This thesis is focused on the development of HIV/AIDS mortality in the world starting from the year 1990 and the main goal is estimating the possible future development of the number of inhabitants of the world and defined regions and the influence of HIV/AIDS on the number of inhabitants up to the year 2065. The possible number of HIV/AIDS deaths and people, who were not born because of HIV and AIDS, is computed up to this year. In the theoretical part of the thesis, the most important institutions, which include fight against HIV and AIDS as a part of ther programme, are presented. Natural history of HIV infection and the successes in the research of HIV vaccine are described. In the analytical part, the demographic reproduction of the population of the world and selected regions between years 1950 and 2010 is described, followed by population projection of the world and regions up to year 2065 using the cohort component method. The projection is created in four variants. The first one eliminates the HIV/AIDS mortality. The second one is the constant variant, which conserve the level of HIV/AIDS mortality from the year 2010 up to the year 2065. Last two variants, higher and lower, consider changing levels of HIV/AIDS mortality at time. According to the results of this population projection,...

國家政策之制定須配合未來人口總數及其結構等特性，藉以達到提高國民福 祉的願景，因此各國均定期公佈人口推估(Population Projection)的結果，目前臺 灣官方人口推估為每兩年公布一次。人口推估主要考量三個要素：出生、死亡、 遷移，以國家層級而言，通常遷徙對未來人口的影響遠小於出生與死亡，所以過 去行政院經濟建設委員會的官方全國人口推估一般專注於出生與死亡。然而，各 國研究發現遷徙是小區域人口推估為最重要的因素，人口數愈少、影響程度有愈 大的傾向，但文獻中較缺乏臺灣內部遷移的研究。如能掌握臺灣小區域人口遷徙 的變遷，將能使政策因地制宜，有助地方政府提高推行政策的有效性，也是本研 究之目標。 由於缺乏完整的縣市、鄉鎮市區層級的詳細遷移資料，本研究以人口平衡公 式反推淨遷移人數，找出各地區的遷移特性後，代入人口變動要素合成法(Cohort Component Method)，搭配屬於機率推估的區塊拔靴法(Block Bootstrap)，推估小 區域的未來人口。關於出生及死亡的推估，過去研究發現使用區塊拔靴法用於小 區域的生育率（曹育欣，2012）及死亡率（金碩，2011），皆有不錯的推估結果。 本研究以臺北市為範例，討論區塊拔靴法在小區域遷徙人口數、年齡別遷徙人口 的推估效果，及是否適合運用在其他不同縣市。 / The population projection is used to provide information for the policy planning of governments. In Taiwan, the Council for Economic Planning and Development is in charge of the official population projection and it release projection results every two years. Basically, three factors are considered in population projection: birth, death, and migration. Since the migration has little impacts in country-level projection, many countries (including Taiwan) assume the future migration is zero or close to zero, and the focus of projection is usually on the birth and death. However, for the projection of small area (such as county- or township-level), past studies found that the effect of migration cannot be ignored. But, partly due to the limitation of migration data, there are not many studies explore the migration patterns of counties or townships in Taiwan. In this study, we use the population records (births and deaths) and the population equation to derive the county-level records of internal migration in Taiwan. We use these data to explore the migration patterns of all counties in Taiwan, and then applying block bootstrap method to modify the county-level population projection. Note that, the block bootstrap is shown to be reliable in forecasting fertility (Tsao, 2012) and mortality (Jin, 2011) for small areas. In this study, we also use the Taipei City to demonstrate the population projection which includes the internal migration, and the result is promising.

