Analysis Of Variance Puns

Do you find it easier to use the tubular format or the condensed formula for variance analysis? No matter how much I think I have variances under control, a newly formatted question proves that I don't. I swear it wasn't this hard in undergrad. What works for you?

Hi, r/statistics!

This is a bit of a long one but bear with me while I try to explain what I'm trying to achieve here.

So, please take a look at the image I've linked below.

https://imgur.com/xAggfe8

What you're looking at is a series of numbers with the relative difference between the price of a forward contract with a 6-month maturity, to the price of the asset at the date of maturity. This is historical data. In this example, if the number in the spreadsheet is X>1, the seller of the contract has made money. Each column is a contract, starting at the 6 month to maturity price, and the further down you get in the column, the closer you get to maturity.

What I'm trying to figure out is: in a given period in the six months leading up to maturity, how likely is it that the seller of the contract will make money with a significance level of a=0.05, based on the historical numbers?

Hypothesis:

H0: forward option price < or = price at maturity
H1: forward option price is > price at maturity

I've marked a period in the picture as an example of a timeframe that I would like to significance test. How do I go about doing this with multiple variables? I've looked at and ANOVA-test, and I think that this is the right one to use, but idk how I do this.

I'm not particularly good at statistics, and I'm struggling a bit on how to explain myself here, but please feel free to ask questions, as I will be sitting at the computer all day.

In case my question isn’t clear, basically what I’m asking is what is significant about raising the difference to a factor of 2? Obviously raising the factor to an odd number doesn’t make sense because of the sign (though you could just use absolute values), but is there a reason specifically why a power of 2 was chosen/is used to calculate variance instead of 4, 6, or 8?

#Somewhat related follow-up question:

Say you have a set of values and you calculate the standard deviation.

Now say you calculate the variance of the set, except instead of raising the differences to a factor of 2 you raise them to a factor of 4 (to try to establish a some clarity, we can call this the adjusted variance), and now take the square of the square (quartic root?) of this adjusted variance (we’ll call this the adjusted standard deviation).

Naturally, unless the variance is “small”, the variance and adjusted variance will not be “close”, though the standard deviation and adjusted standard deviation will be much closer. This leads to my last questions:

• If comparing two sets, is it possible for one set to have a higher standard deviation than the other, while also having a lower adjusted standard deviation

• If it is possible to have a higher standard deviation and lower adjusted standard deviation, is it possible if every value in both sets is greater than 1?

Lab diving is currenly the main midgame activity and the main way to obtain resources needed for character progression (mutagens, CBMs, high-end weaponry and equipment). Each lab has a final, well guarded reward room at the bottom (tower labs have 2 and central labs have up to 9) to provide those to players who can get past the security. The issue, however, is that some reward rooms are clearly more desirable than others by a huge margin. While it's totally fine to get a random reward, randomly getting no real reward at all shouldn't be possible.

In order for a reward to be good, it basically needs to satisfy the following:

• the player wants this reward and can use it
• the reward is rare and valuable enough to be considered a final lab reward
• any duplicate rewards beyond the first one aren't useless

Currently, most lab rewards don't meet these criteria. Below all lab reward rooms are classified based on how close they are to a hypothetic ideal that meets all 3 (spoilers, obviously).

Really good ones (meet all 3)

• Nanofabricator

Gives you enough templates to choose from and even if you don't want any, you at least get raw nanomaterial. Notable for having good synergy with other sources of templates/nanomaterial. This is what all reward rooms should be like - you get to choose which reward you want and finding multiple nanofabricators doesn't diminish their value.

• Energy weapons

Highly valuable weapons and the recipe book everyone wants. Even if you have them already you get hydrogen canisters and solar panels. Having multiples of laser weapons can be useful if you have mods for them (electrolaser conversion, etc).

• Plain mutagen tank

Saves you a lot of tedious crafting and speeds up character progression. Can be turned into any flavour you want. Diminishing returns on finding subsequent ones, but can still be useful for minmaxing mutations.

