d******1
发帖数: 92 | 1 【 以下文字转载自 Statistics 讨论区 】
发信人: dealsea1 (deal2buy), 信区: Statistics
标 题: 问一个关于converge 的问题
发信站: BBS 未名空间站 (Sat Sep 12 10:07:34 2009, 美东)
probabality converge 和almost true converge 到底有什么区别呀，能不能举一个
probabality converge， while almost true not converge 的例子，那位高人指点一
下，很急呀， 马上要交作业了 |
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B*********h
发帖数: 800 | 2 ☆─────────────────────────────────────☆
ilikexck (问天向) 于 (Sat Jul 15 14:36:21 2006) 提到:
根据Martingale convergence theorem, Brownian Motion converges to a random
vairiable B with probability one.
What is B's distribution?
☆─────────────────────────────────────☆
erain (红花会大老板) 于 (Sat Jul 15 18:09:27 2006) 提到:
There are 3 types convergence. w/p 1 convergence is the strongest one.
Here you should fix a specific time t then you can talk about two random variables' convergence result.
so B |
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f*********1
发帖数: 117 | 3 1. convergence in distribution;
2. convergence in probability;
1 doesn't imply 2.
但俺想不出converge in distribution 但是不converge in probability的例子了
谁能给列举几个？
多谢！ |
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g****y
发帖数: 71 | 4 convergence in probability usually refers to the law of large numbers. e.g.
average of iid Xi should converge in p to its expectation.
convergence in distribution usually refers to the central limit theorem.
e.g. square root of n times (average of iid Xi minus its expectation) will
behave like a normal distribution. it converges in distribution to a normal
random variable. but indeed it's not a normal random variable even in the
limit. |
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d******1
发帖数: 92 | 5 probabality converge 和almost true converge 到底有什么区别呀，能不能举一个
probabality converge， while almost true not converge 的例子，那位高人指点一
下，很急呀， 马上要交作业了 |
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a***n
发帖数: 40 | 6 Thank you. Another question is that if Xn converges to X almost surely, then
lim P(Xn=X)=1. Is it correct? My understanding of convergence almost surely is
that after finite many terms, Xn and X and the same except probably on a set
of measure 0. Is that correct?
I am trying to understand the various modes of convergence, and my questions
may be pretty naive. But it clarifies some of my doubts, and your helps are so
much appreciated. |
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a********l
发帖数: 55 | 7 考虑一个measurable space (X,B)，其中X是[0,1]，B是collection of Borel sets on
[0,1].
在(X,B)上，所有measure都可以用cdf来表达。（是吗？）
如果我有一个sequence of measures {m_n} 和一个measure m，请问我怎样用cdf来保
证{m_n}是setwise convergent to m 呢？cdf 是pointwise convergent可以吗？如果
不行，cdf是uniformly convergent可以吗？
先谢过！ |
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b****t
发帖数: 114 | 8 Hi all,
I am in Engineering, so please bear with me for possibly native questions...
A sequence of functions f_n converges to f on (a,b) in R, and if f'n
uniformly converges on (a,b), then f'n converges to f'. This result can be
seen from many testbook (.e.g Rudin's analysis book). But does this result
hold for f_n and f on a set of R^n, with the same assumptions?
Thank you very much.
Beet |
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h********3
发帖数: 2075 | 9 你是说power iteration这个算法会converge吧。
你看看它的矩阵等式。
Perron-Frobenius Theorem: If M is a positive, column stochastic matrix, then:
1 is an eigenvalue of multiplicity one.
1 is the largest eigenvalue: all the other eigenvalues are in modulus
smaller than 1.
the eigenvector corresponding to eigenvalue 1 has all entries positive. In
particular, for the eigenvalue 1 there exists a unique eigenvector with the
sum of its entries equal to 1.
它其实是用largest eigenvector去近
似原来的矩阵，不断拉大largest eigenvector和其他eigenvect... 阅读全帖 |
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a***n
发帖数: 40 | 10 If Xn converges to 0 almost surely, i.e., P(|Xn|>c, i.o.) = 0, for any c>0;
and Xn is uniformly bounded,i.e., |Xn| < k,
then the infinite sum of Xn converges almost surely?
Does P(|Xn|>c, i.o.) = 0, for any c>0, mean that for any event w, except
probably from a null set, Xn(w) is always 0 after a certain number of terms?
