SPF workshop February 2014, UBCO1 CH1. What is what CH2. A simple SPF CH3. EDA CH4. Curve fitting CH5. A first SPF CH6: Which fit is fitter CH7: Choosing.

Slides:



Advertisements
Similar presentations
Normal Probability Distributions
Advertisements

HSM Practitioner’s Guider for Two-Lane Rural Highways Workshop Exercise IV – US 52 from Sageville to Holy Cross – Group Exercise - Session #8 8-1.
Investigation of the Safety Effects of Edge and Centerline Markings on Narrow, Low-Volume Roads Lance Dougald Ben Cottrell Young-Jun Kweon In-Kyu Lim.
DISTRICT PILOT PROJECT PRESENTATION MAY 2, Highway Safety Manual Implementation.
Matrices: Inverse Matrix
Regression Analysis Using Excel. Econometrics Econometrics is simply the statistical analysis of economic phenomena Here, we just summarize some of the.
Spring  Crash modification factors (CMFs) are becoming increasing popular: ◦ Simple multiplication factor ◦ Used for estimating safety improvement.
Investigation of Varied Time Intervals in Crash Hotspot Identification Authors: Wen Cheng, Ph.D., P.E., Fernando Gonzalez, EIT, & Xudong Jia; California.
SPF workshop February 2014, UBCO1 CH1. What is what CH2. A simple SPF CH3. EDA CH4. Curve fitting CH5. A first SPF CH6: Which fit is fitter CH7: Choosing.
Mathematical Modeling. What is Mathematical Modeling? Mathematical model – an equation, graph, or algorithm that fits some real data set reasonably well.
8 TECHNIQUES OF INTEGRATION. There are two situations in which it is impossible to find the exact value of a definite integral. TECHNIQUES OF INTEGRATION.
Module 1-1 Road Safety 101. Module Tracking Your Progress Through Highway Safety Core Competencies Core Competency 1: Core Competency 2: Core Competency.
Introduction In an equation with one variable, x, the solution will be the value that makes the equation true. For example: 1 is the solution for the equation.
Incorporating Temporal Effect into Crash Safety Performance Functions Wen Cheng, Ph.D., P.E., PTOE Civil Engineering Department Cal Poly Pomona.
Normal Probability Distributions 1. Section 1 Introduction to Normal Distributions 2.
Objective - To graph linear equations using x-y charts. One Variable Equations Two Variable Equations 2x - 3 = x = 14 x = 7 One Solution.
Session 10 Training Opportunities Brief Overview of Related Courses in USA / Canada Geni Bahar, P.E. NAVIGATS Inc.
CH1. What is what CH2. A simple SPF CH3. EDA CH4. Curve fitting CH5. A first SPF CH6: Which fit is fitter CH7: Choosing the objective function CH8: Theoretical.
The Empirical Bayes Method for Safety Estimation Doug Harwood MRIGlobal Kansas City, MO.
Section 8-3 Chapter 1 Equations of Lines and Linear Models
Network Screening 1 Module 3 Safety Analysis in a Data-limited, Local Agency Environment: July 22, Boise, Idaho.
1 CH1. What is what CH2. A simple SPF CH3. EDA CH4. Curve fitting CH5. A first SPF CH6: Which fit is fitter CH7: Choosing the objective function CH8: Theoretical.
Evaluation of Alternative Methods for Identifying High Collision Concentration Locations Raghavan Srinivasan 1 Craig Lyon 2 Bhagwant Persaud 2 Carol Martell.
1 CEE 763 Fall 2011 Topic 1 – Fundamentals CEE 763.
Derivatives of exponential and logarithmic functions
Part 2 Processes and approaches associated with the FHWA method 1 1 HPMS Vehicle Summary Data.
Jason J. Siwula, PE – Safety Engineer DOES 24+0=22+2? AN INTRO TO HSM METHODS.
Investigating Patterns. Vocabulary Variable- a letter used to represent one or more numbers Variable Expression- an expression that contains variables,
Odd one out Can you give a reason for which one you think is the odd one out in each row? You need to give a reason for your answer. A: y = 2x + 2B: y.
Part 3 Understand Some HPMS Data Items and Other Related Concepts 1.
Objective: To graph linear equations
