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Jack Baker
United States
Приєднався 1 бер 2013
Research and teaching videos from the Baker Research Group at Stanford University.
Structural Reliability 10j - Conclusions
We conclude the Monte Carlo video series by discussing the strengths and limitations of different sampling-based methods in Monte Carlo simulations, including crude Monte Carlo, importance sampling, Latin hypercube, copulas, and metamodels. This video provides a comparative analysis of these techniques, focusing on their efficiency in terms of sample size, handling dependencies, managing small probabilities of failure, and reducing computational costs in evaluations. The discussion highlights the advantages of importance sampling and its relevance in practical use cases.
00:00 Introduction
00:23 Comparing Sampling Methods
01:36 Strengths and Weaknesses
02:46 Concluding Thoughts
00:00 Introduction
00:23 Comparing Sampling Methods
01:36 Strengths and Weaknesses
02:46 Concluding Thoughts
Переглядів: 75
Відео
Structural Reliability 10i - Metamodels
Переглядів 573 місяці тому
In this brief video, we explore the concept of metamodels used in Monte Carlo simulations. Metamodels are simplified functions that approximate expensive-to-evaluate functions in simulations, reducing computational intensity and potentially simplifying the problem by highlighting insignificant random variables. We discuss various types of metamodels such as polynomial functions, regression anal...
Structural Reliability 10h - Copulas
Переглядів 1143 місяці тому
In this video, we explore the concept of copulas-a technique used in Monte Carlo simulations to simulate random variables from a joint distribution. Unlike the Nataf or Rosenblatt methods, copulas offer an alternative approach frequently utilized in finance, hydrology, and other fields dealing with dependent variables. We delve into the process of generating samples using marginal CDFs and the ...
Structural Reliability 10g - Latin Hypercube sampling
Переглядів 1693 місяці тому
Advanced Monte Carlo Sampling Techniques: Latin Hypercube Sampling In this video, we explore advanced techniques for generating Monte Carlo samples, focusing on Latin hypercube sampling. We'll discuss its benefits and limitations, especially in high-dimensional problems and contexts with small failure probabilities. The video covers the basics of dividing sample spaces into equi-probable areas,...
Structural Reliability 10f - More random number generation
Переглядів 503 місяці тому
In this video, we delve into the simulation of pseudo-random numbers and their crucial role in Monte Carlo simulations. We discuss MATLAB's built-in functions for generating random variables from various distributions, with a focus on the multivariate normal distribution. The video further explains how to generate multivariate random numbers manually using mean vectors and covariance matrices, ...
Structural Reliability 10e - Sampling distributions
Переглядів 483 місяці тому
In this video, we delve deeper into the concept of sampling distributions within the important sampling approach discussed previously. We explore strategies for selecting effective sampling distributions, highlighting potential benefits such as reducing simulation times and handling dependent variables more conveniently. Key considerations for ensuring the efficiency and accuracy of these sampl...
Structural Reliability 10d - Importance sampling
Переглядів 733 місяці тому
In this video, we explore methods to enhance the performance of Monte Carlo simulations, specifically focusing on reducing the coefficient of variation in probability of failure estimates. We discuss three main strategies: increasing the number of samples, reformulating the problem to increase the probability of failure, and using dependent sampling techniques like Latin hypercube sampling and ...
Structural Reliability 10c - Statistical properties of the pf estimator
Переглядів 743 місяці тому
Understanding Monte Carlo Estimators: Statistical Properties and Insights In this video, we delve into the statistical properties of Monte Carlo estimators, focusing on estimating the probability of failure. We explore how to calculate the expected value and variance of derived values and what these mean for the performance of Monte Carlo estimations. Additionally, we examine how the number of ...
Structural Reliability 10b - Reliability formulation
Переглядів 873 місяці тому
Connecting Monte Carlo Methods to Reliability Integral Formulation In this episode, we delve into the mathematical connection between Monte Carlo methods and reliability integral formulation. We explore the use of indicator functions in integral calculations to evaluate system failure probabilities. The video explains how to generate independent samples, form Bernoulli sequences, and estimate f...
Structural Reliability 10a - Monte Carlo Introduction
Переглядів 2803 місяці тому
Introduction to Monte Carlo Methods In this video, we delve into Monte Carlo methods, a numerical sampling strategy for reliability assessment. We contrast it with the analytical approaches previously discussed, explaining its flexibility and ease of implementation. Key steps in the process, including simulating random variables and evaluating limit state functions, are covered. We also address...
