylfurfural and acrylamide content of cocoa shell treated with high voltage electrical discharge, Food Control 110 (2020)
    5-hydroxymethylfurfural (HMF) and acrylamide, as products of Maillard’s reactions, are present in roasted cocoa shell. Since the cocoa shell is increasingly being researched for use in food enrichment due to high fiber content and polyphenols, it is necessary to solve the problem of components that can be harmful to human health. We evaluated the effect of high voltage electrical discharge (HVED) on colour, moisture, HMF and acrylamide content in cocoa shell obtained after roasting cocoa beans. The effects of concentration, frequency and time of cocoa shell treatment were investigated. HVED proved to be a successful method for reducing the content of acrylamide and HMF. In addition, darkening of samples was observed which could mean that further reactions of those components occurred.
  4. L. Jakobek, P. Margetić, Š. Kraljević, Š. Ukić, M. Benšić, A. Barron, Adsorption between quercetin derivatives and beta-glucan studied with a novel approach to modeling adsorption isotherms, Applied Sciences 10/ 1637 (2020), 1-16
    Interactions between polyphenols and fibers are important for polyphenol bioactivities, and have been studied in vitro with adsorption process and isotherms. But the theoretical interpretations of adsorption potentially can be affected by the method of isotherm modeling. The aim was to study the interactions between β-glucan and quercetin derivatives (quercetin-3-glucoside, quercetin-3-galactoside, quercetin-3-rhamnoside) by studying adsorption and to potentially improve the modeling of adsorption isotherms. Quercetin derivatives were determined by using spectrophotometric method. Experimental results were modeled with Langmuir, Dubinin-Radushkevich and Hill isotherms using non-linear regression, linear regression and improved non-linear regression. For improved non-linear regression, a code in R program was developed. All quercetin derivatives adsorbed onto the surface of -glucan. Improved non-linear regression gave somewhat lower errors and was more appropriate for adsorption interpretation. According to isotherms obtained with improved regression, it may be suggested that adsorption is higher for rhamnoside and glucoside of quercetin than for quercetin-3-galactoside which agrees with experimental results. Adsorption could be a physical process. The spatial arrangement of OH groups on the glycoside part of quercetin could affect the adsorption. In conclusion, a novel approach using improved non-linear regression has been shown to be a useful novel tool for the adsorption interpretation.
  5. V. Barišić, I. Flanjak, M. Kopjar, M. Benšić, A. Jozinović, J. Babić, D. Šubarić, B. Miličević, K. Doko, Đ. Ačkar, Does high voltage electrical discharge treatment induce changes in tannin and fiber properties of cocoa shell?, Foods 9/6 (2020)
    Cocoa shell is a by-product of the chocolate industry that is rich in dietary fiber and bioactive components. In this research, the influence of high voltage electric discharge (HVED) treatment on chemical and physical characteristics of the cocoa shell, i.e., the effects of applied time and frequencies on grinding ability, water binding capacity (WBC), dietary fibers and tannin content was investigated. HVED had a significant influence on the chemical and physical properties of cocoa shell, all of which could be linked to changes in fiber properties. Along with the fiber content, grinding ability and water binding capacity were increased. These properties have already been linked to fiber content and soluble/insoluble fiber ratio. However, this research implies that change in fiber properties could be linked to tannin formation via complexation of other polyphenolic components. Additional research is needed to verify this effect and to establish mechanisms of tannin formation induced by HVED and its influence on fiber quantification.
  6. S. Hamedović, M. Benšić, K. Sabo, Estimating the width of a uniform distribution under symmetric measurement errors, Journal of the Korean Statistical Society 49/3 (2020), 822-840
    In this paper we consider the problem of estimating the support of a uniform distribution under symmetric additive errors. The maximum likelihood (ML) estimator is of our primary interest, but we also analyze the method of moments (MM) estimator, when it exists. Under some regularity conditions, the ML estimator is consistent and asymptotically efficient. Errors with Student's t distribution are shown to be a good choice for robustness issues.
  7. R. Bušić, M. Benšić, I. Miličević, K. Strukar, Prediction Models for the Mechanical Properties of Self-Compacting Concrete with Recycled Rubber and Silica Fume, Materijals 13/8 (2020)
    The paper aims to investigate the influence of waste tire rubber and silica fume on the fresh and hardened properties of self-compacting concrete (SCC) and to design multivariate regression models for the prediction of the mechanical properties of self-compacting rubberized concrete (SCRC). For this purpose, 21 concrete mixtures were designed. Crumb rubber derived from end-of-life tires (grain size 0.5–3.5 mm) was replaced fine aggregate by 0%, 5%, 10%, 15%, 20%, 25%, and 30% of total aggregate volume. Silica fume was replaced cement by 0%, 5%, and 10% of the total cement mass. The optimal replacement level of both materials was investigated in relation to the values of the fresh properties and mechanical properties of self-compacting concrete. Tests on fresh and hardened self-compacting concrete were performed according to the relevant European standards. Furthermore, models for predicting the values of the compressive strength, modulus of elasticity, and flexural strength of SCRC were designed and verified with the experimental results of 12 other studies. According to the obtained results, mixtures with up to 15% of recycled rubber and 5% of silica fume, with 28 days compressive strength above 30 MPa, were found to be optimal mixtures for the potential future investigation of reinforced self-compacting rubberized concrete structural elements.
  8. J. Panak Balentić, A. Jozinović, Đ. Ačkar, J. Babić, B. Miličević, M. Benšić, M. Vladetić, S. Jokić, A. Šarić, Nutritionally improved third generation snacks produced by supercritical CO2 extrusion I. Physical and sensory properties, Journal of food process engineering 42/2 (2019)
    This study was aimed at investigating the possible application of defatted hazelnut, camelina, pumpkin, and hemp cakes (by‐products of edible oil production) in the production of corn snack products, and to use supercritical CO2 as a blowing agent in indirectly expanded snack products. Cakes were added in 3, 6, and 9% proportions. Extrusion was performed in a laboratory single screw extruder and expanded by microwave. The obtained extrudates were evaluated for their physical and sensory properties. For comparison, directly expanded products without supercritical CO2, were produced with the same raw materials. The addition of the by‐product had a significant influence on the expansion ratio, bulk density, fracturability, and crispiness, and all four by‐products were successfully incorporated in the production of sensory acceptable, indirectly expanded snack products, produced by supercritical fluid extrusion. This type of products is interesting for consumers since it can be home‐made and produced without additives or any chemical substances.
  9. A. Barron, M. Benšić, K. Sabo, A Note on Weighted Least Square Distribution Fitting and Full Standardization of the Empirical Distribution Function, TEST 27/4 (2018), 946-967
    The relationship between the norm square of the standardized cumulative distribution and the chi-square statistic is examined using the form of the covariance matrix as well as the projection perspective. This investigation enables us to give uncorrelated components of the chi-square statistic and to provide interpretation of these components as innovations standardizing the cumulative distribution values. The norm square of the standardized difference between empirical and theoretical cumulative distributions is also examined as an objective function for parameter estimation. Its relationship to the chi-square distance enables us to discuss the large sample properties of these estimators and a difference in their properties in the cases that the distribution is evaluated at fixed and random points.
  10. S. Hamedović, M. Benšić, K. Sabo, P. Taler, Estimating the size of an object captured with error, Central European Journal of Operations Research 26/3 (2018), 771-781
    In many applications we are faced with the problem of estimating object dimensions from a noisy image. Some devices like a fluorescent microscope, X-ray or ultrasound machines, etc., produce imperfect images. Image noise comes from a variety of sources. It can be produced by the physical processes of imaging, or may be caused by the presence of some unwanted structures (e.g. soft tissue captured in images of bones ). In the proposed models we suppose that the data are drawn from uniform distribution on the object of interest, but contaminated by an additive error. Here we use two one-dimensional parametric models to construct confidence intervals and statistical tests pertaining to the object size and suggest the possibility of application in two-dimensional problems. Normal and Laplace distributions are used as error distributions. Finally, we illustrate ability of the R-programs we created for these problems on a real-world example.


