the limitations of the PPS

How to use the PPS in your own (Python) project

The PPS clearly has some advantages over correlation for finding predictive patterns in the data. However, once the patterns are found, the correlation is still a great way of communicating found linear relationships.

Let’s compare the correlation matrix to the PPS matrix on the Titanic dataset.

Let’s use a typical quadratic relationship: the feature x is a uniform variable ranging from -2 to 2 and the target y is the square of x plus some error.

how do you normalize a score? You define a lower and an upper limit and put the score into perspective.

For a classification problem, always predicting the most common class is pretty naive. For a regression problem, always predicting the median value is pretty naive.

Let’s say we have two columns and want to calculate the predictive power score of A predicting B. In this case, we treat B as our target variable and A as our (only) feature. We can now calculate a cross-validated Decision Tree and calculate a suitable evaluation metric.

More often, relationships are asymmetric

there are many non-linear relationships that the score simply won’t detect. For example, a sinus wave, a quadratic curve or a mysterious step function. The score will just be 0, saying: “Nothing interesting here”. Also, correlation is only defined for numeric columns.

Suppose you have only two rolls of dice. then your best strategy would be to take the first roll if its outcome is more than its expected value (ie 3.5) and to roll again if it is less.

Therefore, En=2n+1−2=2(2n−1)

Repeated measures involves measuring the same cases multiple times. So, if you measured the chips, then did something to them, then measured them again, etc it would be repeated measures. Replication involves running the same study on different subjects but identical conditions. So, if you did the study on n chips, then did it again on another n chips that would be replication.

This volume of paper should be the same as the coaxial plug of paper on the roll.

This shows the nonlinear relationship and how the consumption accelerates. The first 10% used makes just a 5% change in the diameter of the roll. The last 10% makes an 18.5% change.

Toilet paper is typically supplied in rolls of perforated material wrapped around a central cardboard tube. There’s a little variance between manufacturers, but a typical roll is approximately 4.5” wide with an 5.25” external diameter, and a central tube of diameter 1.6” Toilet paper is big business (see what I did there?) Worldwide, approximately 83 million rolls are produced per day; that’s a staggering 30 billion rolls per year. In the USA, about 7 billion rolls a year are sold, so the average American citizen consumes two dozen rolls a year (two per month). Americans use 24 rolls per capita a year of toilet paper Again, it depends on the thickness and luxuriousness of the product, but the perforations typically divide the roll into approximately 1,000 sheets (for single-ply), or around 500 sheets (for double-ply). Each sheet is typically 4” long so the length of a (double-ply) toilet roll is approximately 2,000” or 167 feet (or less, if your cat gets to it).

In the interval scale, there is no true zero point or fixed beginning. They do not have a true zero even if one of the values carry the name “zero.” For example, in the temperature, there is no point where the temperature can be zero. Zero degrees F does not mean the complete absence of temperature. Since the interval scale has no true zero point, you cannot calculate Ratios. For example, there is no any sense the ratio of 90 to 30 degrees F to be the same as the ratio of 60 to 20 degrees. A temperature of 20 degrees is not twice as warm as one of 10 degrees.

As the interval scales, Ratio scales show us the order and the exact value between the units. However, in contrast with interval scales, Ratio ones have an absolute zero that allows us to perform a huge range of descriptive statistics and inferential statistics. The ratio scales possess a clear definition of zero. Any types of values that can be measured from absolute zero can be measured with a ratio scale. The most popular examples of ratio variables are height and weight. In addition, one individual can be twice as tall as another individual.

when AUC is 0.5, it means model has no class separation capacity whatsoever.

ROC is a probability curve and AUC represents degree or measure of separability. It tells how much model is capable of distinguishing between classes.

In multi-class model, we can plot N number of AUC ROC Curves for N number classes using One vs ALL methodology. So for Example, If you have three classes named X, Y and Z, you will have one ROC for X classified against Y and Z, another ROC for Y classified against X and Z, and a third one of Z classified against Y and X.

When AUC is approximately 0, model is actually reciprocating the classes. It means, model is predicting negative class as a positive class and vice versa

AUC near to the 1 which means it has good measure of separability.

