Measuring Community Resilience: a Bayesian Approach CESUN2018
•Download as PPTX, PDF•
1 like•212 views
Analysis of community behavior and its interactions within and without (e.g., with other communities, civil and industrial engineered systems, organizations, governments, etc.) is a critical topic in a diverse variety of domains, from sociology and psychology to marketing science, security analytics, defense operations, political sciences, and other fields. Viewing a community as an engineered system allows the researcher to separate metrics characterizing the behavior of the community as a whole from metrics describing activities within it. One of the fundamental parameters of a community is its resilience. There are several accepted definitions of community resilience; however, translating them into practically applicable mathematical terms is a non-trivial task, due to the difficulties in implementation of such definitions. In this paper, we mathematically derive an applicable metric of community resilience. We further demonstrate how the metric can be estimated iteratively in a Bayesian process. Due to the specifics of community dynamics, implementation of Bayesian correction to metric estimates with real community data is a slow process, as intervals of time between community-affecting events in the real world are usually long (from months to years), while available measurements of community metrics that can be translated into state variables are often excessively aggregated. This limits their usefulness. For these reasons, we use a simulation of community population changes in response to changes in the sentiment of social and public media to demonstrate practical calculation of the proposed metric.
Recommended
Recommended
More Related Content
Similar to Measuring Community Resilience: a Bayesian Approach CESUN2018
Similar to Measuring Community Resilience: a Bayesian Approach CESUN2018 (20)
More from Alex Gilgur
More from Alex Gilgur (11)
Recently uploaded
Recently uploaded (20)
Measuring Community Resilience: a Bayesian Approach CESUN2018
- 1. Alexander Gilgur, Jose Emmanuel Ramirez-Marquez School of Systems and Enterprises, SIT CESUN2018 Global Conference Tokyo, Japan. June, 2018 A Bayesian Approach Measuring Community Resilience The research performed by Jose E. Ramirez Marquez leading to these results has received funding from the National Science Foundation, CRISP Type 2/Collaborative Research: Resilience Analytics: A Data-Driven Approach for Enhanced Interdependent Network Resilience, Award number 1541165.
- 3. 3 Introduction After an adverse event, Will community recover? Will it recover to a new level? Will it evolve into something new?
- 4. 4 Introduction After an adverse event, Will community recover? Will it recover to a new level? Will it evolve into something new? How can we measure community resilience?
- 5. 5 Exploring Community Response Drivers Example: my communities on LinkedIn (http://socilab.com/#home) Community is a complex social network with multiple layers of interactions among the nodes. Nodes and Edges have characteristics (connectedness, centrality; distance, strength) that impact community response to adverse events. Aggregate measures (uniformity, stationarity, distribution, resilience) better describe the community as a whole. State Variable depends on what is important.
- 6. 6 Exploring Community Response Drivers Example: my communities on LinkedIn (http://socilab.com/#home) Community is a complex social network with multiple layers of interactions among the nodes. Nodes and Edges have characteristics (connectedness, centrality; distance, strength) that impact community response to adverse events. Aggregate measures (uniformity, stationarity, distribution, resilience) better describe the community as a whole. State Variable depends on what is important. Traditional approach - Deductive: start with aggregate measures and dive in to the root causes to explain behavior.
- 7. 7 Disaster Recovery Timeline Regardless how we measure state of community, adverse events cause disturbances in state variable. Monotonic @ New LevelOscillatory @ Old Level Oscillatory @ New Level
- 8. 8 Disaster Recovery Timeline After the change, state variable stabilizes at a new or at the old level. Stabilization can take a few months to a few years. Regardless how we measure state of community, adverse events cause disturbances in state variable. Monotonic @ New LevelOscillatory @ Old Level Oscillatory @ New Level
- 9. 9 Proposal
- 10. 10 Proposal
- 11. 11 Proposal Linear regression coefficient is the sensitivity of recovery time to the severity of disturbing events. Then community resilience metric is the inverse of the linear regression coefficient. Measure community resilience as inverse of sensitivity of recovery time to severity of disturbing events
- 12. 12 Methodology 1. Develop a mathematical model of community population growth as a function of Media Positivity and Housing Prices. 2. Simulate disturbances in Housing Prices. These will lead to changes in Population Egress rate. 3. Shared Sentiment will change, leading to changes in Media Positivity. 4. Population Ingress will change accordingly, and Population will be disturbed. 5. Measure, for each disturbance: ○ New stable level of Population ○ Time to stabilization. 6. Fit a regression line. 7. Calculate MR 8. Record R2: it quantifies specificity of the metric