6e - Additional PSHA topics
Переглядів 1253 місяці тому
In this video, we explore various aspects of Probabilistic Seismic Hazard Analysis (PSHA) calculations that didn't fit neatly into our previous categories. Topics include different formulations of PSHA equations, highlighting comparisons between historical and modern methods. We discuss the evolution from Allin Cornell's 1968 paper to contemporary formulations involving discrete distributions a...
6d - Epistemic uncertainty and PSHA
Переглядів 1403 місяці тому
Epistemic Uncertainty in Seismic Hazard Analysis In this video, we delve into epistemic uncertainty. Unlike aleatory uncertainty, which deals with natural randomness, epistemic uncertainty addresses our incomplete understanding of seismic processes. We discuss the use of logic trees to manage this uncertainty, illustrating how different model components (such as earthquake rates, maximum magnit...
6c - PSHA Sensitivity studies
Переглядів 1793 місяці тому
PSHA Sensitivity Studies: Parameters Impacting Ground Motion Hazard Curves In this video, we perform sensitivity studies of Probabilistic Seismic Hazard Analysis (PSHA) results by varying different input parameters and observing their effects on the ground motion hazard curves. Using the Gutenberg-Richter example as a baseline, we explore the impact of changes in earthquake rupture rates, the m...
6b - Poisson process and PSHA
Переглядів 2083 місяці тому
This video provides an overview of the Poisson Process, and discusses its relevance to PSHA calculations. This video is based on material from the book “Seismic Hazard and Risk Analysis” by Jack Baker, Brendon Bradley, and Peter Stafford (Cambridge University Press, 2021). See www.pshabook.com for links to purchase the book, code to demonstrate calculations, and more. Publisher website: www.cam...
6a - Basics of PSHA
Переглядів 3153 місяці тому
Understanding PSHA Calculations: A Step-by-Step Guide In this video, we explore the details of Probabilistic Seismic Hazard Analysis (PSHA) calculations. Covering sections 6.1 through 6.8 of the textbook, we break down the important ingredients, including seismic source models and ground motion models, and how they fit together. Through examples, we demonstrate the relationships between inputs ...
Spatial correlation in ground motion intensities: Measurement, prediction, and implications
Переглядів 1,7 тис.Рік тому
Spatial correlation in ground motion intensities: Measurement, prediction, and implications
Developing and giving technical presentations
Переглядів 1 тис.Рік тому
Developing and giving technical presentations
PSHA primer: Seismic hazard calculations
Переглядів 7 тис.2 роки тому
PSHA primer: Seismic hazard calculations
Random vibrations lecture 5c, Frequency response functions
Переглядів 1 тис.2 роки тому
Random vibrations lecture 5c, Frequency response functions
Random vibrations lecture 5b, Impulse response functions
Переглядів 7952 роки тому
Random vibrations lecture 5b, Impulse response functions
Random vibrations lecture 5a, Linear systems analysis
Переглядів 3222 роки тому
Random vibrations lecture 5a, Linear systems analysis
Random vibrations lecture 3e, Moment and order stationarity
Переглядів 3252 роки тому
Random vibrations lecture 3e, Moment and order stationarity
Random vibrations lecture 3f, Comparison of moment and order stationarity
Переглядів 2482 роки тому
Random vibrations lecture 3f, Comparison of moment and order stationarity
Random vibrations lecture 3g, Properties of Autocorrelation and Autocovariance
Переглядів 3642 роки тому
Random vibrations lecture 3g, Properties of Autocorrelation and Autocovariance
Random vibrations lecture 3h, Gaussian processes
Переглядів 3192 роки тому
Random vibrations lecture 3h, Gaussian processes
Random vibrations lecture 3d, Moments of stochastic processes
Переглядів 5682 роки тому
Random vibrations lecture 3d, Moments of stochastic processes
Random vibrations lecture 3c, Specification of stochastic processes
Переглядів 7402 роки тому
Random vibrations lecture 3c, Specification of stochastic processes
Thank You, you helped me understand.
Dear Professor, thanks for the clear explanation!
Good❤
But, we can't say anything about the independence b/w two random variables provided the Covariance between them is zero, right? Then how is 4th property working? Can you clarify please.
Is it possible for a PDF copy of the lecture
Best teacher
👍👍👍
Thank you!
