Putting people into models Social networks and Bayesian networks

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Putting people into models Social networks and Bayesian networks. Ingrid van Putten CSIRO – Marine and Atmospheric research (Hobart- Australia). Jacopo A. Baggio School of Human Evolution &Social Change, Arizona State University. What are networks and what are social networks.
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Putting people into modelsSocial networks and Bayesian networksIngrid van PuttenCSIRO – Marine and Atmospheric research (Hobart- Australia)Jacopo A. BaggioSchool of Human Evolution &Social Change,Arizona State UniversityWhat are networks and what are social networksWhere did it all start?Small world, random, and scale-free networksFisheries example – quota trade marketLinking qualitative, networks and Bayesian networksHow do Bayesian networks work?Leonhard Euler (1707 – 1783)Networks: How did it all start?Commentarii Academiae Scientiarum Imperialis Petropolitanae, vol. 8, pp. 128-140, 1736The problem, which I am told is widely known, is as follows: in Königsberg in Prussia, there is an island A, called the Kneiphof; the river which surrounds it is divided into two branches, as can be seen in the figure, and these branches are crossed by seven bridges, a, b, c, d, e, f and g.Concerning these bridges, it was asked whether anyone could arrange a route in such a way that he would cross each bridge once and only once.Networks: How did it all start?Definitions (in modern words): A network is a figure of points (vertices/nodes/actors) connected by non-intersecting curves (edges/links/ties). A vertex is called odd if it has an odd number of arcs leading to it. An Euler path is a continuous path that passes through every arc once and only once. Theorems: If a network has more than two odd vertices, it has no Euler paths;if it has two or less odd vertices, there is at least one Euler path.What is a network?An arrangement of intersecting horizontal and vertical lines 1 a network of arteries WEB, lattice, net, matrix, mesh, crisscross, grid, reticulum, reticulation; Anatomy plexus.2 a network of lanes MAZE, labyrinth, warren, tangle.3 a network of friends SYSTEM, complex, nexus, web, webwork.What is a SOCIAL network?A social structure that is made up of entities/ agents/ individuals/ or organisations that have ties/ relationships (interactions) between them. Physical networksTies or relationships could be anything ….Kinship FriendshipInformationexchangeMarketexchange[http://serialconsign.com/2007/11/we-put-net-network]Physical interaction networksThe BlogosphereBiochemical networksGene-protein networksFood webs: who eats whomThe World Wide Web (?)Airline networksCall centre networksPaper citationsSocial interaction networksFriendshipsAcquaintancesBoards and directorsOrganizationsfacebook.comtwitter.comnode, vertex, actorlink, edge, tie V = {v1…vn}Graph G(V,E) E = {e1…en}11424235351124243535Networks and MatricesUndirectedDirectedNot symmetricalSymmetricalHow did interest in social networks start?……………. Six degrees of separation …………………Stanley Milgram (and other researchers) carried out what is now known as “The small world experiment”The experiments are often associated with the phrase "six degrees of separation", although Milgram did not use this term himself.The research was groundbreaking human society is a network characterized byshort path (chain) lengths How did Milgramdo the experiment?1Information packets sent to "randomly" selected individuals around USA. Packets had basic information about a target contact person in Boston (Boston stockbroker). This person is the end destination for the packet.If the recipient personally knew the Boston stockbroker described in the letter, they should forward the letter directly. 2If they did not know the Boston stockbroker personally, then the person was to think of a friend or relative he knew personally who was more likely to know the target. Could only send to someone with whom they were on a first-name basisRecipient was directed to sign his name on a roster and forward the packet to the next person3When and if the package eventually reached the contact person in Boston, researchers could examine the roster to count the number of times it had been forwarded from person to person420% of packets reached targetChain length ' 6.5CSIRO.Milgram’s experimentJohn Guare wrote a play called Six Degrees of Separation, based on this concept. One of the main character’s lines (Quisa)Chain length ' 6.5“Everybody on this planet is separated by only six other people. Six degrees of separation. Between us and everybody else on this planet. The president