- 13. 13 Illustration for Measurements and Calculations Monotonic @ New Level
- 14. 14 Illustration for Measurements and Calculations Oscillatory @ New Level
- 15. 15 Algorithm Resilience Metric Computation Algorithm
- 16. 16 Algorithm Resilience Metric Computation Algorithm
- 17. 17 Algorithm Resilience Metric Computation Algorithm ● Bayesian process ● Reiterates the prior at each event ● Stabilizes as N grows
- 18. 18 Experiment AnyLogic Simulation Dashboard Population Growth Rate: Equilibrium: Population Ingress Rate Population Egress Rate = household sensitivity to media = media positivity index = time-dependent coefficient = time-dependent coefficient = expensive housing index = household sensitivity to prices 𝐸 𝑃 𝑡 = 𝐵 𝑡 ∗ 𝑆 𝐻 𝑃 ∗ 𝐻 𝐸(𝑡) 𝐼 𝑃 𝑡 = 𝐴 𝑡 ∗ 𝑆 𝐻 𝑀 ∗ 𝑀+ (𝑡)
- 19. 19 Experimental Data Analysis PopulationPositiveMediaPopulationGrowth Severity StabilizationTime[days] Population Stabilization Time Disturbances in Population can be detected as outliers in Media Positivity or in Population Growth Stabilization is achieved when Population Growth becomes zero Regression Analysis Data From Simulation The high R2 points to high specificity of the metric: 93.1% of the variance in Stabilization Time is explained linearly by the Severity of Disturbance. Simulation Dashboard
- 20. 20 Conclusion and Further Work Proposed a new metric of community resilience Developed a bayesian method for calculating it Developed a model where the metric can me measured Demonstrated its usability via a simulation Identify real communities where this metric can be applied Quantify impact of media positivity on such communities Quantify impact of cost of living on such communities Apply this methodology to study their resilience
- 21. 21 Thank you!
- 22. Alexander Gilgur, Jose E. Ramirez-Marquez agilgur@stevens.edu, jmarquez@stevens.edu +1(408)828-2115
Editor's Notes
- Hello. My name is Alex Gilgur. I am a 3rd-year PhD student at Stevens, working under the advisorship of Professor Dr. Ramirez-Marquez. I am honored to be here presenting this paper. If you find it useful, it will be the highest reward for me.
- When I am not taking classes and not working on my research, I help keep 2 (now 2.2) billion people connected. I forecast FB network demand. We have many data centers, which communicate for thousands of services, and we need to know in advance how many terabits per second we will have 2-3-4-5 years from now. Forecasted demand goes to a set of simulation+optimization tools, which tell us how vulnerable our network is under the forecasted load, and where we need to augment capacity and boost its resilience. Multiple datacenters Thousands of services; Millions of servers, sometimes in different parts of the world. All these services and products need to talk to each other in a variety of patterns. Things get complicated really fast. What does this have to do with community resilience?
- (From previous slide) – ----------------------------------- Everything. There are similarities in structure and in questions that we are answering: how big will the network be? (Tbps and # of nodes and links) how vulnerable will it be? how do we boost network resilience without affecting the users?
- (From previous slide) – ----------------------------------- And the first question we need to answer when it comes to boosting resilience is: how do we benchmark network resilience? How do we measure it? Same thing for community.
- This is an ego-centric view of my community on LinkedIn. I am sure you have similarly complex and complicated communities around you. I encourage you to give it a shot; just follow this link. ------------------------------------------------ Community is a network, and same questions apply to it. Community can be characterized by a state variable (or a set of state variable), which depends on what is important for the work we are doing. It may be language distribution; education level; availability of jobs; population.
- (From previous slide) – ------------------------------ I am taking the traditional top-down (holistic, deductive) approach: observe aggregate measures and then dive into the community response drivers: how do we preserve community or if it is a gang, how do we destroy it?
- After a disturbance, the response dynamics varies from community to community. Communities have something in common - at least communities with measured state variable - they may take a different trajectory, but unless they fall apart completely and stop being a community, they do stabilize after a disturbance, and we can use this property to quantify community resilience. Can we quantify community resilience if a community only got hit once? After San Francisco earthquake of 1906 the city was rebuilt in two years. A very good resilience: the city was destroyed and burned down, and yet in 1908 it was full of life and business activity (primarily banking and entertainment) at a level never seen before since the Gold Rush. The 1989 earthquake was far less devastating, yet the city took a good 10 years to recover, and there still are neighborhoods in SF and Oakland that blame their misery on the earthquake. But the communities stabilized in about the same time, close to 2 -3 years. These are only two events, 83 years apart, in the same geographical location. Are these different communities? Or is it same community whose resilience changed? Did it change? If so, can we come up with a stable metric of community resilience?
