PODCAST

IEE 475: Simulating Stochastic Systems

Theodore P. Pavlic

Archived lectures from undergraduate course on stochastic simulation given at Arizona State University by Ted Pavlic

education higher education

All Episodes

Lecture J4 (2024-11-14): Estimation of Relative...

IEE 475: Simulating Stochastic Systems ·

2024/11/15

In this lecture, we review what we have learned about one-sample confidence intervals (i.e., how to use them as graphical versions of one-sample t-tests) for absolute performance estimation in order to motivate the problem of relative performance estimation. We introduce two-sample confidence intervals (i.e., confidence intervals on DIFFERENCES based on different two-sample t-tests) that are tested against a null hypothesis of 0. This means covering confidence interval half widths for the

en-us

Lecture J3 (2024-11-12): Estimation of Absolute...

IEE 475: Simulating Stochastic Systems ·

2024/11/12

In this lecture, we start by further reviewing confidence intervals (where they come from and what they mean) and prediction intervals and then use them to motivate a simpler way to determine how many replications are needed in a simulation study (focusing first on transient simulations of terminating systems). We then shift our attention to steady-state simulations of non-terminating systems and the issue of initialization bias. We discuss different methods of "warming up" a steady-state simulation

en-us

Lecture J2 (2024-11-07): Estimation of Absolute...

IEE 475: Simulating Stochastic Systems ·

2024/11/12

In this lecture, we review estimating absolute performance from simulation, with focus on choosing the number of necessary replications of transient simulations of terminating systems. The lecture starts by overviewing point estimation, bias, and different types of point estimators. This includes an overview of quantile estimation and how to use quantile estimation to use simulations as null-hypothesis-prediction generators. We the introduce interval estimation with confidence intervals and

en-us

Lecture J1 (2024-11-05): Estimation of Absolute...

IEE 475: Simulating Stochastic Systems ·

2024/11/05

In this lecture, we introduce the estimation of absolute performance measures in simulation – effectively shifting our focus from validating input models to validating and making inferences about simulation outputs. Most of this lecture is a review of statistics and reasons for the assumptions for various parametric and non-exact non-parametric methods. We also introduce a few more advanced statistical topics, such as non-parametric methods and special high-power tests for normality. We then switch

en-us

Lecture I (2024-10-31): Statistical Reflections

IEE 475: Simulating Stochastic Systems ·

2024/11/05

In this lecture, we review statistical fundamentals – such as the origins of the t-test, the meaning of type-I and type-II error (and alternative terminology for both, such as false positive rate and false negative rate) and the connection to statistical power (sensitivity). We review the Receiver Operating Characteristic (ROC) curve and give a qualitative description of where it gets its shape in a hypothesis test. We close with a validation example (from Lecture H) where we use a power analysis on

en-us

Lecture H (2024-10-29): Verification, Validation, and...

IEE 475: Simulating Stochastic Systems ·

2024/10/30

During this lecture slot, we start with slides from Lecture G3 (on goodness of fit) that were missed during the previous lecture due to timing. In particular, we review hypothesis testing fundamentals (type-I error, type-II error, statistical power, sensitivity, false positive rate, true negative rate, receiver operating characteristic, ROC, alpha, beta) and then go into examples of using Chi-squared and Kolmogorov–Smirnov tests for goodness of fit for arbitrary distributions. We also introduce

en-us

Lecture G3 (2024-10-24): Input Modeling, Part 3:...

IEE 475: Simulating Stochastic Systems ·

2024/10/25

In this lecture, we (nearly) finish our coverage of Input Modeling, where the focus of this lecture is on parameter estimation and assessing goodness of fit. We review input modeling in general and then briefly review fundamentals of hypothesis testing. We discuss type-I error, p-values, type-II error, effect sizes, and statistical power. We discuss the dangers of using p-values at very large sample sizes (where small p-values are not meaningful) and at very small sample sizes (where large p-values

en-us

Lecture G2 (2024-10-22): Input Modeling, Part 2:...

IEE 475: Simulating Stochastic Systems ·

2024/10/22

In this lecture, we continue discussing the choice of input models in stochastic simulation. Here, we pivot from talking about data collection to selection of the broad family of probabilistic distributions that may be a good fit for data. We start with an example where a histogram leads us to introduce additional input models into a flow chart. The rest of the lecture is about choosing models based on physical intuition and the shape of the sampled data (e.g., the shape of histograms). We close

en-us

Lecture G1 (2024-10-17): Input Modeling, Part 1: Data...

