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1500 questions
106
votes
2 answers
Solving for regression parameters in closed-form vs gradient descent
In Andrew Ng's machine learning course, he introduces linear regression and logistic regression, and shows how to fit the model parameters using gradient descent and Newton's method.
I know gradient descent can be useful in some applications of…
Jeff
- 3,927
106
votes
5 answers
Convergence in probability vs. almost sure convergence
I've never really grokked the difference between these two measures of convergence. (Or, in fact, any of the different types of convergence, but I mention these two in particular because of the Weak and Strong Laws of Large Numbers.)
Sure, I can…
raegtin
- 9,930
106
votes
33 answers
Is there a way to remember the definitions of Type I and Type II Errors?
I'm not a statistician by education, I'm a software engineer. Yet statistics comes up a lot. In fact, questions specifically about Type I and Type II error are coming up a lot in the course of my studying for the Certified Software Development…
Thomas Owens
- 1,101
106
votes
2 answers
How scared should we be about convergence warnings in lme4
If we a re fitting a glmer we may get a warning that tells us the model is finding a hard time to converge...e.g.
>Warning message:
In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model failed to converge with max|grad| =…
user1322296
- 1,615
105
votes
12 answers
What, precisely, is a confidence interval?
I know roughly and informally what a confidence interval is. However, I can't seem to wrap my head around one rather important detail: According to Wikipedia:
A confidence interval does not predict that the true value of the parameter has a…
dsimcha
- 8,739
105
votes
17 answers
Under what conditions does correlation imply causation?
We all know the mantra "correlation does not imply causation" which is drummed into all first year statistics students. There are some nice examples here to illustrate the idea.
But sometimes correlation does imply causation. The following example…
Rob Hyndman
- 56,782
105
votes
13 answers
What is the best way to identify outliers in multivariate data?
Suppose I have a large set of multivariate data with at least three variables. How can I find the outliers? Pairwise scatterplots won't work as it is possible for an outlier to exist in 3 dimensions that is not an outlier in any of the 2 dimensional…
Rob Hyndman
- 56,782
105
votes
4 answers
What is an "uninformative prior"? Can we ever have one with truly no information?
Inspired by a comment from this question:
What do we consider "uninformative" in a prior - and what information is still contained in a supposedly uninformative prior?
I generally see the prior in an analysis where it's either a frequentist-type…
Fomite
- 23,134
104
votes
5 answers
What is the reason that a likelihood function is not a pdf?
What is the reason that a likelihood function is not a pdf (probability density function)?
John Doe
- 1,556
- 3
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104
votes
10 answers
What is a complete list of the usual assumptions for linear regression?
What are the usual assumptions for linear regression?
Do they include:
a linear relationship between the independent and dependent variable
independent errors
normal distribution of errors
homoscedasticity
Are there any others?
tony
- 1,049
104
votes
9 answers
Is this really how p-values work? Can a million research papers per year be based on pure randomness?
I'm very new to statistics, and I'm just learning to understand the basics, including $p$-values. But there is a huge question mark in my mind right now, and I kind of hope my understanding is wrong. Here's my thought process:
Aren't all researches…
n_mu_sigma
- 1,101
104
votes
7 answers
Calculating the parameters of a Beta distribution using the mean and variance
How can I calculate the $\alpha$ and $\beta$ parameters for a Beta distribution if I know the mean and variance that I want the distribution to have? Examples of an R command to do this would be most helpful.
Dave Kincaid
- 1,678
103
votes
25 answers
Locating freely available data samples
I've been working on a new method for analyzing and parsing datasets to identify and isolate subgroups of a population without foreknowledge of any subgroup's characteristics. While the method works well enough with artificial data samples (i.e.…
EAMann
- 163
103
votes
1 answer
Interpreting plot.lm()
I had a question about interpreting the graphs generated by plot(lm) in R. I was wondering if you guys could tell me how to interpret the scale-location and leverage-residual plots? Any comments would be appreciated. Assume basic knowledge of…
Guest
- 1,031
103
votes
5 answers
Why is ANOVA taught / used as if it is a different research methodology compared to linear regression?
ANOVA is equivalent to linear regression with the use of suitable dummy variables. The conclusions remain the same irrespective of whether you use ANOVA or linear regression.
In light of their equivalence, is there any reason why ANOVA is used…
user28