1 7. What to Optimize? In this session: 1.Can one do better by optimizing something else? 2.Likelihood, not LS? 3.Using a handful of likelihood functions.
Putting Together a Safety Program Kevin J. Haas, P.E.—Traffic Investigations Engineer Oregon Department of Transportation Traffic—Roadway Section (Salem,
1 CH1. What is what CH2. A simple SPF CH3. EDA CH4. Curve fitting CH5. A first parametric SPF CH6: Which fit is fitter CH7: Choosing the objective function.
July 29 and 30, 2009 SPF Development in Illinois Yanfeng Ouyang Department of Civil & Environmental Engineering University of Illinois at Urbana-Champaign.
Calibrating Highway Safety Manual Equations for Application in Florida Dr. Siva Srinivasan, Phillip Haas, Nagendra Dhakar, and Ryan Hormel (UF) Doug Harwood.
Calibration of SPFs in the HSM, IHSDM, and SafetyAnalyst Doug Harwood Midwest Research Institute.
5.7 Curve Fitting with Quadratic Models Learning Objective: To find a quadratic function that exactly fits three data points and to find a quadratic model.
Copyright © 2013 Pearson Education, Inc. Section 3.2 Linear Equations in Two Variables.
SPF workshop UBCO February CH1. What is what CH2. A simple SPF CH3. EDA CH4. Curve fitting CH5. A first SPF CH6: Which fit is fitter CH7: Choosing.
Chapter II Methods for Describing Sets of Data Exercises.
Session 2 History How did SPF come into being and why is it here to stay? Geni Bahar, P.E. NAVIGATS Inc.
Role of Safety Performance Functions in the Highway Safety Manual July 29, 2009.
CE 552 Week 3 The national problem Importance of data.
Evgeniya Tyson University of Wyoming.  Elk Mountain ( Mileposts, 77)  Evanston – Sisters (6-29 Mileposts, 23 total)  Rock Springs – Green River.
1 The Highway Safety Manual Predictive Methods. 2 New Highway Safety Manual of 2010 ►Methodology is like that for assessing and assuring the adequacy.
NC Local Safety Partnership Evaluation Methods. Workshop Roadmap Program Background and Overview Crash Data Identifying Potential Treatment Locations.
Scatter Plots and Lines of Fit
Population (millions)
Number of Kilometers Driven 1987 to 1999
HSM Practicitioner's Guide for Two-Lane Rural Highways Workshop
6.1 - Slope Fields.
HSM Applications to Multilane Rural Highways and Urban Suburban Streets Safety and Operational Effects of Geometric Design Features for Two-Lane Rural.
Transportation Engineering Basic safety methods April 8, 2011
HSM Practitioner’s Guider for Two-Lane Rural Highways Workshop
HSM Practioner's Guide for Two-Lane Rural Highways Workshop
HSM Practicitioner's Guide for Two-Lane Rural Highways Workshop
The national problem Importance of data
HW 7b: HSM Practitioner’s Guider for Two-Lane Rural Highways Workshop
Learning Targets Students will be able to: Compare linear, quadratic, and exponential models and given a set of data, decide which type of function models.
HSM Applications to Multilane Urban Suburban Multilane Intersections
HSM Applications to Multilane Urban Suburban Multilane Intersections
HSM Practioner's Guide for Two-Lane Rural Highways Workshop
HSM Practioner's Guide for Two-Lane Rural Highways Workshop
IMPLICIT Differentiation.
HSM Practitioner’s Guider for Two-Lane Rural Highways Workshop
Objectives Compare linear, quadratic, and exponential models.
HSM Practitioner’s Guider for Two-Lane Rural Highways Workshop
Numerical Computation and Optimization
Chapter 7 Section 7.2 Matrices.
Presentation transcript:

SPF workshop February 2014, UBCO1 CH1. What is what CH2. A simple SPF CH3. EDA CH4. Curve fitting CH5. A first SPF CH6: Which fit is fitter CH7: Choosing the objective function CH8: Theoretical stuff Ch9: Adding variables CH10. Choosing a model equation 2. A Simple SPF We defined ‘Safety’, ‘Unit’, ‘Traits’, ‘Population’, and SPF as a tool to get estimates of E{μ} and σ{μ}. In this session: I will make all this tangible with a simple SPF for a real population.

