dess

Hans Rova begravdes i snömassorna under en lavin. Nannie Fredriksson sögs upp i luften av en tromb i den svenska fjällvärlden. Ulf Rydberg var på fisketur utanför Vinga då blixten slog ner i honom.

Lyssna på alla avsnitt i Sveriges Radio Play.

Det handlar om naturkrafter som skrämmer, fascinerar och inspirerar. Många är metaforerna; dikterna och musiken som handlar om starka vindar, laviner och blixtnedslag. Nu får vi höra

berättelser inifrån; om hur det bokstavligt talat är att hamna i närgångna och livsfarliga möten med naturfenomen.

Vi möter:

• Hans Rova, officer på helikopterskvadronen på F21 i Luleå. På fritiden har han ett brinnande intresse för toppturer på skidor. Den tur han gjorde i italienska alperna hade kunnat bli hans sista. Han hamnade i en lavin och under en halvtimme låg Hans begravd i snömassorna. “Det blev plötsligt knäpptyst och det var som om någon placerat mig i betong.”

• Jenny Råghall, lavinexpert, fjällräddare och ansvarig lavinprognoser i Kebenekaisefjällen. Jenny var 23 år och skidpatrullör när hon tillsammans med sin kollega hamnade i en lavin under ett rutinupprag. Jenny klarade sig, men hon förlorade sin kollega och sen dess har hon vigt sitt liv åt fjällsäkerhet.

• Ulf Rydberg som under en fisketur hamnade mitt i ett åskväder utanför Vinga fyr i Göteborg. “Jag hann notera ett par blixtar på avstånd, sen minns jag ingenting”. Läkare uppskattar att Ulf fick 1000 ampere genom överkroppen. Han räddades av sonen Victor, som utförde hjärt- och lungräddning i väntan på sjöräddningen.

• Nannie Fredriksson fjällguiden som under en tur i Saltoluokkta befann sig i ögat av en tromb. Hon befann sig vid ett tält där en av turdeltagarna låg och sov. “Instinktivt höll jag fast i tältet och hängde under den som en fallskärm”, berättar Nannie.

I programmet möter vi även Andreas Livbom, meteorolog vid försvarsmaktens vädertjänstcentrum i Enköping som förklarar hur väderfenomenen uppstår.

Ett program av Lena Callne

Ljuddesign: Maths Källqvist

Specialmusik: Album: Gongbad för djup avslappning. Kompositör: Frida Helsing Ohlsson/GongbadOnline. Bolag: YogaKloster AB

In this lecture, we prepare for the final exam and give a brief review of all topics from the course.

In this lecture, we wrap up the course content in IEE 475. We first do a quick overview of the four variance reduction techniques (VRT's) covered in the previous unit. That is, we cover: common random numbers (CRN's), antithetic variates (AV's), importance sampling, and control variates. We then  remember some general comments about the goal of modeling and commonalities seen across simulation platforms (as well as the different types of simulation platforms in general).

In this lecture, we start by reviewing approaches for absolute and relative performance estimation in stochastic simulation. This begins with a reminder of the use of confidence intervals for estimation of performance for a single simulation model. We then move to different ways to use confidence intervals on mean DIFFERENCES to compare two different simulation models. We then move to the ranking and selection problem for three or more different simulation models, which allows us to talk about analysis of variance (ANOVA) and post hoc tests (like the Tukey HSD or Fisher's LSD). After that review, we move on to introducing variance reduction techniques (VRTs) which reduce the size of confidence intervals by experimentally controlling/accounting for alternative sources of variance (and thus reducing the observed variance in response variables). We discuss Common Random Numbers (CRNs), which use a paired/blocked design to reduce the variance caused by different random-number streams. We start to discuss control variates (CVs), but that discussion will be picked up at the start of the next lecture.

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 paired-difference t-test, the equal-variance (pooled) t-test, and Welch's unequal variance t-test. Each of these different experimental conditions sets up a different standard error of the mean formula and formula for degrees of freedom that are used to define the actual confidence interval half widths (centered on the difference in sample means in the pairwise comparison of systems). We then generalize to the case of more than 2 systems, particularly for "ranking and selection (R&S)." This lets us review the multiple-comparisons problem (and Bonferroni correction) and how post hoc tests (after an ANOVA) are more statistically powerful ways to do comparisons.