Leader of the following projects

University J.J. Strossmayer in Osijek: 

Exploration of optimization and estimation properties of Generalized method of moments and Nonlinear least squares (2016)

Croatian Ministry of Science: 

Statistical aspects of estimation problem in nonlinear parametric models (2006-2013) 

Statistical aspects of parameter identification problems (2001-2006) 

Poticajni projekt za mlade znanstvenike "Statistički aspekti problema identifikacije parametara" (1998-2000)


Participation  in work of the following projects 

  • "Development and application of the advanced building materials for construction of healthy buildings: protection from non-ionizing radiation", (Faculty of Civil Engineering and Architecture, J. J. Strossmayer University of Osijek - European Regional Development Fund) - Project coordinator (MATHOS) (2020-2022)
  • The optimization and statistical models and methods in recognizing properties of data sets measured with errors, researcher, leader: Rudolf Scitovski (founded by Croatian Science Foundation, 2017-2021)
  • Limiting behavior of intermittent processes and diffusions, researcher, Project coordinator: Danijel Grahovac (UNIOS - ZUP 2018 - Youth Research Projects) 
  • Frakcionalne Pearsonove difuzije, researcher, leader: Nenad Šuvak (founded by  University J.J. Strossmayer in Osijek, 2015-2016)
  • Stanična i tkivna diferencijacija tijekom razvoja biljnih organa, researcher, leader: Vera Cesar (founded by MZOS, 2007.-2013. )
  • Posttraumatski stresni poremećaj djece ratnh veterana: kauzalni model, konzultant
    leader: doc.dr.sc. Ž. Vukšić-Mihaljević (founded by MZOS, 2001-2006)
  • Parameter identification problem in mathematical models, researcher 
    leader: prof.dr.sc. R. Scitovski (founded by MZOS, 1996-2000)
  • Teorijske i institucionalne pretpostavke poduzetničke ekonomije, istraživač
    leader: prof.dr.sc. S. Singer (1991.-1996.)
  • Theory of probability and mathematical statistics, researcher
    leader: prof.dr.sc. N. Sarapa (1991-1996)
  • Zakon vrijednosti u funkciji upravljanja razvojem, istraživač
    leader: prof.dr.sc. S. Singer (1986-1990)