After finding so many videos over the topic my research ends here...
❤❤❤good
❤very good
Analogy with bivariate is shown very elegantly. Thanks.
Important concepts, clear explained! thanks
Is there a way to derive the marginal pdf of each component X_i without resorting to the moment generating function?
Great video. Thank you!
Mr Baker's teaching is very well and clear! And am I the only one who thinks he looks and sounds like Woody from Toy Story?
This is good, thanks for uploading
Thanks!
Thank you!
How large should be the area considered for the analysis? 10 x 10 km? 100 x 100 km?
Very great classes!
thank you!
Thank you, Dr. Baker. Great points..
why my professor is not you.
Thank you for the great presentation. I just ordered the book from Aamazon.
Thank you! That was very good
Hello Sir, Can you please tell what plotting tools and font and line width specifications do you use for your figures? They look really elegant. I would certainly like to replicate the same in my presentations. I usually have problems when i import images to the latex environment and am forced to rescale the image to fit the document appropriately. Looking forward to hearing from you. Thanks. 😊
Thank you Mr. Baker, the video was very useful to me, greetings from Lima, Peru
very clear explanation! thanks
Nice suggestions, Prof. Baker. Which software do you suggest to use for making plots/graphics?
Excellent video... Really helped me to understand the concepts in depth... Thank you Prof.Baker. - Reena,India
Thank you, professor. Can you make a video on how to calculate weights for GMPEs used in PSHA with example. It will be very helpful.
Clear explanation. Thank you.
Thank you Professor for uploading these lectures! They have been of great help to me.
Thank you! Concepts are very well-explained!
Excuse me, sir. Thank you for the video. But I don’t understand yet. Can you please give us an example about how to find variance and covariance of random vector, if expected values is real number?
For variance, you need to construct an E[(X-E[X])]. E'[(X-E[X])] which is the second moment. This will give Var[X]. For the cov[X,Y], you should calculate E[X-mx, Y-my] .E'[X-mx, Y-my] (be careful because this includes Transpose.) Then you will have nxn matrix ((nx1) x (1xn) matrix gives nxn matrix). The diagonal of that matrix will include variances of each vector and the other terms are just covariances between related xi and yi. (m for mean) Hope that clears!
Thank you
Thank you Sir
How can we get for n random x values in one data set , n mean values? I mean if I have a data set with Gaussian shape, shouldn't have only one mean and sigma. Bu the way, I have a histogram showing counts per channel up to 1024 channels for instance. The example you gave at the minute of 13.14, how would you construct it if you had one mean and one sigma but a vector of random variables as in my example I tried to explain above? (instead of having the mean and Sigma matrices) Actually, in that exmple at the minute of 15.00, you decided to change x matrix having x1 and x1 variables to x (underlined matrix with x1 vector and x2 vector . That confused everything.
I hope this answers: In X vector, we have x1, x2 and so xn. These xi variables also a vector containing numbers. So X is initially a set of random vectors. Then you will have different mean values for each x1, x2 and so xi.
How do you call x, mu and sigma in likelihood function of a Gaussian distribution in statistics or in math (Variable, domain, data, parameter in univariate, bivariate, and multivariate case seperately) ? I am also asking this when there is only one data point or when you have a data set of x, when you have a vector of mean and sigmas, so on , so forth. Thanks in advance.
Hi! Prof. Baker, the videos are really helpful! Thank you so much from Canada, Can you please upload such videos covering other chapters of the book (Seismic Hazard and Risk Analysis)?. They boost the comprehension and motivate to go through the book in a more detailed and systematic manner.
Could you do an example of DSHA as well. Thank you.
Could you an example of DSHA as well
𝕡𝐫o𝕄o𝔰𝓶
Thank you for this! My doctoral thesis is in this area! These videos are of invaluable help. Greetings from Chile, the land of earthquakes :)
Excellent video, greetings from Arequipa-Peru
Thanks. Btw, there is a typo: 0.16 should be 0.016 in the example.
Good catch. You are correct. Unfortunately, I can't find an way to correct the video file to reflect this.
It í very useful and compressive explanation professor Baker
Dear professor Thanks for perfect videos. But when you derived the complex response frequency function in terms of c and d, the zeta is missed (around 16 min of video) although the the final function at next slide is correct.
Yes, you are correct. Thank you for pointing out this error Navid.
So, not so "perfect" after all!?
Thanks for your useful videos.