一個國家對全國人口有充分瞭解，方能依據國情制定適合的政策，地方發展更是如此，更須洞悉各地的人口結構，以善用有限的資源。台灣近年人口老化日益明顯，各縣市的老化速度及人口問題也不盡相同，若可獲得各地區未來的人口相關數值 (亦即人口推估)，當能減輕未來人口老化對台灣造成的衝擊。本文以縣市層級的人口推估，也就是小區域人口推估為研究目標，探討需注意的事項，尋找適合台灣地區的小區域推估方法。 本文整理小區域人口推估方法，並使用人口要素變動合成法 (Cohort Component Method)，以雲嘉兩縣、臺北市、澎湖縣為範例，測試縣市層級的人口推估。人口推估與生育、死亡、遷移三者的假設有密切關係，我們以死亡率為目標，比較不同模型的優劣，考慮的模型包括 Lee-Carter 模型、區塊拔靴法 (Block Bootstrap)、篩網拔靴法 (Sieve Bootstrap) 以及泛函資料分析 (Functional Data Analysis) 中的主成份分析 (Principle Component Analysis)，以估計誤差為衡量方法優劣的標準。分析發現篩網拔靴法、區塊拔靴法、Lee-Carter 模型三者的結果較佳，因此在小區域推估中使用較簡便的區塊拔靴法。研究發現對小區域的人口推估而言，遷移假設扮演非常重要的角色，此與全國規模的人口推估結果截然不同。研究過程亦發現人口三要素對人口推估有明顯的影響，若假設三要素間互相獨立 (也就是傳統推估時的假設)，推估結果的預測區間遠小於三要素不獨立。 / The government can make policy according to the population change in this country, while the local government can develop their district by using their limited resources well after realizing the populaton structure. The population ageing is becoming more serious and being more different among every counties in Taiwan day by day. If we can get the relative numbers of population in the future (population projection), we can decrease the attack of population ageing for Taiwan. The aim of this paper is to find an appropriate method and some notations of small area population projection in Taiwan. The paper includes the summary of methods of small area population projection and the results by using cohort component method on three areas in Taiwan, YunLin & ChiaYi, Taipein City and PengHu. Population projection is highly related with birth, death and migration, hence we test the mortality rate by using several methods, Lee-Carter, block bootstrap, sieve bootstrap and principal component analysis of functional data analysis are included. We found that the result of sieve bootstrap, block bootstrap and Lee-Carter are much better than the others, therefore, we take block bootstrap which is much simpler than the other two to analysis the effect of birth, death and migration in population projection. The sutdy found that, in small area population projecton, migration plays an important role, which is totally different from the whole country population projection.

Selected Methodical Approaches to Regional Population Forecast: A case study in the South Bohemian Region Abstract The aim of this thesis is to introduce selected methodological approaches to population forecasts, focusing on the regional level and considering different lengths of time series. Specific procedures are applied to create a population forecast for the South Bohemian Region. In the theoretical part of this thesis, the stages of population forecasts processing are determined. The Cohort Component method with migration, which can be used to create population forecast, is characterized. Another part describes selected analytical models and functions for partial mortality, fertility and migration forecasts, including Indirect estimation of net migration. To extrapolate parameters, selected trending functions and the Box-Jenkins methodology are characterized in the part of the time series analysis. The analytical part of this thesis focuses on the creation of the South Bohemian Region forecast from short initial time series and long initial time series. From short initial time series, the partial forecast of mortality is analyzed by the Heligman-Pollard model, the partial forecast of fertility is analyzed by the Beta function and the partial forecast of migration is analyzed by 25%, 50% and 75%...

Moravskoslezský region population forecast to 2050 Abstract The main goal of this thesis is to calculate Moravskoslezský region population forecast to 2050 and show how future population growth will likely be in the next decades. It includes a detailed population development analysis which is an important part of this thesis. Moravskoslezský region is still one of the most populous regions of Czechia, despite of natural decrease and negative net migration in past 21 years (except 2007 and 2008). Based on the analysis, we can assume that population decline will continue in the future and population forecast results confirm this hypothesis. Declining population size will be followed by significant age-structure changes in population and progressive demographic ageing. From the perspective of future population development Moravskoslezský region will face brand new situations and related problems. Keywords: population forecast, Moravskoslezský region, analysis of population development, age structure, fertility, mortality, migration, regional development, cohort-component method