Softmax turns arbitrary real values into probabilities

1. Logistic regression IS a binomial regression (with logit link), a special case of the Generalized Linear Model. It doesn't classify anything *unless a threshold for the probability is set*. Classification is just its application. 2. Stepwise regression is by no means a regression. It's a (flawed) method of variable selection. 3. OLS is a method of estimation (among others: GLS, TLS, (RE)ML, PQL, etc.), NOT a regression. 4. Ridge, LASSO - it's a method of regularization, NOT a regression. 5. There are tens of models for the regression analysis. You mention mainly linear and logistic - it's just the GLM! Learn the others too (link in a comment). STOP with the "17 types of regression every DS should know". BTW, there're 270+ statistical tests. Not just t, chi2 & Wilcoxon

An exploratory plot is all about you getting to know the data. An explanatory graphic, on the other hand, is about telling a story using that data to a specific audience.

(Återkommande forskning visar att 85-90 procent av tonårskillar begår brott. Allt från snatteri upp till rån och mord. Och det oavsett om de har invandrarbakgrund eller inte. Cirka 97-98 procent av de här killarna blir sedan skötsamma arbetande vuxna medborgare – som beklagar sig över ungdomsbrottsligheten.)

The average IQs of adopted children in lower and higher socioeconomic status (SES) families were 85 (SD = 17) and 98 (SD = 14.6), respectively, at adolescence (mean age = 13.5 years)

If you are running a regression model on data that do not have explicit space or time dimensions, then the standard test for autocorrelation would be the Durbin-Watson test.

For most of the twentieth century, Census Bureau administrators resisted private-sector intrusion into data capture and processing operations, but beginning in the mid-1990s, the Census Bureau increasingly turned to outside vendors from the private sector for data captureand processing. Thisprivatization led to rapidly escalating costs, reduced productivity, near catastrophic failures of the 2000 and 2010 censuses, and high risks for the 2020 census.

This booklet itells you how to use the R statistical software to carry out some simple analyses that are common in analysing time series data.

Top 20 topic categories.

Pages in category "Passengers"

On public transport ridership in the EU

In statistical testing, we structure experiments in terms of null & alternative hypotheses. Our test will have the following hypothesis schema: Η0: μtreatment <= μcontrol ΗA: μtreatment > μcontrol Our null hypothesis claims that the new shampoo does not increase wool quality. The alternative hypothesis claims the opposite; new shampoo yields superior wool quality.

Ministries will be involved in close monitoring and supervision of the field work to ensure data quality and good coverage. This is the first time that the rigours of monitoring and supervision of field work exercised in NSS will be leveraged for the Economic Census so that results of better quality would be available for creation of a National Statistical Business Register. This process has been catalysed by the establishment of a unified National Statistical Office (NSO).  

It’s as if they’d been “describing the life cycle of unicorns, what unicorns eat, all the different subspecies of unicorn, which cuts of unicorn meat are tastiest, and a blow-by-blow account of a wrestling match between unicorns and Bigfoot,” Alexander wrote.

Parametric statistics is a branch of statistics which assumes that sample data comes from a population that can be adequately modelled by a probability distribution that has a fixed set of parameters.[1] Conversely a non-parametric model differs precisely in that the parameter set (or feature set in machine learning) is not fixed and can increase, or even decrease, if new relevant information is collected.[2] Most well-known statistical methods are parametric.[3] Regarding nonparametric (and semiparametric) models, Sir David Cox has said, "These typically involve fewer assumptions of structure and distributional form but usually contain strong assumptions about independencies".[4]

Statistical hypotheses concern the behavior of observable random variables.... For example, the hypothesis (a) that a normal distribution has a specified mean and variance is statistical; so is the hypothesis (b) that it has a given mean but unspecified variance; so is the hypothesis (c) that a distribution is of normal form with both mean and variance unspecified; finally, so is the hypothesis (d) that two unspecified continuous distributions are identical. It will have been noticed that in the examples (a) and (b) the distribution underlying the observations was taken to be of a certain form (the normal) and the hypothesis was concerned entirely with the value of one or both of its parameters. Such a hypothesis, for obvious reasons, is called parametric. Hypothesis (c) was of a different nature, as no parameter values are specified in the statement of the hypothesis; we might reasonably call such a hypothesis non-parametric. Hypothesis (d) is also non-parametric but, in addition, it does not even specify the underlying form of the distribution and may now be reasonably termed distribution-free. Notwithstanding these distinctions, the statistical literature now commonly applies the label "non-parametric" to test procedures that we have just termed "distribution-free", thereby losing a useful classification.

