Probability management

Stochastic simulation | Monte Carlo methods | Probability distributions

The discipline of probability management communicates and calculates uncertainties as data structures that obey both the laws of arithmetic and probability. The simplest approach is to use vector arrays of simulated or historical realizations and metadata called Stochastic Information Packets (SIPs). A set of SIPs, which preserve statistical relationships between variables, is said to be coherent and is referred to as a Stochastic Library Unit with Relationships Preserved (SLURP). SIPs and SLURPs allow stochastic simulations to communicate with one another. For example, see Analytica (Wikipedia), Analytica (SIP page), Oracle Crystal Ball, Frontline Solvers, and Autobox. The first large documented application of SIPs involved the exploration portfolio of Royal Dutch Shell in 2005 as reported by Savage, Scholtes, and Zweidler, who formalized the discipline of probability management in 2006. The topic is also explored at length in. Vectors of simulated realizations of probability distributions have been used to drive stochastic optimization since at least 1991. Andrew Gelman described such arrays of realizations as Random Variable Objects in 2007. A recent approach does not store the actual realizations, but delivers formulas known as Virtual SIPs that generate identical simulation trials in the host environment regardless of platform. This is accomplished through inverse transform sampling, also known as the F-Inverse method, coupled to a portable pseudo random number generator, which produces the same stream of uniform random numbers across platforms. Quantile parameterized distributions (QPDs) are convenient for inverse transform sampling in this context. In particular, the Metalog distribution is a flexible continuous probability distribution that has simple closed form equations, can be directly parameterized by data, using only a handful of parameters. An ideal pseudo random number generator for driving inverse transforms is the HDR generator developed by Douglas W. Hubbard. It is a counter-based generator with a four-dimensional seed plus an iteration index that runs in virtually all platforms including Microsoft Excel. This allows simulation results derived in R, Python, or other readily available platforms to be delivered identically, trial by trial to a wide audience in terms of a combination of a few parameters for a Metalog distribution accompanied by the five inputs to the HDR generator. In 2013, ProbabilityManagement.org was incorporated as a 501(c)(3) nonprofit that supports this approach through education, tools, and open standards. Executive Director Sam Savage is the author of The Flaw of Averages: Why we Underestimate Risk in the Face of Uncertainty and is an adjunct professor at Stanford University. Harry Markowitz, Nobel Laureate in Economics, was a co-founding board member. The nonprofit has received financial support from Chevron Corporation, General Electric, Highmark Health, Kaiser Permanente, Lockheed Martin, PG&E, and Wells Fargo Bank. The SIPmath 2.0 Standard supports XLSX, CSV, and XML Formats. The SIPmath 3.0 Standard uses JSON objects to convey virtual SIPs based on the Metalog Distribution and HDR Generator. (Wikipedia).

(PP 6.1) Multivariate Gaussian - definition

Introduction to the multivariate Gaussian (or multivariate Normal) distribution.

From playlist Probability Theory

Planning how to Solve a Probability Problem

Learn to make sense of a probability problem before grabbing the numbers. An insightful, structured approach is wise.

From playlist Unit 5 Probability A: Basic Probability

What is a conditional probability?

An introduction to the concept of conditional probabilities via a simple 2 dimensional discrete example. If you are interested in seeing more of the material, arranged into a playlist, please visit: https://www.youtube.com/playlist?list=PLFDbGp5YzjqXQ4oE4w9GVWdiokWB9gEpm For more inform

From playlist Bayesian statistics: a comprehensive course

Probability Distribution Functions and Cumulative Distribution Functions

In this video we discuss the concept of probability distributions. These commonly take one of two forms, either the probability distribution function, f(x), or the cumulative distribution function, F(x). We examine both discrete and continuous versions of both functions and illustrate th

From playlist Probability

The connection between probability and area

From a mathematical point of view, probability, and ultimately the p-value, can be calculated from the area under a graph. In this lesson we develop an intuitive understanding of how geometrical area translates to probability.

From playlist Learning medical statistics with python and Jupyter notebooks

(PP 6.6) Geometric intuition for the multivariate Gaussian (part 1)

How to visualize the effect of the eigenvalues (scaling), eigenvectors (rotation), and mean vector (shift) on the density of a multivariate Gaussian.

From playlist Probability Theory

Probability Distribution Functions - EXPLAINED!

