Statistics, methods, and models in ecology: 統計模型的基本概念

"Equations are simply a mathematical shorthand for conveying sets of ideas or concepts"

學習統計模型方程式就像學習語言一樣，我們絕對鼓勵讀者「完全弄懂」這篇所要討論的概念。妥善運用統計推論是成功分析生物多樣性研究的核心技能。由於生物多樣性怡就常見的柱況是樣本數太少，或是有部份不確定的估計。統計推論可視為執行研究的嚴謹方法，描繪議題結論的方針，妥善處理取樣上的變異。

"Likelihood" "maximum likelihood estimation" "likelihood ratio test" "goodness of fit test" "Bayesian methods"
"Akaike Information Criteria AIC"

1. 定義與基本概念

希望瞭解研究目標族群中未知的參數，則須在取樣單位(sampling unit)中以適當的取樣過程(sampling procedure)，取出可描繪族群母體的樣本資料。

Population 族群: The complete set of sampling units that we are interested in studying.
Sample 樣本: (1) The set of sampling units that we actually study.
(2) A part of the population.
(3) Chosen based on some assumed probability mechanism.
Parameter 參數: (1) A characteristic of the population that we would like to know about

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

the probability of occupancy

Estimator of a Parameter 參數的估計值: as we never know the value of a parameter exactly, we have to use an estimator of the parameter based on a sample

the estimator of the parameter

Random Variables, Probability Distributions and the Likelihood Function

random variable 隨機變數：以隨機過程觀察所得的結果。

<範例>

有五個樣區，假設偵測度沒有問題，結果其中兩個樣區有發現目標物種、三個沒有。
U 代表 unoccupied、O 代表 occupied

U, O, U, O, U

定義發現該物種(O)的機率是 This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

沒發現(U)的機率則是 This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.