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Small Cohort Population Forecasting via Bayesian Learning
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2017 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Befolkningsprognoser för små kohorter genom Bayesiansk inlärning (Swedish)
Abstract [en]

A set of distributional assumptions regarding the demographic processes of birth, death, emigration and immigration have been assembled to form a probabilistic model framework of population dynamics. This framework was summarized as a Bayesian network and Bayesian inference techniques are exploited to infer the posterior distributions of the model parameters from observed data. The birth, death and emigration processes are modelled using a hierarchical beta-binomial model from which the inference of the posterior parameter distribution was analytically tractable. The immigration process was modelled with a Poisson type regression model where posterior distribution of the parameters has to be estimated numerically. This thesis suggests an implementation of the Metropolis-Hasting algorithm for this task. Classifi cation of incomings into subpopulations of age and gender is subsequently made using a Dirichlet-multinomial hierarchic model, for which parameter inference is analytically tractable. This model framework is used to generate forecasts of demographic data, which can be validated using the observed outcomes. A key component of the Bayesian model framework used is that is estimates the full posterior distributions of demographic data, which can take into account the full amount of uncertainty when forecasting population growths.

Abstract [sv]

Genom att använda en mängd av distributionella antaganden om de demografiska processerna födsel, dödsfall, utflyttning och inflyttning har vi byggt ett stokastiskt ramverk för att modellera befolkningsförändringar. Ramverket kan sammanfattas som ett Bayesianskt nätverk och för detta nätverk introduceras tekniker för att skatta parametrar i denna uppsats. Födsel, dödsfall och utflyttning modelleras av en hierarkisk beta-binomialmodell där parametrarnas posteriorifördelning kan skattas analytiskt från data. För inflyttning används en regressionsmodell av Poissontyp där parametervärdenas posteriorifördelning måste skattas numeriskt. Vi föreslår en implementation av Metropolis-Hastingsalgoritmen för detta. Klassificering av subpopulationer hos de inflyttande sker via en hierarkisk Dirichlet-multinomialmodell där parameterskattning sker analytiskt. Ramverket användes för att göra prognoser för tidigare demografisk data, vilka validerades med de faktiska utfallen. En av modellens huvudsakliga styrkor är att kunna skatta en prediktiv fördelning för demografisk data, vilket ger en mer nyanserad pronos än en enkel maximum-likelihood-skattning.

Place, publisher, year, edition, pages
2017.
Series
TRITA-MAT-E ; 2017:38
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-209274OAI: oai:DiVA.org:kth-209274DiVA, id: diva2:1116991
External cooperation
BizOne
Subject / course
Mathematical Statistics
Educational program
Master of Science - Applied and Computational Mathematics
Supervisors
Examiners
Available from: 2017-06-28 Created: 2017-06-28 Last updated: 2017-06-28Bibliographically approved

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CiteExportLink to record
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