Decent ones (meet 2 out of 3)

• Flavoured mutagen tank

Extremely highly valuable if you want that flavour, completely useless otherwise. Bonus points for allowing illiterate characters to go post-threshold in a reasonable amount of time. Severe diminishing returns but finding multiple identically flavoured tanks is extremely rare.

• CBM storage

In theory, CBMs are highly valuable. In practice, the finale can't spawn the really good CBMs and instead tends to have a few mediocre ones. The quantity is low and comparable to a single bionic vault.

• CVD machine

I recently had an interview where I got asked to state the definition of the bias-variance trade off. I gave the text book definition about avoiding the extremes of overfitting and underfitting and using learning/validation curves to examine for it.

However the interviewer said my answer was wrong and that the kurtosis and skew is a more accurate way of examining the bias-variance trade off.

Confused, I didn’t want to argue with them and moved on. But can some please clarify from where this new interpretation is from?

Autism Gender Link

So I've been gaming since the SNES and I guess I'm behind now on gaming terms. I understand that an RPG means role playing game such as Skyrim and The Witcher 3 and so on. I'm kind of old school but an RPG to me meant the original final fantasy and such. But I'm confused on what makes a game a RPG or a JRPG and others compared to just standard RPG games. Does Far Cry 5 count as an RPG because it has a progression system? I'm just trying to figure out how I fell out of the loop so quickly.

I've been playing Arena since vanilla, it has always been my preferred and favorite game mode. There have been metas I've enjoyed, and metas I've hated, for various reasons, but I cannot recall a time in memory I've felt this hopeless this often due to the simple fact of deck quality.

I've seen decks in this meta as ridiculous as anything from the brief "everyone has nothing but S tier cards" period. I've been hit with high quality board clears four turns in a row (Blizzard into Blizzard into Flamestrike into Flamestrike). I've played (pre adjustment) a Rogue with 5 Miscreants. I've run into no fewer than a half dozen N'Zoth decks laden with quality deathrattles. I've been run over by Kel'Thuzad. I've had Warlocks chain Abyssal Enforcers on me. I've had Priests drop 3 Talon Priests in the first four turns of the game. I had a shaman play 12 S tier cards in a row, finally breaking my back through pure value.

And I've had some stupidly powerful decks myself. Rogue pre-adjustment was like found money, you almost had to try to lose. But more often than not, I get "the sea of neutral trash" deck. I've seen more Ancient Mages in the past week than I'd seen in the previous year and a half. I've had decks with 10+ picks from the lower buckets, completely polluted with janky, trashy cards. And that's okay, that's the fun of Arena right? Trying to make your trash come together into something special.

Except not really, because of the parade of value on the other side of the playing field. Can't make interesting decisions about whether to hold or spend removal if you're never offered any. Can't make interesting decisions about whether to extend on the board or hold back to dodge AoE when extending on the board is your only win condition due to your low value/low power minions. Can't play around multiple "I win" cards with ludicrously over the top power levels.

This is meant to be a premium game mode, and while a certain amount of variance is inevitable, my 150 gold should spend as well as anyone else's. They have GOT to tighten up bucket offerings between runs. Why is it reasonable for one deck to get 1-2 picks out of the top buckets and another deck to get 15? "I guess you just lose now, today wasn't your day, that's Hearthstone" is a fine motto for constructed play, but goes down a little sour in a game mode they charge an entry fee for. "Thanks for your entry fee, here is your shit deck, enjoy 0-3" is a bit dubious.

I cannot recall the last time I had this mu

At least we know they are used in the hypothetical world of Billions. Literally worked a few of these an hour before the episode, thought I was seeing things again. My wife was not nearly as amused as me.

Billions

I'm trying to understand the reason for the difference in the formulas for 𝜎^(2) and s^(2); the denominator for 𝜎^(2) is n, but the denominator for s^(2) is (n - 1).

I've seen a lot of arguments based on the concept of degrees of freedom, saying that calculating the sample mean removes a degree of freedom. They say that because the sample mean is known, knowing (n - 1) of the sample values constrains the nth term because it can only have one value.

This sort of makes sense, but I don't see why the same argument doesn't apply to the population variance as well. Any clues?