Thanks a lot. |
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a***n
发帖数: 40 | 11 I just found that I made a mistake. the number c is arbitrary for these two
questions:
If Xn converges to 0 almost surely, i.e., P(|Xn|>c, i.o.) = 0, for any c>0;
and Xn is uniformly bounded,i.e., |Xn| < k,
then the infinite sum of Xn converges almost surely?
Does P(|Xn|>c, i.o.) = 0, for any c>0, mean that for any event w, except
probably from a null set, Xn(w) is always 0 after a certain number of terms?
If we let c goes to 0, are they true? Thanks. |
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a***n
发帖数: 40 | 12 (1) lim sup P(|Sn+j - Sn|>c)=O, lim is for n-->infinity, sup is over j>=1.
Is (1) the Cauchy criterion for Sn to converge in probablity?
(2) lim P{sup(|Sn+j - Sn|)>c}=O, lim is for n-->infinity, sup is over j>=1.
Is (2) the Cauchy criterion for Sn to converge almost surely? In other words,
can we take the limit inside and outside the probablity freely?
Thank you! |
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b****t
发帖数: 114 | 13 Hi all,
suppose a sequence of functions {f_n} defined on a countable set of vectors
X
(e.g. integer vectors Z^n), these functions pointwise converge to function f
defined on set X. Is it true that f_n converge to f uniformly?
Thanks,
Beet |
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Q***5
发帖数: 994 | 14 I guess the condition that 'cdf pointwise convergence' does not guarentee
the setwise convergence. Here is a counter example:
Let m has point mass at 1/2, with prob = 1, so the cdf of m is step function
with value 0 on [0 1/2) and 1 on [1/2, 1]
Let m_n be measures with cdf of (2x)^n on [0,1/2) and 1 on [1/2,1]. |
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Q***5
发帖数: 994 | 15 No. Example:
Let m be the flat distribution on [0,1], the cdf is y=x
For each n, divide [0,1] evenly into n segments and define m_n to have point
mass probability 1/(n+1) at end points and 0 otherwise.
Then the cdf of m_n is a piecewise constant function, which uniformly
converges to y=x, but m_n do not set wise converges to m on Q, the set of
all ratinonal numbers on [0,1]. |
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m*********w
发帖数: 408 | 16 有没有人给个准确的理解。我认为convergence讲的是数值解能够收敛，但不一定是真
实的解。不属于validation的概念。我看有的人写paper把数值解的convergence讲成是
数值validation，我认为是不对的。
validation是把数值解跟real world的实验值对比，检查数值解的准确性。
希望各位给点意见。谢谢。 |
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n***p
发帖数: 7668 | 17 When one talks about convergence, it means the numerical solution
converges to the real solution. |
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j****x
发帖数: 943 | 18 convergence does not necessarily mean that the numerical solution approaches
the analytical solution. Remember, there is arbitrarily set convergence
criteria. |
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jl
发帖数: 398 | 19 A random varible converge to -\infty in provability
是什么定义? 多谢!
A random varible converge to -\infty with probability 1 s
是什么定义? 多谢! |
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B********e
发帖数: 10014 | 20 如果你所有的convergence都是指uniform convergence，fn ，fn'，f都连续可微，那
么yes。
因为任何一闭区间上都yes。
设fn'一致收敛于g。
在任一有界区间上，写出积分关系，取极限。 |
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f****e
发帖数: 590 | 21 不是，就是iid
convergence in distribution就是说他们的cumulative function收敛，但是这些rv有
没有关系就不管了
convergence almost sure, in probability包括in Lp，都要求这些rv's之间要有联系 |
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n******r
发帖数: 1247 | 22 this is not right
a sequence of iid random variables converges with probability 1
an example for 1 doesn't imply 2 can be
toss a fair coin
X=1 if head, 0 if tail
Y=1 if tail, 0 if head
X Y have the same cumulative distribution, but for e<1,P(|X(w)-Y(w)|>e)=1
therefore no convergence in probability |
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k*******d
发帖数: 1340 | 23 X_n are N(0,1)
X_0 is -X_n
clearly X_n -> X_0 in distribution since they have the same distribution;
However
P(|X_n-X_0|>\eps) = P(|2X_0| > \eps), where X_0 is N(0,1), clearly this prob
does not go to zero.