人口政策的制定需要人口推估作基礎。近年世界各國人口推估逐漸從專家意見推估走向機率推估，常見的機率推估分成三大類，隨機推估、模擬情境、推估誤差三種，本文所使用的人口推估方法為隨機推估法結合生育率之模擬情境方法，在人口變動要素組合法 (Cohort Component Method) 之下輔以電腦模擬的區塊拔靴法 (Block Bootstrap)，針對台灣地區與台灣北、中、南、東四地區進行人口推估。另外，本文試圖在隨機模型人口推估中加入遷移人口之考量，以期針對遷移人口在數量與其影響上都能有較深入的了解，比較區塊拔靴法與經建會推估之差異後發現遷移之考量確實會影響人口推估之結果。 / 針對與全區相符的小區域人口推估，本文亦提出可使得推估一致的方法，但其缺點為限制了生育、死亡人口要素之變動性。此推估在總數上與隨機推估方法差異不大，但在人口結構上則有明顯的差別，此差別可能是來自於死亡率在四區間差異造成。 / Population projection is important to policy making, and only with accurate population projection can the government achieve suitable policy planning and improve the welfare of the society. The most popular and well-known population projection method is the Cohort Component method, proposed since 1930’s. The trends of future fertility, mortality and migration are required, in order to apply the cohort component method. Currently in Taiwan, these trends are determined according to experts’ opinions (or scenario projection) and three future scenarios are assumed: high, median and low scenarios. One of the drawbacks in applying experts’ opinions is that the projection results of these three scenarios do not have the meaning in probability. / To modify the expert’ opinions and let the projection results carry the meaning in probability, many demographic researchers have developed stochastic projection methods. The proposed stochastic methods can be categorized into three groups: stochastic forecast, random scenario and ex post methods. In this study, we introduce these stochastic methods and evaluate the possibility of applying the methods in projecting the population in Taiwan. / In this study we use block bootstrap, a computer simulation and stochastic forecast method, to determine the trends of future fertility, mortality and migration in Taiwan, and combine it with the cohort component method for population projection in Taiwan. We compare the projection results with those from the Council for Economic Planning and Development (a scenario projection). We found that the block bootstrap is a possible alternative to the scenario projection in population projection, and the numbers of migration is small but have a non-ignorable influence on the future population. However, we also found that the block bootstrap alone might not be appropriate for population projection in small areas.

台灣地區的人口隨著生育率及死亡率的雙重下降而呈現快速老化，其中生育率的降低影響尤為顯著。民國50年時，台灣平均每位婦女生育5.58個小孩，到了民國70年卻只生育1.67個小孩，去年（民國90年）生育率更創歷年新低，只有1.4。死亡率的下降可由平均壽命的延長看出，民國75年時男性為70.97歲，女性為75.88歲；到了民國90年，男性延長到72.75歲，女性延長到78.49歲。由於生育率的變化幅度高於死亡率，對人口結構的影響較大，因此本文分成兩個部份，主要在研究台灣地區15至49歲婦女生育率的變化趨勢，再將研究結果用於台灣地區未來人口總數及其結構的預測。 　　本研究第一部分是生育率的研究，引進Gamma函數、Gompertz函數、Lee-Carter法三種模型及單一年齡組個別估計法，以民國40年至84年（西元1951年至1995年）的資料為基礎，民國85年至89年（西元1996年至2000年）資料為檢測樣本，比較模型的優劣，尋求較適合台灣地區生育率的模型，再以最合適的模型預測民國91年至140年（西元2002年至2051年）的生育率。第二部分是人口推估，採用人口變動要素合成方法（Cohort Component Projection Method）推估台灣地區未來50年的人口總數及其結構，其中生育率採用上述最適合台灣地區的模型、死亡率則引進國外知名的Lee-Carter法及SOA法（Society of Actuaries），探討人口結構，並與人力規劃處的結果比較之。 / Both the fertility rate and mortality rate have been experiencing dramatic decreases in recent years. As a result, the population aging has become one of the major concerns in Taiwan area, and the proportion of the elderly (age 65 and over) increases promptly from 2.6% in 1965 to 8.8% in 2001. The decrease of fertility rate is especially significant. For example, the total fertility rate was 5.58 in 1961, and then decreases dramatically to 1.67 in 1981 (1.4 in 2001), a reduction of almost 70% within 20 years. 　　The goal of this paper is to study the population aging in Taiwan area, in particular, the fertility pattern. The first part of this paper is to explore the fertility models and decide which model is the most suitable based on age-fertility fertility rates in Taiwan. The models considered are Gamma function, Gompertz function, Lee-Carter method and individual group estimation. We use the data from 1951 to 1995 as pilot data and 1996 to 2000 as test data to judge which model fit well. The second part of this study is to project the Taiwan population for the next 50 years, i.e. 2002-2051. The projection method used is Cohort Component Projection method, assuming the population in Taiwan area is closed. We also compare our projection result to that by Council for Economic Planning and Development, the Executive Yuan of the Republic of China.