臺灣博碩士論文加值系統

本論文主要是探討在二維度空間上二母體分佈是否一致。我們利用排列
(permutation)檢定方法來做比較, 並藉由費雪(Fisher)正確檢定方法的想法而提出重標記 (relabel)排列檢定方法或稱為費雪排列檢定法。
我們透過可交換性的特質證明它是正確 (exact) 的並且比 Syrjala (1996)所建議的排列檢定方法有更高的檢定力 (power)。
本論文另提出二個空間模型: spatial multinomial-relative-log-normal 模型 與 spatial Poisson-relative-log-normal 模型
來配適一般在漁業中常有的右斜長尾次數分佈並包含很多0 的空間資料。另外一般物種可能因天性或自然環境因素像食物、溫度等影響而有群聚行為發生, 這二個模型亦可描述出空間資料的群聚現象以做適當的推論。

This thesis proposes the relabel (Fisher's) permutation test inspired by Fisher's exact test to compare between distributions of two (fishery) data sets locating on a two-dimensional lattice. We show that the permutation test given by Syrjala (1996} is not exact, but our relabel permutation test is exact and, additionally, more powerful.
This thesis also studies two spatial models: the spatial multinomial-relative-log-normal model and the spatial
Poisson-relative-log-normal model. Both models not only exhibit characteristics of skewness with a long right-hand tail and of high proportion of zero catches which usually appear in fishery data, but also have the ability to describe various types of aggregative behaviors.

1 INTRODUCTION 10
2 SYRJALA’s PERMUTATION TEST 13
2.1 Introduction 13
2.2 Test statistic 17
2.3 Switch permutation is exchangeable? 18
3 SPATIAL MODEL 20
3.1 Model description 21
3.1.1 Conditionally autoregressive model 22
3.1.2 Spatial multinomial-relative-log-normal model 23
3.1.3 Spatial Poisson-relative-log-normal model 24
3.2 Model justification 24
3.2.1 Examples of spatial multinomial-relative-log-normal distribution 26
3.2.2 Examples of spatial Poisson-relative-log-normal distribution 29
3.2.3 Highly skewed with a long right-hand tail 32
4 RELABEL PERMUTATION 35
4.1 Procedure of the relabel permutation 35
4.2 Illustration 36
4.3 Exchangeable 38
4.4 The relabel permutation test 42
5 NUMERICAL ANALYSIS 44
5.1 Simulation design 44
5.2 Size comparison 45
5.3 Power comparison 47
6 CONCLUSION AND DISCUSSIONS 55
6.1 Auto-models 55
6.2 Test statistic 57
6.3 Invariant property 58
6.4 Dimension reduction 59
REFERENCE 60
A APPENDIX 63

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