I've read up online that we lose a degree of freedom as if we set the sample mean to equal 0 and allow all X observations to vary, the last term of the observations isn't allowed to vary so we lose a degree of freedom.

Can anyone explain this?

I was listening to the Thinking Poker Podcast and they were talking about something interesting pertaining to playing tournaments and the adjustments you need to make from playing cash.

They were talking about a spot where one of the guys (I don’t remember their name, I’m a newer listener) was in a spot where he made a large bluff which was probably slightly plus-EV in isolation, but he determined was a big mistake because of ICM implications when he lost because the chips he lost were worth more than the chips he stood to gain (from an ICM perspective).

Being someone who plays exclusively small-stakes cash, I hadn’t thought much about these situations, but I do find the math behind the game interesting in all circumstances. I started wondering if certain high variance plays are bad in a tournament setting, even with ICM implications aside. I tried some searching for information about related to this, but when I search for “variance math poker tournaments”, etc other interesting things come up. I’m sure I’m not the person to have discovered any of this—it would be awesome if anyone has references to related work.

Let me give an example in about the most simplified circumstance possible.

Hero is in a heads up situation to win a tournament with, but hero has 300 chips while villain has 100. To make the math easy in this first example, let’s say that both players just so happen to get dealt hands every hand that have .5 equity vs each other with no chance of splitting the pot, and they’ve made an agreement that they will go all-in vs each other every hand.

In order to figure out hero’s chance to win the tournament, we can basically run a simple simulation of this mathematically. After the first hand, half of the time hero wins, so we put .5 in his “equity bank” and save that shit for later. The other half the time hero loses and we run this flip again.

Now stacks are even at 200. Half the time hero wins and wins the tournament. So out of the remaining .5 he takes .25 more equity, adds that shit to his equity bank for a new total of .75. The other half of the time hero loses.

Hero wins 75% of the time and loses 25%.

I specifically chose stack sizes where this only iterates twice, but with other stack sizes, different odds of winning a hand, and more players, this tree would go much deeper.

That is an example of how variance plays out with different stack sizes but equal pot equity on each iteration. Now let’s look at an example with different chances

This is starting to really impact my performance and I have no clue what to about it. I'm on a Helios 500 Ryzen 2700/Vega56 and normally I have no trouble getting about 200 fps steadily. If I overclock it things easily get in to the mid-200s.

Big big fights with lots of effects usually dropped me about 10-15%, like it was never a big issue. Suddenly a couple of nights ago I couldn't get even a steady 144, let alone 200.

I've re-installed drivers, Afterburner, repaired the game, loaded my AMD settings called "240hz guaranteed settings" looked for everything I can find. Something feels fucked and I can't quite figure out if it's me or not.

Thanks in advance for whatever help is out there.

If you throw a dice 13 times and get
1: x1
2: x3
3: x2
4: x0
5: x1
6: x6

what will be the average, variance and standard deviation?

Hello,

I am working on dynamic pricing on a hourly basis for the company I work and I decided to model it as a multi-armed bandit problem. With that in mind I had on question about the reward:

Lets assume that our product sales is strongly associated with the time of the day, it sells a lot near lunch. What is the best way to tackle this problem?

1. Should I normalize the reward by some kind of score calculated by the representativeness of the time regarding the total sales of the day? Some thing in the lines:
   1. if at noon, 40% of the sales are made, the hour score normalizer for the reward at noon would be (1.0 - 0.4) = 0.6 whereas at midnight the representativeness of the hour is 0.05 than the score normalized should be (1.0 - 0.05) = 0.95
2. Or should I create a context of hour for each product? Maybe one MAB for each hour of the day and product?
   1. With this, the convergence is slower, because each or of the day, would be a context that will only repeat once per day. If we normalize the score, we would have 24 samples a day.

What do you suggest?

Let's say I have a List<TestClass> from the code below. I would like to order the list to maximize the variance between TestClass objects in the list near each other. The variance is determined by the number of matching Prop enums.

For instance:

These two test classes would have MORE variance

new TestClass { Prop1 == enum1, Prop2 == enum2 }

new TestClass { Prop1 == enum3, Prop2 == enum4 }

than these two test classes

new TestClass { Prop1 == enum1, Prop2 == enum2 }

new TestClass { Prop1 == enum1, Prop2 == enum3 }

because the first two test classes share none of the same enums, while the second two test classes share the same enum1.