Non-parametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars). The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences. In terms of levels of measurement, non-parametric methods result in ordinal data. As non-parametric methods make fewer assumptions, their applicability is much wider than the corresponding parametric methods. In particular, they may be applied in situations where less is known about the application in question. Also, due to the reliance on fewer assumptions, non-parametric methods are more robust. Another justification for the use of non-parametric methods is simplicity. In certain cases, even when the use of parametric methods is justified, non-parametric methods may be easier to use. Due both to this simplicity and to their greater robustness, non-parametric methods are seen by some statisticians as leaving less room for improper use and misunderstanding. The wider applicability and increased robustness of non-parametric tests comes at a cost: in cases where a parametric test would be appropriate, non-parametric tests have less power. In other words, a larger sample size can be required to draw conclusions with the same degree of confidence.

The concept of data type is similar to the concept of level of measurement, but more specific: For example, count data require a different distribution (e.g. a Poisson distribution or binomial distribution) than non-negative real-valued data require, but both fall under the same level of measurement (a ratio scale).

Even if Muslims were hypothetically behind every single one of the 140,000 terror attacks committed worldwide since 1970, those terrorists would represent barely 0.009 percent of global Islam

That is, deaths from terrorism account for 0.025 of the total number of murders, or 2.5%

American Muslims have killed less than 0.0002 percent of those murdered in the USA during this period

How many people did toddlers kill in 2013? Five, all by accidentally shooting a gun

you actually have a better chance of being killed by a refrigerator falling on you

Since 9/11, Muslim-American terrorism has claimed 37 lives in the United States, out of more than 190,000 murders during this period

pproximately 60 were carried out by Muslims. In other words, approximately 2.5% of all terrorist attacks on US soil between 1970 and 2012 were carried out by Muslims.

94 percent of the terror attacks were committed by non-Muslims

Muslim terrorists were responsible for a meagre 0.3 percent of EU terrorism during those years.

in 2013, there were 152 terrorist attacks in Europe. Only two of them were “religiously motivated”, while 84 were predicated on ethno-nationalist or separatist beliefs

in the 4 years between 2011 and 2014 there were 746 terrorist attacks in Europe. Of these, only eight were religiously-inspired, which is 1% of the total

official data from Europol

info-request

info-request

要保持谦逊：兼容性评估的前提是用于计算区间的统计假设是正确的

在给定假设的情况下，区间内数值与研究数据的兼容性并不完全相同

我们看到了大量具有“统计学显著性”的结果；而不具有“统计学显著性”的结果则被显著低估

在置信区间包含风险显著增高的情况下，仅因为结果不具有统计学显著性就推论药物与房颤发生“无关”十分可笑；据此就认为前后两项研究矛盾——即便风险比完全一致——同样非常荒谬。这些常见情况表明我们依赖的统计学显著性阈值有可能误导我们。

At The Economist, we take data visualisation seriously. Every week we publish around 40 charts across print, the website and our apps. With every single one, we try our best to visualise the numbers accurately and in a way that best supports the story. But sometimes we get it wrong. We can do better in future if we learn from our mistakes — and other people may be able to learn from them, too.

the strongest first factor accounted for 86.3% of observed variable variance

The weakest first factor accounted for 18.3% of variance

The Doomsday argument

Basic Statistics

Online Options Give Adults Access, but Outcomes Lag

Double-centering a matrix M

Relationship between ridge regression and PCA regression

Lack of metrics

LDLC workers and their needs

predictive analysis

Boxplots and Beyond – Part II: Asymmetry

Using the Median Absolute Deviation to Find Outliers

Power analysis and sample size estimation for RNA-Seq differential expression

Polyester: simulating RNA-seq datasets with differential transcript expression

Combining data from multiple RNASeq experiments: release the Kruskal! (...Wallis test)

Neural correlates of interspecies perspective taking in the post-mortem Atlantic Salmon: an argument for multiple comparisons correction