- After a disturbance, the response dynamics varies from community to community. Note that in the case of an earthquake, or a hurricane, or another natural disaster, we can measure its power (e.g., Richter scale; hurricane category; etc.). But other disturbances that do not have an objective measurement defined can affect the community. We measure strength of disturbance by its effect on the state variable. Details are in the paper. We will talk about it a few slides down the road.
- What if we plot on the horizontal axis the strength of the disturbance, and on the vertical access, time to stabilization? We can fit a line through these points, and the slope of this line, measured by its tangent, or the regression parameter, will tell us how sensitive the stabilization time is to the severity of the disturbance. The steeper the slope, the longer it takes to recover after a small disturbance; so if we revert the computed regression parameter, we will have a metric of community resilience.
- What if we plot on the horizontal axis the strength of the disturbance, and on the vertical access, time to stabilization? We can fit a line through these points, and the slope of this line, measured by its tangent, or the regression parameter, will tell us how sensitive the stabilization time is to the severity of the disturbance. The steeper the slope, the longer it takes to recover after a small disturbance; so if we revert the computed regression parameter, we will have a metric of community resilience.
- What if we plot on the horizontal axis the strength of the disturbance, and on the vertical access, time to stabilization? We can fit a line through these points, and the slope of this line, measured by its tangent, or the regression parameter, will tell us how sensitive the stabilization time is to the severity of the disturbance. The steeper the slope, the longer it takes to recover after a small disturbance; so if we revert the computed regression parameter, we will have a metric of community resilience.
- That was the preamble. Now consider this very simple community model. We assume that we can quantify sensitivity to cost of living, media sensitivity, shared sentiment, etc. Further, we assume that the media will report positively or negatively about this community. This is quantified as Media Positivity [0…1] Positive reporting will lead to more people coming in. Negativity of shared sentiment in the community (e.g., about housing prices) will lead to people leaving the area. A change in media positivity will lead to a change in ingress rate, shifting the balance, and the community will grow or become smaller Then we repeatedly turn any of the knobs, we introduce disturbances and can fit a regression line into the data and measure the response time sensitivity to disturbance severity.
- We are measuring disturbance severity by the size of the change in the state variable (again, 1906 earthquake was devastating to the city infrastructure, but had relatively little effect on the community sentiment). Response time is measured as the total time it takes to restabilize the community. ------------------------ With monotonic restabilization, we use Eq. (6) to measure the size of the disturbance. Eq. (9) is the form of the model we are fitting, and (10) is the community resilience metric.
- ------------------------ With oscillatory restabilization, we propose using Eq. (12). Eq. (9) is the form of the model we are fitting, and (10) is the community resilience metric.
- We are measuring disturbance severity by the size of the change in the state variable (again, 1906 earthquake was devastating to the city infrastructure, but had relatively little effect on the community sentiment). Response time is measured as the total time it takes to restabilize the community. ------------------------ This algorithm describes how it is done and how the model is adjusted as we collect more data.
- And here it is all put together with the formulae.
- We follow the Bayesian definition of regression process: adjust our prior assumptions based on new evidence. When the hit is only once, we can just divide the stabilization time by the size of the hit, and we are done; every new hit gets an adjustment in the regression line. --------------------------- It will converge, for a number of reasons, not least of which is the Central Limit Theorem: from the community’s perspective, the disturbances happen randomly, and the community’s response to them can be treated as random sampling. The linear regression process is unbiased, meaning it draws the best-fitted line through the means of the distributions of Y for each X, and CLT states that the means of samples converge to the mean of the population.
- We did an experimental analysis on a simulated community, collecting ingress, egress, media positivity while hitting the simulated community with different disturbances. Results are on the next slide. Here the validity of the model is irrelevant: the goal was to build an engine that would allow us to produce disturbances, measuring a state variable and its stabilization time. But as part of my dissertation research, I am now conducting an analysis of validity of this model: investigating the impact of news-media positivity on population growth.
- So in the simulated experiment, we measured population (as the state variable); and computed population growth rate. Here it is very easy to see when the state variable (population) stabilizes after the disturbance. These values and times were put into a regression model, and the value of the resilience metric for this community was obtained. Note the high value of R^2 - it means the metric is very specific: disturbance severity, measured by the state variable, explains 93% of the variance in the stabilization time.
- And that concludes my presentation. Next I am planning to study real communities, focusing on media sentiment and population growth during and after economic recessions in the Silicon Valley and San Francisco.
- And that concludes my presentation. Next I am planning to study real communities, focusing on media sentiment and population growth during and after economic recessions in the Silicon Valley and San Francisco.