SPF workshop February 2014, UBCO2 When originally conceived (1995) SPF gave expected crashes as function of only exposure Since then broadening in two ways: 1.Not only estimate of E{  } but also of σ{  } 2.Not only function of exposure but also of other traits Function = Function can be table, graph, algorithm,... I will develop first a simple SPF in form of table & graph because in this case populations are real.

SPF workshop February 2014, UBCO3 Used in all illustrations. Two-lane, rural roads, Colorado 5323 segments, 6029 miles, 13 years, 21,718 Fatal & Injury accidents Segment Length [miles] AADT The Data

SPF workshop February 2014, UBCO4 Continued... Segment Length [miles] Total accidentsTerrain … … Rolling … Rolling...… Segment Injury and Fatal accidents

5 Period: ; Segment Length: 0.5 to 1.0 miles; N=2228 segments. AADT Bins No. of I&F accidents No. of mile segments 0-1, ,000-2, ,000-10, ,000-11, Data An average segment in this bin had 102/19=5.37 I&F crashes in 5 years. Bins and Computations The first element of simple SPF, the

SPF workshop February 2014, UBCO6 AADT Bins 0-1, ,000-2, ,000-10, ,000-11, Ordinate,, is estimate of average number of crashes/ segment in bin

SPF workshop February 2014, UBCO7 Moral: SPFs are about populations AADT Bins 0-1, ,000-2, ,000-10, ,000-11, Here there are 20 different populations. Each population defined by five traits: (1) State: Colorado, (2) Road Type: two-lane, (3) Setting: rural, (4) Segment Length: 0.5 to 1.5 miles (5)Traffic: AADT bin. Each estimate in a row, each point on the graph, is a guess at the mean of the μ’s in a population.

SPF workshop February 2014, UBCO8 How close are E{  } and ?

SPF workshop February 2014, UBCO9 the accuracy of Data Estimates AADT Bins I&F accidents mile segments ± 0-1, ,000-2, ,000-10, ,000-11, √102/19=±0.53

SPF workshop February 2014, UBCO The first element of (simple) SPF Note the widening of ±σ limits. Why?

SPF workshop February 2014, UBCO11 Is this real? If yes, what could explain it?

SPF workshop February 2014, UBCO12 And now to the second element of the SPF, the  {  } Recall Only this! Nothing to do with this

How to estimate the  {  } 13 One way AADT Bins I&F acc. SegmentsS2S2... 9K-10K ± SPF workshop February 2014, UBCO

If we estimate the  of a road segment with the same traits as the population to be 5.37 then

15 Now both elements of the (simple) SFP are in hand SPF workshop February 2014, UBCO

16 A Simple SPF - Summary 1.As SPF gives estimates of E{  } and of  {  } as a function of traits; 2.A function is not only an equation. We used a table to highlight the concept of ‘population’; 3.Using Colorado data we built a simple SPF and showed how both its elements are estimated; 4.Two groups of reasons for our interest in E{  } were given. The second group (estimation of specific μ’s) requires knowledge of  {  }.

SPF workshop February 2014, UBCO17 2. A Simple SPF – Summary continued 5. A third reason for interest in E{  } is of the cause-effect kind. I am skeptical; you keep an open mind. 6. I showed how  can be estimated and how it is used. 7. The simple SPF has broad bins, few traits, and is of no practical use. To be of use, more traits have to be added and some variables have to be made continuous.