Unit STATISTICAL COMPUTING METHODS
- Course
- Finance and quantitative methods for economics
- Study-unit Code
- A000208
- Location
- PERUGIA
- Curriculum
- Statistical data science for finance and economics
- Teacher
- Francesco Bartolucci
- CFU
- 12
- Course Regulation
- Coorte 2023
- Offered
- 2024/25
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa integrata
MOD. I STATISTICAL COMPUTING
| Code | A000209 |
|---|---|
| Location | PERUGIA |
| CFU | 6 |
| Teacher | Silvia Pandolfi |
| Teachers |
|
| Hours |
|
| Learning activities | Affine/integrativa |
| Area | Attività formative affini o integrative |
| Academic discipline | SECS-S/01 |
| Type of study-unit | Obbligatorio (Required) |
MOD. II BAYESIAN COMPUTING
| Code | A000210 |
|---|---|
| Location | PERUGIA |
| CFU | 6 |
| Teacher | Francesco Bartolucci |
| Teachers |
|
| Hours |
|
| Learning activities | Affine/integrativa |
| Area | Attività formative affini o integrative |
| Academic discipline | SECS-S/01 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | English |
| Contents | The module gives the first notions of Bayesian inference and an illustration of the main algorithms for the application of Bayesian inferential methods for data analysis. |
| Reference texts | Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2020). Bayesian data analysis. Chapman and Hall/CRC. Robert, C. (2007). The Bayesian choice: from decision-theoretic foundations to computational implementation. New York: Springer. Robert, C. and Casella, G. (2010). Introducing Monte Carlo methods with R. New York: Springer. |
| Educational objectives | Students who successfully complete the module will possess the capability to implement algorithms of Bayesian inference for analysis of dataset of itermediate complexity. |
| Prerequisites | Basic courses of probability and statistics. |
| Teaching methods | Four/six hours of lectures including practical exercises on a weekly basis. |
| Other information | Students will use statistical software R. |
| Learning verification modality | Written and oral exam. |
| Extended program | - Review of principles of frequentist inference - Principles of the Bayesian inferential approach in comparison to the frequentist approach - Conjugate prior distributions - Specific cases: Beta-Binomial, Dirichlet-Multinomial, Gamma-Poisson - The case of Normal-Normal-Inverse Gamma and of linear regression - Objective and Jeffreys priors - Prediction, Confidence intervals and Hypothesis testing - Computation of posterior distribution via deterministic approaches: quadrature method, Laplace approximation, EM algorithm - Computation of posterior distribution via stochastic approaches: Monte Carlo method, Importance sampling, Metropolis-Hastings algorithm, Gibbs sampler, Reversible Jump algorithm |
| Obiettivi Agenda 2030 per lo sviluppo sostenibile | Quality education |