of the United States. A gondolier in Venice… It’s not just the big names. It’s anyone. A native in a rain forest. A Tierra del Fuegan. An Eskimo. I am bound to everyone on this planet by a trail of six people…”CSIRO.Erdős Number (Bacon game for the scientist)Paul Erdős was an influential and itinerant mathematician (often living out of a suitcase boarding with his colleagues). He published more papers during his life (at least 1,525) than any other mathematician in history (with 507 co-authors)Number of links required to connect scholars to Erdős, via co-authorship of papersPaul Erdős (1913-1996) Jerry Grossman’s (Oakland Univ.) website allows mathematicians to compute their Erdos numbers: http://www.oakland.edu/enp/
  • Connecting path lengths, among mathematicians only:
  • average is 4.65
  • maximum is 13
  • Random Graphs --- or why does the “small world” phenomena exist?N = nodes (individuals)p= number of nodes with links(A pair of nodes has probability p of being connected)K=number of links(Average degree, k ≈ pN)p=1.0 ; k≈Np=0 ; k=0N = 12N = 12Now put in few random connectionsEach person is connected to two neighbours either sideBNumber of steps to get from A to B reduced to twoATakes three steps to get from A to Bsmall-world networkL= avg shortest path lengthC = avg clustering coefficientMost networks are not random but are ‘scale free’
  • Tend to have a relatively few nodes of high connectivity (the “Hub” nodes – or “broker” nodes)
  • Our world complies with the Pareto principle (also known as the 80–20 rule, the law of the vital few) Degree Distribution & Power LawsAlbert and Barabasi (1999)Many real-world networks exhibit a power-law distribution (also called “Heavy tailed” distribution)P(k)Number of nodes with k linksLots of nodes with only a few links(k)Number of links Power laws in real networks:(a) WWW hyperlinks(b) co-starring in movies(c) co-authorship of physicists(d) co-authorship of neuroscientists(e) Distribution of wealthPower-law distributions are straight lines in log-log spacePower Laws ….. Scale-Free NetworksCSIRO.Power Laws ….. What happens if you take out a few hubs?Take out 9 centresTake out 7 centres – but target the hubsEpidemic spreadingStructure matters: Power law versus random networksStructure matters: what do we know?- Structural properties influence a system strengths and weaknesses.- Structural properties influence diffusion processes such as viruses, pests, communication, information, migration and so on.- There is no golden rule (the “perfect” structure for all systems does not exist)Australian fisheries example of network analysis:Lease quota trade for lobstersIndustry structural change after tradeable quota introducedMapping the lease quota trade
  • (each line is a trade between two individuals)
  • 1999 (year after the introduction of quota)2007 (8 years later)New relationships – more brokers / hubsIncome supplementerLease market network Lease quota dependent fisher Investor Quota redistributorIndependent fisher Active fishers 25Portfolio investorsDCOwnership characteristics (number of quota units owned by fisher)Concentration of ownershipB75AFishing effort (number of quota units fished)Income supplementers (A-C-D)Lease dependent fishers (A-B-C)Investors (A-D)Quota redistributors (A-B-C-D)Independent fishers (A-C)Van Putten(2011)Putting people into modelsSocial networks and Bayesian networksIngrid van PuttenCSIRO – Marine and Atmospheric research (Hobart- Australia)Jacopo A. BaggioSchool of Human Evolution &Social Change,Arizona State UniversityLinking qualitative, networks and Bayesian networksHow do Bayesian networks work?Bayesian modelsNetwork modelsQualitative modelsConditional probabilitiesp2p3N1N2Cold (1)Flu (2)++undirectedp1N3Fever (3)-Road between power station 1-2, and 1-3, but not between 2-3If you have a cold (1) there is a chance you have a fever (3), and if you have the flu (2) there is also a chance you have a feveri2i3Animal 3 experiences external factors that limit it (self effect). Animal 1 has a positive effect on animal 2, and animal 2 also has a positive effect on animal 3, but animal 2 has no effect on animal 1 (commensalism)directedi1ColdFluFeverTrueFalseFeverTrueFalse00.60.1True0.7TrueIndividuals 1-3 are friends with each other, and 1 is friends with 2, but 2 doesn’t feel like 1 is their friend and 2-3 are not friends at allFalse0.41False0.30.9Bayes' theorem gives the relationship between the probabilities of Aand BP(A) and P(B)and the conditional probabilities of Agiven B and B given AP(A| B) and P(B | A)Thomas Bayes(1701-1761)A Bayesian network is a directed graphEach node represents a random variable. Each node represents a variable A