Probability distribution functions are functions that map an event to the probability of occurrence of that event. Let's talk about them. For more information, check out the blog post on probability fundamentals in Machine Learning: https://towardsdatascience.com/probability-for-machine-l

From playlist The Math You Should Know

(PP 6.7) Geometric intuition for the multivariate Gaussian (part 2)

How to visualize the effect of the eigenvalues (scaling), eigenvectors (rotation), and mean vector (shift) on the density of a multivariate Gaussian.

From playlist Probability Theory

Bayes Theorem, adding a bit of complexity (FRM T2- 9b)

[Here is my XLS at http://trtl.bz/122717-YT-Bayes-2nd-Star-Mgr] and Here is the question: "You are an analyst at Astra Fund of Funds. Based on an examination of historical data, you determine that all fund managers fall into one of two groups. Stars are the best managers. The probability t

From playlist Quantitative Analysis (FRM Topic 2)

Bayes Theorem, Three-state variable (FRM T2-9c)

[https://trtl.bz/220122-bayes-three-states] This explores the answer to Miller's sample question in Chapter 6 of http://amzn.to/2C88m0i. There are three types of managers: Out-performers (MO), in-line performers (MI) and under-performers (MU). The prior probability that a manager is an out

From playlist Quantitative Analysis (FRM Topic 2)

Probability & Statistics (8 of 62) The Probability Function - A First Look

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is the probability function. http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 Next video in series: http://youtu.be/zReGHNdWvIo

From playlist Michel van Biezen: PROBABILITY & STATISTICS 1 BASICS

Qualitative And Quantitative Risk Analysis Explained | Risk Analysis Techniques | Simplilearn

In this video on Qualitative and Quantitative Risk Analysis, we'll go into detail about how each of them work, how it's performed and the tools and techniques required to document it. 🔥Explore Our Free Courses With Completion Certificate by SkillUp: https://www.simplilearn.com/skillup-free

From playlist PMI-RMP® Training Videos [2022 Updated]

Qualitative Risk Analysis | What Is Qualitative Risk Analysis? | PMI-RMP Course | Simplilearn

This video will help you know how to perform Qualitative Risk Analysis. How to identify critical ridk factors and tools and techniques required to document the result of the Analysis. 🔥Free Project Management Course: https://www.simplilearn.com/learn-project-management-fundamentals-skillup

From playlist PMI-RMP® Training Videos [2022 Updated]

Quantitative Risk Analysis | What Is Quantitative Risk Analysis? | PMI-RMP Course | Simplilearn

This video on Quantitative Risk Analysis will help you understand how to perform Quantitative RIsk Analysis, List the tools and Techniques required for the analysis.This Video will also help you in EMV analysis and Probability Distribution. #QuantitativeRiskAnalysis #WhatIsQuantitativeRis

From playlist PMI-RMP® Training Videos [2022 Updated]

Quantitative Risk Analysis | What Is Quantitative Risk Analysis? | PMI-RMP Course | Simplilearn

This video on Quantitative Risk Analysis will help you understand how to perform Quantitative RIsk Analysis, List the tools and Techniques required for the analysis. This Video will also help you in EMV analysis and Probability Distribution. 🔥Free Project Management Course: https://www.sim

From playlist PMI-RMP® Training Videos [2022 Updated]

Quantitative Risk Analysis | What Is Quantitative Risk Analysis? | PMI-RMP Course | Simplilearn

From playlist PMI-RMP® Training Videos [2022 Updated]

CERIAS Security: Shifting focus: Aligning security with risk management 1/7

Clip 1/7 Speaker: Jack Jones · Founder · Risk Management Insight With few exceptions, executive management doesnt care about security. They care about risk. In this session, Jack will discuss the differences and share his experiences in taking the information security program at a Fortun

From playlist The CERIAS Security Seminars 2008

More Examination of the Addition Rule in Probability

Additional explanation of the Addition Rule in probability

From playlist Unit 5 Probability A: Basic Probability

More Help with Expected Value of Discrete Random Variables

Additional insight into calculating the mean [expected vale] of joint discrete random variables

From playlist Unit 6 Probability B: Random Variables & Binomial Probability & Counting Techniques

QRM L1-1: The Definition of Risk

Welcome to Quantitative Risk Management (QRM). In this first class, we define what risk if for us. We will discuss the basic characteristics of risk, underlining some important facts, like its subjectivity, and the impossibility of separating payoffs and probabilities. Understanding the d

From playlist Quantitative Risk Management

Probability management

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