还有，converge in distribution不要求随机变量在同一个probability space上，
converge in probablity 要求在同一个prob space上，除非X_0是常数
Note that if X_n -->(in distr) X_0, where P(X_0 = c) = 1, c is a constant
then X_n --> X_0 in prob |
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g*******i
发帖数: 258 | 24 it should be. This is the idea of Gelman-Rubin convergence diagnostic
if the markov chain has good mixing, then no matter where you start, it will
converge to a same level
regardless |
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b*****s
发帖数: 11267 | 25 Gibbs sampling 是MH的一种特殊形式，
sample size你burn啦嘛？
我想你说的convergence是根据generate出来的sample作黎曼积分，也就是Expectation
不converge。 这只能说明：
1 你算的postierior 有错
2 run的次数不够多
3 你没有burn first thousand run
请自我对照查错
[在 CherryG86 () 的大作中提到：]
:模型没法简化的，是个survival model，有四个参数，其中两个跟covariate的
:coefficients，
:也不是叫metropolis hasting，是metropolis hasting的一种替代的algorithm。
:因为是simulation，所以我试了sample size 500和1000，足够大了，应该跟这个也没
:关系。初始值设置接近也试了，结果没差。 |
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w*******y
发帖数: 60932 | 26 Massively Networked: How the convergence of social media and technology is
changing your life:
http://www.amazon.com/Massively-Networked-convergence-technolog
Product Description
Massively Networked is not just another book on social media; it gets to the
heart of surprising changes that are rattling assumptions about health,
work, the home environment, politics, the economy, and our place in the
global ecosystem. Consider the following radical ideas that could soon
reshape your life:
o Going sh... 阅读全帖 |
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m**********w
发帖数: 4161 | 27 【 以下文字转载自 Stock 讨论区 】
发信人: mountainview (山景城), 信区: Stock
标 题: XOM/CVX/RDS-B/BP not converging since mid May
发信站: BBS 未名空间站 (Tue Jun 30 16:34:44 2009, 美东)
From Dec 30 to May 14, these big 4 had very similar trends.
However, interesting to notice that since May 15, the trend divergenced. BP and Shell up while XOM and CVX down.
Is this because of USD rate fluction?
It's more interesting to see their comparison on 1-yr, 2-yr and 5-yr charts.
If you buy all of them 5 yr ago, US Petro giants still gi |
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M*******a
发帖数: 1633 | 28 最近无聊在看这个，不理解为啥iterative算算到后来肯定会converge |
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A*********c
发帖数: 430 | 29 因为过程中不停地乘一个stochastic matrix，所以由markov property保证了
convergence。 |
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M*******a
发帖数: 1633 | 30 您给证明下满足markov property必然converge行不？ |
|
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a***n
发帖数: 1993 | 32 【 以下文字转载自 ME 讨论区 】
发信人: atman (齐物), 信区: ME
标 题: 大家有没有听过convergent science这个公司
发信站: BBS 未名空间站 (Wed Nov 2 16:04:19 2011, 美东)
最近有个工作机会，但不了解这个公司和他们的产品如何？ |
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t*******0
发帖数: 134 | 33 both A and B are signal molecules and both of them can activate C. 这样的话
我说：A and B are converged on C对么？
谢谢 |
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h***o
发帖数: 539 | 34 我要解一个ODE, 形式比较复杂点，假设x是自变量，y是函数，y', y", y"'是y对
x的1, 2, 3阶导数，ODE差不多是这样的
F(y",y',y,x)*y" = G(y"',y",y',y,x)*y'
F, G这两个函数里面，y的各阶导数加减乘除纽在一块的(非线性).
为了解它，我把y"'从G里面抽出来，变成
y"' = Y(y",y',y,x)
当然，Y()里面的y",y',y和x都是非线性的纽在一块的，然后用
ODE solver去解，结果总出不converge的问题。
请问，什么样的ODE, 才可以用数值来解呢？ |
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gi
发帖数: 496 | 35 We design small antennas.
with different S values, or choice different radiation surface, we got
pretty different Gain (and S11), Do you know how to have HFSS convergent?
Thanks a lot. |
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m*********s
发帖数: 368 | 36 ☆─────────────────────────────────────☆
okla (ok 啦) 于 (Thu Jul 28 18:05:45 2005) 提到:
This is about one of the argument in Alfors' <>.