The natural selection of bad science

HarvardX Biomedical Data Science Open Online Training

pairwise overlaps using Fisher’s test and mutual exclusion (Leiserson et al., 2016xA weighted exact test for mutually exclusive mutations in cancer. Leiserson, M.D.M., Reyna, M.A., and Raphael, B.J. Bioinformatics. 2016; 32: i736–i745Crossref | PubMed | Scopus (4)See all ReferencesLeiserson et al., 2016)

Gene Set Enrichment Analysis Made Simple

An Introduction to Odds, Odds Ratios and Exponents

One of the main ways computers are changing the textual humanities is by mediating new connections to social science. The statistical models that help sociologists understand social stratification and social change haven’t in the past contributed much to the humanities, because it’s been difficult to connect quantitative models to the richer, looser sort of evidence provided by written documents.

s. If we want to understand the effects of global warming or whether the economy is headed for a recessio

The annual drop in Maine wood demand since 2014 would fill that imaginary 1,770-mile caravan. The loss equals about 350 fewer truckloads of wood a day, every day of the year.

The state has pumped more than 100 million pounds of low bush fruit into the frozen market each year for the last three growing cycles.

A typical acre of blueberry barrens will yield about 2,000 to 4,000 pounds of berries, depending on pollination and other factors.

I never regret the eleven months which hardened my resolve, to go beyond 98 'Nos' to get to the precious, unexpected 'Yes's'. I was nobody, I was selling nothing, I could be nobody selling anything.

That two dice marked in the common way will tum up seven, is thrice as probable as that they will tum up eleven, and six times as probable as that they will tum up twelve

In moral reasoning we ascend from pos-~ibility, by an insensible gradation, to probabil-ity, and thence, in the same manner, to the sum-mit of moral certainty.

The course of nature will be the same tomorrow that it is today; or, the future will resemble the past"

With figures like those, it's clear that the education system isn't going away anytime soon.

According to the language periodical Språktidningen, ‘hen’ was by 2014 used once in the Swedish media for every 300 used of ‘hon’ or ‘han’, up from one in every 13,000 in 2011

the algorithm was somewhat more accurate than a coin flip

3,068 adults in August 2014, found that 72 percent of Americans reported feeling stressed about money at least some of the time during the past month. Twenty-two percent said that they experienced extreme stress about money during the past month (an 8, 9 or 10 on a 10-point scale, where 1 is “little or no stress” and 10 is “a great deal of stress”). For the majority of Americans (64 percent), money is a somewhat or very significant source of stress, but especially for parents and younger adults (77 percent of parents, 75 percent of millennials [18 to 35 years old] and 76 percent of Gen Xers [36 to 49 years old]).

He expects that the logging project near Quimby’s land will likely generate about $755,250 at the state’s average sale price, $50.35 per cord of wood. The land has about 1,500 harvestable acres that contain about 30 cords of wood per acre, or 45,000 cords, but only about a third of that will be cut because the land is environmentally sensitive, Denico said. The Bureau of Parks and Lands expects to generate about $6.6 million in revenue this year selling about 130,000 cords of wood from its lots, Denico said. Last year, the bureau generated about $7 million harvesting about 139,000 cords of wood. The Legislature allows the cutting of about 160,000 cords of wood on state land annually, although the LePage administration has sought to increase that amount.

The science of the individual relies on dynamic systems theory rather than group statistics. Its research methodology is characterized by “analyze, then aggregate” (analyze each subject separately, then combine individual patterns into collective understanding) rather than “aggregate, then analyze” (derive group statistics based on aggregate data, then use these statistics to evaluate and understand individuals).

P(B|E) = P(B) X P(E|B) / P(E), with P standing for probability, B for belief and E for evidence. P(B) is the probability that B is true, and P(E) is the probability that E is true. P(B|E) means the probability of B if E is true, and P(E|B) is the probability of E if B is true.

The probability that a belief is true given new evidence equals the probability that the belief is true regardless of that evidence times the probability that the evidence is true given that the belief is true divided by the probability that the evidence is true regardless of whether the belief is true. Got that?

Initial belief plus new evidence = new and improved belief.

This criterion is not based on any specific shape of the dose-response relationship.