Gov2001 October 2004

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[gov2001-l] numerical integration in R

by sbignami＠camail.harvard.edu

What is the command to do numerical integration via the grid method in R? Thanks, Simona.

19 years, 6 months

[gov2001-l] Fw: Assignment 2 Solution Set

by olau＠fas.harvard.edu

Thanks for pointing this out, Alex. Note that if you plot the birthday distribution for i in 1:100, you asymtotically approach 1 for values of i > 50 or so. At 0.99, the values are not particularly well differentiated (because the CDF is nearly 1 and nearly flat), so I'll accept a small range of answers for this subpart. On numerical stability in general, you should probably try to use the summation of the log terms for the Negative Binomial problem this week rather than actually multiplying the probabilities. Just remember to exp() the numbers you get back to restore them to the proper scale. ----- Original Message ----- From: "Alex Montgomery" <ahm(a)stanford.edu> To: "Olivia Lau" <olau(a)fas.harvard.edu> Sent: Friday, October 08, 2004 12:13 AM Subject: Assignment 2 Solution Set > Hi Olivia- > > One minor discrepancy in the solution set: You need 57 people > for 0.99 (if you work it out analytically, it comes to > 0.9901225) - if you make sims high enough, it ends up with > this answer, too. > > -A >

19 years, 6 months

[gov2001-l] #6: Beta-binomial

by olau＠fas.harvard.edu

Hi, everyone. For the beta binomial, skip step 1 of Gary's instructions. Draw pi.tilde from the beta distribution and then follow the rest of the steps. pi.tilde is just one draw from the beta distribution, for one simulation from the beta binomial. You can use rbeta() to get this value, but you will have to reparameterize gamma and mu to get the inputs (alpha and beta) to the rbeta() function. You cannot use rbeta() for question 5. ______________________________ Hi Olivia, I'm trying to follow the steps on how to simulate the beta-binomial but no luck. My questions are (sorry if the answers are very obvious): In step 1: how do we define pi_j at this point? Could it just be any random variable from 0 to 1? In step 3: I understand it is that pi_tilda is just one draw from the beta distribution. Is that correct? Can we use rbeta() to get this value? If we can, the parameters u and and gamma correspond to the parameters needed in the rbeta() comand? Thanks a lot, Cecilia Olivia.

19 years, 6 months

[gov2001-l] questiions

by fukumoto＠dg8.so-net.ne.jp

Does anybody know 1) how to find mode, the most frequent value in a variable, NOT R attribution of an object? 2) how to make histogram which can distinguish the frequency of value 0 cases and that of value 1 cases? Thank you in advance, Kentaro

19 years, 6 months

[gov2001-l] curves and plotting

by allan.friedman＠gmail.com

We were a little curious about how to plot the PDFs in 3 and 5. In 3, we should be plotting from the simulation, right? That is, is the PMF going to be a histogram of simulations? Or can we plot from the probability mass function itself. What about 5? I don't see an obvious way to simulate it from other more basic distributions. If we use the functional form (reparameterized by King in class), I'm not sure what should be on the X axis. Thanks! /\llan

19 years, 6 months

[gov2001-l] correction to #6

by olau＠fas.harvard.edu

Hi, Thanks to Jens for pointing this out. In part 6, it should be: "Write a function which generates iid draws from the Beta-Binomial distribution for user-specified values of mu, gamma and n. (Not pi and n -- pi is unobserved.) A corrected version is online. Yours, Olivia.

19 years, 6 months

[gov2001-l] Benford's Law

by allan.friedman＠gmail.com

If anyone out there as big a geek as me, they might like this article on Benford's Law from the American Scientist Hill, T.P.; "The First Digit Phenomenon," American Scientist, 86:358, 1998. PDF: www.math.gatech.edu/~hill/ publications/cv.dir/1st-dig.pdf I was kind of curious about the coin flipping thing. Sure enough, the algebra is a little prickly, but the simulation was a breeze. Code if anyone wants to tinker: #Simulates flipping a coin 200 times to see if six heads or tails arrive in a row #Based on class exercise of TP Hill to show use of probability in auditing sixheads <- function(sims) { counter <- 0 for(i in 1:sims) { flips <- berns(.5, 200) ## toss a coin 200 times flips <- paste(flips, collapse="") ## make a string for grep if(any(grep("111111", flips))) {counter <- counter + 1} ##look for the string of 6 heads else if(any(grep("000000", flips))) {counter <- counter + 1} ##and tails } counter/sims ##returns percentage where a string occured }

19 years, 6 months

[gov2001-l] questions on beta-binominal simulation

by jens_hainmueller＠ksg05.harvard.edu

A couple of dumb questions regarding problem 6. I am unclear about the correct interpretation of the steps to simulate the beta-binominal outlined in the lecture notes. There it says: 1. Begin with N Bernoulli trials with parameter pi.j, j = 1, . . . ,N (not necessarily independent or identically distributed) So pi.j is allowed to vary across each of N trials, but not across simulations of each N, right? In the former interpretation we would have as many pi.js as Ns, but each pi.j remains constant across simulations. In the latter interpretation we would have N*sims pi.js. 2.1 Choose mu = E(pi.j) I guess this refers to the mean of pi.j over all Ns and not the mean of pi.j across simulations of each N? So for each simulation, mu will be a single number. 3. Draw pi.tilda from Beta(pi|mu,gamma) Which pi (given mu & gamma) is this referring to? In the slide this pi has no subscript or tilda or anything. Thanks, Jens

19 years, 6 months

[gov2001-l] email this week

by olau＠fas.harvard.edu

Hi, In anticipation of the deluge tonight (since most of the study groups are meeting tonight), you should be aware that I will only be answering email intermittently from 6pm to 11pm tonight, but you should feel free do drop by the basement of the Carpenter Center and look for me. I will respond to all email (sent during that period) by Wed morning. Also, some of you sent email on Thursday afternoon last week -- I have class all Thursday afternoon until section, so you should not expect a reply (from me) during that period. Yours, Olivia.

19 years, 6 months

[gov2001-l] new version of HMDC tool

by olau＠fas.harvard.edu

Hi, everyone. All of you who use the HMDC VNC connection tool ("Double_click_me") need to download a new version available at: http://www.hmdc.harvard.edu/HMDC_VNC.EXE Please do so IMMEDIATELY. This should cut down on the number of multiple sessions. And those of you with multiple sessions need to kill them immediately. This is getting out of hand. Yours, Olivia

19 years, 6 months

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Gov2001 October 2004