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 to reduce initialization bias and then merge that discussion with the prior discussion on how to choose the number of replications. In the next lecture, we'll finish up with a discussion of the method of "batch means" in steady-state simulations.

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 prediction intervals. Confidence intervals, which are visualizations of t-tests, provide an alternative way to choose the number of required replications without doing a formal power analysis.

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 to focusing on simulations and their outputs, starting with the definition of terminating and non-terminating systems as well as the related transient and steady-state simulations. We will pick up next time with discussing details related to performance measures (and methods) for transient simulations next time and steady-state simulations after that. Our goal was to discuss the difference between point estimation and interval estimation for simulation, but we will hold off to discuss that topic in the next lecture.

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 the previous lecture) where we use a power analysis on a one-sample t-test to help justify whether we have gathered enough data to trust that a simulation model is a good match for reality when it has a similar mean output performance to the real system.

In this lecture, we mostly cover slides from Lecture G3 (on goodness of fit) that were missed during the previous lecture. 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 Anderson–Darling (for flexibility and higher power) and Shapiro–Wilk (for high-powered normality testing). We close with where we originally intended to start – with definitions of testing, verification, validation, and calibration. We will pick up from here next time.

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 are not meaningful). We give some examples of this applied to best-of-7 sports tournaments and voting. We then discuss different shape parameters (including location, scale, and rate), and then introduce summary statistics (sample mean and sample variance) and maximum likelihood estimation (MLE), with an example for a point estimate of the rate of an exponential. We introduce the chi-squared (lower power) and Kolmogorov–Smirnov (KS, high power) tests for goodness of fit, but we will go into them in more detail at the start of the next lecture.

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 with a discussion of probability plots – Q-Q plots and P-P plots, as are used with "fat-pencil tests" – as a good tool for justifying the choice of a family for a certain data set. The next lecture will go over the actual estimation of the parameters for the chosen families and how to quantitatively assess goodness of fit.

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 related to data collection.

Midterm review session for ASU IEE 475 for Fall 2022. 

Whiteboard notes for this lecture can be found at: https://www.dropbox.com/s/ljc61rarhns41u2/2022-Fall-Midterm_Review_Notes.pdf?dl=0

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 smaller numbers of samples. For independence, we discuss autocorrelation tests and runs test, and then we demonstrate a runs above-and-below-the-mean test. We then shift to discussing inverse-transform sampling for continuous random variates and discrete random variates and how the resulting random-variate generators might be implemented in a tool like Rockwell Automation's Arena.

In this lecture, we first cover some discrete distributions (and the Poisson process) that we ran out of time for during the previous lecture. We then launch into a discussion of how to generate pseudo-random numbers distributed uniformly between 0 and 1 (which are necessary for us to easily generate random variates of any distribution). We talk about the two most important properties of a pseudo-random number generator (PRNG), uniformity and independence. We then talk about desirable properties. Some examples are given of some early PRNG's, and then we introduce the linear congruential generator (LCG) and its variants (like the Combined Linear Congruential Generator, CLCG), which represent a much more modern PRNG that has a number of good properties. We close with a discussion of tests of uniformity. We will continue this discussion and add on tests for independence during next lecture (which will primarily cover random-VARIATE generation).

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. We will finish the discussing next time with the Bernoulli-based discrete variables and Poisson processes.

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 ability to shift the mean significantly, as in physical leverage). This sets us up to talk about random processes and particular random variables in the next lecture.

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 ABM describes applications in life sciences, social sciences, and engineering (Multi-Agent Systems, MAS)/operations research. NetLogo is introduced, and it is used to present examples of running ABM's as well as the code behind them. At the end of the ABM/NetLogo introduction, comments about the previous lab on Monte Carlo simulation are given. These comments focus on interval estimation (which is right 95% of the time, as opposed to point estimation that is right 0% of the time) and the role of non-trivial distributions of random variables (as opposed to just their means).

In this lecture, 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 (SAN's). Although we show that spreadsheets can be very powerful for this kind of work, we highlight that this approach is cumbersome for systems with increasing complexity. So this motivates why we would use more sophisticated tools specifically built for simulation (but perhaps not so great for data analysis by themselves), like Arena, FlexSim, Simio, and NetLogo.