Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Masterat
Domeniul: Informatica
Programul de studii: Modelare si simulare - în limba engleză
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MMC1007	Computational Statistical Models	

Semester	Hours: C+S+L+P	Category	Status	
1	2+1+0+1	speciality	compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
BLAGA Petru	Ph.D.	Prof.	Mathematics	*	*		

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
surname	title		position	C	S	L	

III. Course objectives
Knowledge and simulation of some statistical models oriented on software products. Correct using of the mathematical statistical models. Knowledge some statistical software. Development and construct of procedures for statistical methods.

IV. Course contents
1. Basics of probability theory. 
2. Sampling theory and estimation theory.
3. Confidence intervals and testing statistical hypotheses for mean values and variances.
4. Nonparametric and parametric goodness-of-fit tests.
5. Multiple linear regression.
6. Analyse of variance (ANOVA).

V. Bibliography
1. Agratini, O., Blaga, P., Coman, Gh., Lectures on Wavelets, Numerical Methods, and   Statistics, Casa Cartii de Stiinta, Cluj-Napoca, 2005.
2. Blaga, P., Calculul probabilitatilor si statistica matematica. Vol. II. Curs si    culegere de probleme, UBB, Cluj-Napoca, 1994.
3. Blaga, P., Statistica matematica. Lucrari de laborator, UBB, Cluj-Napoca, 1999.
4. Blaga, P., Statistica... prin Matlab, Presa Universitara Clujeana, Cluj-Napoca, 2002.
5. Blaga, P., Muresan, A. S., Matematici aplicate în economie, Vol. I, Transilvania    Press, Cluj-Napoca, 1996.
6. Blaga, P., Radulescu, M., Calculul probabilitatilor, UBB, Cluj-Napoca, 1987.
7. Iosifescu, M., Mihoc, Gh., Theodorescu, R., Teoria probabilitatilor si statistica    matematica, Editura Tehnica, Bucuresti, 1966.
8. Mihoc, I., Calculul probabilitatilor si statstica matematica, Part. I-II, UBB, Cluj-Napoca, 1994, 1995.
9. Vaduva, I., Analiza dispersionala, Editura Tehnica, Bucuresti, 1977.	

VI. Thematic of didactic activities per weeks
Probability space. Random variables. Random vectors. Distribution function. Probability 
  density function. Conditional distribution function. Conditional probability density 
  function. Numerical characteristics of random variables. Mean value. Variance.  
  Standard deviation. Covariance. Correlation coefficient.
 Mean value and  covariance matrix of  random vector aleator. Conditional mean value. 
  Conditional varaince. Chebyshev inequality. Convegence in probability. Convergence in   
  distribution (law). Weak law of large numbers. Limit theorems (Lindeberg-Lévy, Moivre-
  Laplace, corrections of continuity). 
 Sampling theory. Sample functions. Sample mean. Sample moment. Sample central moment. 
  Sample variance. Sample distribution function. Glivenko theorem. Kolmogorov theorem.
 Estimation theory. Consistent estimator. Unbiased estimator. Absolutely correct 
  estimator. Correct estimator. Likelihood function. Maximum likelihood method. Maximim 
  likelihood estimator. Fisher information. Rao-Cramér inequality. Efficient estimator. 
  Method of  confidence intervals. 
 Testing statistical hypotheses. Test for statistical hypothesis. Error of type I. 
  Error of type II. Power of a test. Z-test, T-test and confidence interval for mean 
  value of a variable. χ-square test and confidence interval  for variance of a variable. 
 Z-test, T-test and confidence intervals for difference of two mean values. F- test for 
  ratio of two variances.
 Goodness-of-fit χ-square test for multinomial distribution. Nonparametric goodness-of-fit  
  χ-square test. Parametric goodness-of-fit χ-square test. Homogeneity  χ-square test. Independence χ-square test. Goodness-of-fit Kolmogorov test. . Goodness-of-fit Kolmogorov-Smirnov test.
 Regression problem. Multiple linear model. Fitted least-squares multiple linear 
  regression model. Multiple linear model with constant term. Coefficient of 
  determination. Total variance equation.
 Gauss-Markov linear model. Gauss-Markov theorem. Unbiased estimators for coefficients. 
  Unbiased estimator for variance.
 Classical linear model. Probability law of the coefficient estimators. Probability law 
  of the variance estimator. T-test for the coefficients of  model, confidence intervals 
  for the coefficients of model.
 Maximum likelihood estimators for coefficients and variance.  Linear prediction 
  problem. Estimator for prediction. Confidence interval for prediction.
 F-test for all coefficients. F-test for a subset of coefficients. F-test for classical 
  linear model with constant term. F-test for equality of some coefficients . F-test for 
  identity of two linear models. ANOVA table.
 One-way analysis of variance. Total variance equation. F-test for equality of means of 
  categories. ANOVA table.
 Analysis of variance with two and more factors. Two-way ANOVA without interaction. F-  
  test for the null effect of a factor. Two-way ANOVA with interaction. F-test for the 
  null effect of a factor. F-test for the null interaction effects.	

VII. Didactic methods used
Lectures, interactive presentations, exercises, individual study, homework assignments.	

VIII. Assessment
Final grade consists from:
 Final written exam:           50%
 Activity during the semester: 25% 
 Evaluation of homeworks:      25%

IX. Additional references
1.	Ermakov, S. M., Metoda Monte Carlo şi probleme înrudite, Editura Tehnică, Bucureşti, 1976.
2.	Lebart, L., Morineau, M. G., Fenelon, J.-P., Traitment des données statistiques, Dunod, Paris, 1982.
3.	Lehmann, E. L., Testing statistical hypotheses, Springer, New York, 1997.
4.	Montgomery, D. C., Peck, E. A., Vining, G. G., Introduction to linear analysis, John Wiley & Sons (3rd ed.), New York, 2001.
5.	Saporta, G., Probabilités, analyse des données et statistique, Édition Technip, Paris, 1990.
6.	Tassi, Ph., Methodes statistiques, Economica (2nd ed.), Paris, 1989.
7.	Schervish, M. J., Theory of statistics, Springer, New York, 1995.
8.	Stapleton, J. H., Linear statistical models, John Wiley & Sons, New York, 1995.
9.	Weerahndi, S., Exact statistical methods for data analysis, Springer, New York, 1994	

	Dean,
Prof. Dr. Leon Tâmbulea					Chair head,
							Prof. Dr. Octavian Agratini

	Date,	
September 27th, 2011					Course responsible,
							Prof. Petru BLAGA, Ph.D.