Now my question is, how to maximize the total distance between all objects in this list of N size? Or in other words, how do I decrease the likelihood of similar objects being near each other in the list?

public class TestClass
{
    public TestEnum Prop1 { get; set; }
    public TestEnum Prop2 { get; set; }
    public TestEnum Prop3 { get; set; }
    public TestEnum Prop4 { get; set; }
    public TestEnum Prop5 { get; set; }
    public TestEnum Prop6 { get; set; }
    public TestEnum Prop7 { get; set; }
    public TestEnum Prop8 { get; set; }
    public TestEnum Prop9 { get; set; }
    public TestEnum Prop10 { get; set; }
}

public enum TestEnum
{
    enum1, enum2, enum3, etc
}

In a previous part to the question, we were asked to form 49 gamma distributions, which I stored in a dataframe. We were asked to compare the theoretical expected value and variance with the sample mean and variance of the gamma distributions.

Here is my attempt at the task; (our course hasn't done any R, but we share a module with a larger course who does R, so if you see something that you think is stupid, you're probably right :) )

df = data.frame(Gamma=names(gammadists[1:50]))
sample_evalue <- c()
theoretical_evalue  <- c()
sample_variance <- c()
theoretical_variance <- c()

j <- 1
for (d in gammadists)
{
   if (j != 1)
   {
      s <- strsplit(names(gammadists)[j], " ")[[1]]
      evalue <- as.numeric(s[2]) / as.numeric(s[4])
      variance <- as.numeric(s[2]) / (as.numeric(s[4]) *  as.numeric(s[4]))
      theoretical_variance[j] <- variance
      sample_variance[j] <- var(d)
      theoretical_evalue[j] <- evalue
      sample_evalue[j] <- weighted.mean(d)
   }
   else
   {
      sample_evalue[1] <- NA
      theoretical_evalue[1] <- NA
      sample_variance[1] <- NA
      theoretical_variance[1] <- NA
   }
   j <- j + 1
}

df['Sample expected value'] <- sample_evalue
df['Theoretical expected value'] <- theoretical_evalue
df['Sample variance'] <- sample_variance
df['Theoretical variance'] <- theoretical_variance

print(df)

I tried using a while loop, but when I said 'gammadists[1]', it did not return a vector like I expected. (again, I'm certainly going wrong with my method but anyways). If a vector is formed by writing 'rgamma(10000, 0.1, 0.5)', then the name of the vector in the dataframe is of the format '( 0.1 , 0.5 )'.

I'm sure there's lots wrong with my code, but what I'm looking to find whats the right way to go about finding the expected values and variance, because I seem to be getting funny answers. Any help would be appreciated :)

These win/loss totals are within 1 game of being correct, I don't know where to find full records but I've counted the losses on each. Usually I've been a solo queue player but I started using a full-stack in RBQ after placing much lower than I had been for multiple seasons prior:

• Full-Stack - 24w, 5l
• Solo-Queue - 17l, 4w

I know the matchmaker attempts to find what it believes are pretty even odds when it comes to team vs. team, but the ~80% winrate in a full-stack seems to strong to justify every playing solo queue again. It's been abysmal since 2-2-2 started in solo queue and I'm not making it any better it looks like.

Thoughts? Anyone gone from all solo-queue to all full-stack, and if so, what were the results? Tips for putting together good tips outside of just LFG?

Thanks

Hello.

I was reading articles about Machine Learning techniques and some models that the algoritm builds are evaluated using the PVE (Proportion of explained variance).

I search through a lot of articles and of course google it, but none of the explanations were "simple" for understanding.

For what i understood, PVE is a measurement that explains the variance of the data used to build a model (in my case).

Can someone confirm this? I would like to ask for a better definition of PVE if someone has it.

Thanks in advance :)

https://imgur.com/gallery/l8g6eUK

I need help on part b on how the equation for the variance of the estimator is derived. I believe it has to do with covariance? Any advice is appreciated.