with parent nodes representing variables B1, B2,..., BnEach node is assigned a conditional probability table (CPT)SmokingVisit to AsiaTuberculosisLung CancerBronchitisTuberculosisor CancerXRay ResultDyspnoea(SOB)Example from Medical DiagnosticsPatient InformationMedical DifficultiesDiagnosisDiagnostic TestsNetwork represents a knowledge structure between medical difficulties, their causes and effects, patient information and diagnostic testsSmokingVisit to AsiaTuberculosisLung CancerBronchitisTuberculosisor CancerXRay ResultDyspnoea (SOB)Example from Medical DiagnosticsDyspneaBronchitisMedical DifficultiesTub or CanTrueTrueFalseFalseBronchitisPresentAbsentPresentAbsentPresent0.900.700.800.10Absent0.l00.300.200.90Medical DifficultiesCSIRO.SmokingVisit to AsiaTuberculosisLung CancerBronchitisTuberculosisor CancerXRay ResultDyspnoea (SOB)Example from Medical DiagnosticsCSIRO.We have some information about the patientWe know the person has been to AsiaFrom P=1.04From P=6.48From P=43.6From P=11.0Given evidence about a cause, what are the predicted effects (e.g. you know the person has been to Asia what is the probability that they have tuberculosis?)Predictive reasoningWe also can now see the x ray results are normalIncreases the probability that it’s not tuberculosis or cancerX-ray results are normal ….Given evidence about an effect (symptom) how does this change our beliefs in the causes? (e.g. I observe there is nothing abnormal about the x-ray– how does that the affect the probability that it’s tuberculosis or cancer?)DiagnosticAustralian fisheries example of BBN: Torres Strait(between Papua New Guinea and far northern Australia)Australian Examples: Torres StraitNon-indigenous commercial catchSEC fisheryPre-season surveyLobster abundanceCost related driversPapuanPrice related driversHookah ownershipPrivate freezerSeasonExchange rateFuel costsFunctional Island freezerPrice liveWeatherFishing costsRegional Authority ($)Price tailsEase of catching lobsterOther lobster availableCommunity business knowledgeSocio-cultural driversReturns from fishingFull time alternative incomeCommunity role modelsGovernment employment schemeCrew availabilityWorking age menIncidental household paymentsSocial capitalTradition & cultureProfit driversCasual fisherPart time fisherFull time fisherAustralian Examples: Torres StraitNon-indigenous commercial catchSEC fisheryPre-season surveyLobster abundance
  • Objective: more full time indigenous fishers (use olympic quota, ITQ, community quota ?)
  • Assumed: economic drivers = key
  • Actually: socio-cultural & infrastructure
  • Cost related driversPapuanPrice related driversHookah ownershipPrivate freezerSeasonExchange rateFuel costsFunctional Island freezerPrice liveWeatherFishing costsRegional Authority ($)Price tailsEase of catching lobsterOther lobster availableCommunity business knowledgeSocio-cultural driversReturns from fishingFull time alternative incomeCommunity role modelsGovernment employment schemeCrew availabilityWorking age menIncidental household paymentsSocial capitalTradition & cultureProfit driversCasual fisherPart time fisherFull time fisherAustralian Examples: Torres StraitNon-indigenous commercial catchSEC fisheryPre-season surveyLobster abundance
  • Full time fishers
  • Economics (profit) is a driver
  • Social capital important too (crew, freezers)
  • Cost related driversPapuanPrice related driversHookah ownershipPrivate freezerSeasonExchange rateFuel costsFunctional Island freezerPrice liveWeatherFishing costsRegional Authority ($)Price tailsEase of catching lobsterOther lobster availableCommunity business knowledgeSocio-cultural driversReturns from fishingFull time alternative incomeCommunity role modelsGovernment employment schemeCrew availabilityWorking age menIncidental household paymentsSocial capitalTradition & cultureProfit driversCasual fisherPart time fisherFull time fisherAustralian Examples: Torres StraitNon-indigenous commercial catchSEC fisheryPre-season surveyLobster abundance
  • Part time fishers
  • Socio-cultural is key
  • Ease of access vs other income
  • Cost related driversPapuanPrice related driversHookah ownershipPrivate freezerSeasonExchange rateFuel costsFunctional Island freezerWeatherPrice liveFishing costsEase of catching lobsterRegional Authority ($)Price tailsSocio-cultural driversOther lobster availableCommunity business knowledgeReturns from fishingGovernment employment schemeFull time alternative incomeCommunity role modelsCrew availabilityIncidental household paymentsWorking age menSocial capitalTradition & cultureProfit driversCasual fisherPart time fisherFull time fisher
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