In sec 2.1 of chap 5, Alfors tried to prove that
\sum 1/(z-n)^2 goes to 0 uniformly as |y| goes to infinity, where the sum is
for n goes from negative infinity to infinity.
He reasoned like this,
(1) The series \sum 1/(z-n)^2 converges uniformly for |y|>=1
(2) By (1), we can take limit term by term, so ...
My question is, how to prove (1)? T |
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D*******a
发帖数: 3688 | 37
The infinite sum cannot converge a.s.
Suppose your prob space is [0,1].
Xn=1 if 0
For all M, as long as 0M |
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b********e
发帖数: 28 | 38 Why can not take in? I think:
lim P(sup|Sn+j-Sn|>c)=lim E I(sup|Sn+j-Sn|>c)=E lim I (sup|Sn+j-Sn|>c)=
P(lim (sup|Sn+j-Sn|>c) by bounded convergent theorem.
,
Yes
No |
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a***n
发帖数: 40 | 39 If Xn converges to X in probability, i.e.,
for any e>0, lim P( |Xn - X| < e ) = 1,
can we let e -> 0, and conclude that lim P( Xn = X ) = 1 ?
I really doubt it, but cannot see why not? Thanks for your help. |
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A****e
发帖数: 44 | 40 x is arbitrary. The assumption is true for any sequence (x_n) converging to
x. |
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h***n
发帖数: 276 | 41 I have a problem as follows.
There is a experiment in which its result can be characterized as a discrete
R.V. following some known PMF. In addition, such a PMF does not change alon
g the time. Now, I start to conduct the experiment and gather the result ove
r and over again. Then I reconstruct the PMF based on the observed results a
fter each experiment. It is obviously that, as the time goes by, the estimat
ed PMF will converge to the true PMF. My question is that what is the coverg
ence rate |
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h***n
发帖数: 276 | 42 多谢回答。
不过当我使用中心极限定理时，在贝努利实验下去估计真实概率p，得到的所需要样本数
目n是形如下面的式子
n>=p*(1-p)*f(tolerance to real p)
好像结论和你的相反，真实概率离1/2近的反而要多些？
还有既然大家收敛速度有快慢，如何理解Glivenko-Cantelli theorem 给出的uniform
convergence的结论呢？ |
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n***s
发帖数: 1257 | 43 The definition says "{Xn} converges in probability to X iff P(|Xn - X| >= ε
) ---> 0 for every ε > 0". I am wondering if it can be defined without
introducing ε? Specifically, what's the difference between "P(|Xn - X| > ε
) ---> 0 for every ε > 0" and "P(|Xn - X| > 0) ---> 0"? If they are not the
same, as a condition which one is stronger ? Please give some clarification
. Thanks in advance! |
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a********l
发帖数: 55 | 44 补充：
m_n 和 m 是 measures, 所以是 set functions.
根据Royden "Real Analysis"上的定义：
m_n converges setwise to m if for each E in B we have m(E) = lim m_n(E). |
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a********l
发帖数: 55 | 45 Thank you very much! You are right!
Then do you think uniform convergence of cdf is sufficient? Thanks. |
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Q***5
发帖数: 994 | 46 The assumption of bounded Lipschitz constant B (B should be something
greater than 1 ) and point wise convergence of the cdf's will be
sufficient.
Sketch of proof: ( Let p be the flat distribution on [0 1] )
(1) For any measurable set A, we can show that m_n(A)<= B p(A) and m(A)<=B p
(A)
(2) To prove by contradiction, we can assume (without loss of generality)
that there is a Borel-measurable set D, such that m_n(D)>m(D)+delta,for all
n. (delta>0 is a constant). Then by (1), we can find a open |
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H****h
发帖数: 1037 | 47 cdf逐点收敛等价于weak convergence.
on |
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a********l
发帖数: 55 | 48 Thanks so much for the sketch of the proof, QL.
I think it's correct. I just have a problem to find a rigorous proof for
your step (1), although it is "obviously" true. Could you please give me
some hints, or a reference?
Actually, does this sufficient condition for setwise convergence of measure
appear in books, so that I can quote.
Thanks.
p
all
union |
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l******e
发帖数: 470 | 49 convergence theorem of the following type would be particular interesting to
me:
if {X_i} i=1..N satisfies xxx condition,
then for the n-term partial sum Sn of the DFT of {X_i}
we have |Sn(i)-X_i| f(N,eps) (f is some function..).
Thanks a lot. |
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