IEE 475: Simulating Stochastic Systems ·

2024/10/18

In this lecture, we introduce the detailed process of input modeling. Input models are probabilistic models that introduce variation in simulation models of systems. Those input models must be chosen to match statistical distributions in data. Over this unit, we cover collection of data for this process, choice of probabilistic families to fit to these data, and then optimized parameter choice within those families and evaluation of fit with goodness of fit. In this lecture, we discuss issues

en-us

Lecture F (2024-10-03): Midterm Review

IEE 475: Simulating Stochastic Systems ·

2024/10/03

During this lecture, we review the topics covered up to this point in the course as preparation for the upcoming midterm exam. Students are encouraged to bring their own questions to class so that we can focus on the topics that students feel like they need the most help with.

en-us

Lecture E2 (2024-10-01): Random-Variate Generation

IEE 475: Simulating Stochastic Systems ·

2024/10/01

In this lecture, we review pseudo-random number generation and then introduce random-variate generation by way of inverse-transform sampling. In particular, we start with a review of the two most important properties of a pseudo-random number generator (PRNG), uniformity and independence, and discuss statistically rigorous methods for testing for these two properties. For uniformity, we focus on a Chi-square/Chi-squared test for larger numbers of samples and a Kolmogorov–Smirnov (KS) test for

en-us

Lecture E1 (2024-09-06): Random-Number Generation

IEE 475: Simulating Stochastic Systems ·

2024/09/26

In this lecture, we introduce the measure-theoretic concept of a random variable (which is neither random nor a variable) and related terms, such as outcomes, events, probability measures, moments, means, etc. Throughout the lecture, we use the metaphor of probability as mass (and thus probability density as mass density, and a mean as a center of mass). This allows us to discuss the "statistical leverage" of outliers in a distribution (i.e., although they happen infrequently, they still have the

en-us

Lecture D2 (2024-09-24): Probabilistic Models

IEE 475: Simulating Stochastic Systems ·

2024/09/24

In this lecture, we review basic probability fundamentals (measure spaces, probability measures, random variables, probability density functions, probability mass functions, cumulative distribution functions, moments, mean/expected value/center of mass, standard deviation, variance), and then we start to build a vocabulary of different probabilistic models that are used in different modeling contexts. These include uniform, triangular, normal, exponential, Erlang-k, Weibull, and Poisson variables

en-us

Lecture D1 (2024-09-19): Probability and Random...

IEE 475: Simulating Stochastic Systems ·

2024/09/19

en-us

Lecture C2 (2024-09-17): Beyond DES – SDM, ABM, and...

IEE 475: Simulating Stochastic Systems ·

2024/09/17

This lecture (slides embedded below) provides some historical background and motivation for System Dynamics Modeling (SDM) and Agent-Based Modeling (ABM), two other simulation modeling approaches that contrast with Discrete Event System (DES) simulation.In particular, in this lecture, we briefly introduce System Dynamics Modeling (SDM) and Agent-Based/Individual-Based Modeling (ABM/IBM) as the two ends of the simulation modeling spectrum (from low resolution to high resolution). The introduction of

en-us

Lecture C1 (2024-09-12): Basic Simulation Tools and...

IEE 475: Simulating Stochastic Systems ·

2024/09/12

This lecture covers content related to implementing simulations with spreadsheets and the motivations for the use of special-purpose Discrete Event System Simulation tools. In particular, we discuss different approaches to implementing Discrete Event System (DES) simulations (DESS) with simple spreadsheets (e.g., Microsoft Excel, Google Sheets, Apple Numbers, etc.). We cover inventory management problems (such as the newsvendor model) as well as Monte Carlo sampling and stochastic activity networks

en-us

Lecture B3 (2024-09-10): Discrete-Event Simulation...

IEE 475: Simulating Stochastic Systems ·

2024/09/11

In this lecture, we close out our review of DES fundamentals and hand simulation. After going through a hand-simulation example one last time, we show how to implement a Discrete Event System (DES) simulation using a spreadsheet tool like Microsoft Excel without any "macros" (VBA, etc.). This involves defining relationships ACROSS TIME that allow the spreadsheet to (in a declarative fashion) reconstruct the trajectory that is the output of the simulation.We then pivot to discussing the previous "Lab

en-us

Lecture B2 (2024-09-05): Discrete-Event Simulation...

IEE 475: Simulating Stochastic Systems ·

2024/09/05

In this lecture, we review fundamentals of Discrete Event System (DES) simulation (e.g., entities, resources, activities, processes, delays, attributes) and we run through a number of DES modeling examples. These examples show how different research/operations questions can lead to different choices of entities/resources/etc. We close with a hand-simulation example of a single-channel, single-server queue with provided interarrival times and service times.

en-us

Lecture B1 (2024-09-03): Fundamental Concepts of...

IEE 475: Simulating Stochastic Systems ·

2024/09/03

In this lecture, we cover fundamentals of discrete-event system (DES) simulation (DESS). This involves reviewing basic simulation concepts (entities, resources, attributes, events, activities, delays) and introducing the event-scheduling world view, which provides a causality framework on which an automatic simulation of a DES system can be built. We also discuss briefly how the stochastic modeling inherent to DESS means that outputs will be variable and thus will require rigorous statistics to make

en-us

Lecture A2 (2024-08-29): Introduction to Simulation...

IEE 475: Simulating Stochastic Systems ·

2024/08/30

In this lecture, we introduce the three different simulation methodologies (agent-based modeling, system dynamics modeling, and discrete event system simulation) and then focus on how stochastic modeling is used within discrete-event system simulation. In particular, we define terms such as system, dynamic system, state, state variable, activity, delay, resource, entity, and the notion of "input modeling."

en-us

67 results

IEE 475: Simulating Stochastic Systems

All Episodes

Similar Podcasts

Science Talk

Albert Einstein College of Medicine

Les dents et dodo

BFMTV

一起读书吧！

一起读书吧！

五分钟心理学

柠檬心理

Rock it - dein Raketenstart in den Tag

Hannes kann es