Professional Activities

Editorial Boards

Mathematical Communications

Osječki matematički list

Matematički kolokvijum (MAT-KOL), Banja Luka, ISSN 0354-6969, stručno-metodički časopis


Committee Memberships


Refereeing/Reviewing (Selection)

Mathematical Communications
Communications in Statistics - Theory and Methods
Computational Statistics & Data Analysis
IEEE Transactions on Reliability
Inteligent Systems in Accounting, Finance and Management
Osječki matematički list
Matematički kolokvijum (MAT-KOL), Banja Luka, ISSN 0354-6969, stručno-metodički časopis

AMS Mathematical Review


Selected Service Activities

2013-2017 - Head of the Department of Mathematics, University of Osijek

2012-2013 - Member of the University board for quality assurance in higher education

2008-2013 - Substitute Head of the Department of Mathematics, University of Osijek

2008-2013 - member of the committee for teacher credentialing (Education and Teacher Training Agency)

2005-2011 - Head of the Dept. of Mathematics board for quality assurance in higher education

2001-2008 - Assistant Head of the Department of Mathematics, University of Osijek

2000–2004 - Head of the Mathematical Colloquium in Osijek

Nastava (Teaching)

Konzultacije (Office Hours): 

Nakon termina nastave kolegija ili po dogovoru.

Kontaktirati me možete putem emaila.



Aktualna nastava:

Multivarijatna analiza (Multivariate Analysis), Odjel za matematiku

Statistika (Statistics), Odjel za matematiku

Vjerojatnost i statistika (Probability and Statistics), Građevinski i arhitektonski fakultet Osijek

Planiranje eksperimenata i obrada rezultata (Doktorski studij, Prehrambeno tehnološki fakultet Osijek)

Primijenjena multivarijatna statistika (Applied Multivariate Statistics) (Doktorski studij, Građevinski i arhitektonski fakultet Osijek)


Usmeni ispiti

Studenti koji su ostvarili pravo pristupanja usmenom ispitu trebaju odabrati termin i  prijaviti svoj dolazak najkasnije 7 dana prije odabranog termina korištenjem poveznice navedene ispod ovog odjeljka. Termini su navedeni na istoj poveznici. Naglašavam da je potrebno prijaviti ispit i preko ISVU sustava da bih mogla upisati ocjenu.  Ukoliko je prijavljeno pristupanje usmenom uspitu za jedan termin, eventualnu ponovnu prijavu moguće je napraviti nakon  14 dana. 

 Poveznica za prijavu usmenih ispita 



Prijedlog tema diplomskih radova na Odjelu za matematiku:

  1. Visokodimenzionalni linearni modeli i LASSO
  2. Modeliranje razlika u razlikama
  3. Regresija vremenskog niza
  4. Statistička analiza usklađenosti ocjenjivača
  5. Moguće su i druge teme u dogovoru sa zainteresiranim studentom




Primijenjena statistika (udžbenik, baze podataka)

Uvod u vjerojatnost i statistiku (udžbenik)

Projekt u nastavi matematike srednjih škola

Buffonov pokus u nastavi matematike


Nastava koju sam izvodila (Teaching experiance)

Na Odjelu za matematiku:

Uvod u vjerojatnost i statistiku (Introduction to Probability and Statistics)

Analiza vremenskih nizova (Time Series Analysis)

Statistički praktikum (Stat Labs)

Vjerojatnost (Probability)

Slučajni procesi (Random Processes)

Metodika nastave matematike 1

Metodika nastave matematike 2


Na ostalim sastavnicama Sveučilišta u Osijeku

Statistika (Statistics), Sveučilišni preddiplomski studij kineziologije

Matematika i statistika (Doktorski studij, Strojarski fakultet, Slavonski Brod)

Matematika 1, Matematika 2 (Ekonomski fakultet Osijek)

Teorijska statistika (Ekonomski fakultet Osijek)

Matematika 1, Matematika 2 (Prehrambeno tehnološki fakultet Osijek)

Primijenjena statistika (Građevinski fakultet Osijek)

Primijenjena statistika (Prehrambeno tehnološki fakultet Osijek)

Statistika (Učiteljski fakultet Osijek) 





  • Birth year:  1961
  • Birthplace: Đakovo, Croatia
  • Citizenship: Croatian
  • Family: Married with two children (Tin, Anja)