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15h
comment When is beta distribution bell-shaped?
@gung The black line is not concave (nor is a Gaussian density) though it might be seen as bell-shaped
Aug
3
comment Name for the Bayesian posterior probability that a regression coefficient is larger than zero
@Cam.Davidson.Pilon: I think the posterior probability the coefficient is greater than 0 is... is a better choice than anything to do with p-values
Jul
25
comment Creating a cluster analysis on multiple variables
Then you do not want to use a Euclidean metric on unscaled variables
Jul
8
comment How to treat x=0, y=0 in a linear model with no intercept?
@tiantianchen: If you assume there is no intercept then the $(0,0)$ values should give you no information about estimating $\beta$ or the uncertainty in any estimate of $\beta$ since your estimate of $\beta$ is presumably $\dfrac{\sum x_i y_i}{\sum x_i^2}$. The $(0,0)$ values do not fit your $y_i=\beta x_i + \epsilon_i$ model since they all have $\epsilon_i=0$, and so they be ignored in calculating the uncertainty in $\beta$.
Jul
7
comment How to treat x=0, y=0 in a linear model with no intercept?
As soon as you said "establish a linear relationship without intercept" you implicitly said something like "observation of values of $(0,0)$ support the assumption of no intercept, but will take no further part in estimation of the model".
Jul
3
comment History: the role of statistics in astronomy
Laplace used inverse (i.e. Bayesian) probability to give margins of error on the mass of Saturn. The Le Verrier/Adams projections which led to the discovery of Neptune were effective a form of regression.
Jul
2
comment Example of how the log-sum-exp trick works in Naive Bayes
The problem is more likely to be underflow than overflow.
Jun
28
comment Model Tuning and Model Evaluation in Machine Learning
I see cross-validation as sometimes using the same data for training and sometimes using it for validation and error estimation. The price you pay for this use of the same data for training and validation is potential overfitting and so less credibility for the out-of-model error estimate, which it why it may be worth holding out a test set completely from the entire training process.
Jun
22
comment Non-central scaled Student's t cumulative density function required (alternatively the pdf)
That is no different to the standard deviation of a non-scaled $t$-distribution as usually used, which is $\sqrt{\frac{\nu}{\nu-2}}$, at least when $\nu \gt 2$. So $\sigma$ is the scaling parameter but not the standard deviation.
Jun
11
comment Estimating the distribution from data
@Scott Kaiser: I do not think so. fitdist() is a function in the fitdistrplus package, and this is what I was using. Meanwhile fitdistr() is a function in the MASS package, and would not work here in this form.
Jun
10
comment Given the moment generating function of $X$, find the distribution of $X$
@Stéphane: I am making a slightly different point: the convergence of my example to a single value is (thanks to the strong law of large numbers) almost sure, but not sure, and other possible values of the limit of the mean (which together have probability $0$ but are not impossible) make up a continuous and uncountable set; in addition there are cases (again with combined probability $0$) where there is no convergence of the mean.
Jun
10
comment Given the moment generating function of $X$, find the distribution of $X$
@whuber: Would you say, with $X_i$ i.i.d normally distributed, that $Y=\displaystyle \lim_{n \to \infty} \frac1n \sum_{i=1}^n X_i$ was "a discrete random variable". I do not think I would, though I would say it was "almost surely $E[X_i]$".
Jun
10
comment Given the moment generating function of $X$, find the distribution of $X$
$X$ is $2$ with probability $1$. You cannot tell from the moment generating function whether it can surely only take the value $2$, or almost surely; if the latter then you cannot tell whether it is a continuous random variable or a discrete random variable
Jun
9
comment Log and natural log
That is at least two questions. For (1): $\ln(x) \approx 2.302585\times \log_{10}(x)$ so the only impact should be that of a scaling factor
Jun
4
comment Is there any MOOCS on statistical analysis of Applied behavioral economics?
@Dimitriy: I would have thought applied behavioural economics was more like A/B testing combined with some psychological rationalisation of the results
Jun
4
comment Is there any MOOCS on statistical analysis of Applied behavioral economics?
@Andy: MOOC is Massive Open Online Course such as Coursera and edX
May
13
comment What does “likelihood is only defined up to a multiplicative constant of proportionality” mean in practice?
So do $f(x)$ and $f(x)+2$ but they would not be equivalent likelihood functions
May
11
comment How to estimate unknown parameter via maximum likelihood?
Given $\theta$, what is the probability of seeing $x$ out of $n$ heads? So what is the likelihood function for $\theta$ given $x$ out of $n$ heads? How would you find a $\theta$ which maximises this likelihood?
Apr
26
comment If $Z_i =\min \{k_i, X_i\}$, $X_i \sim U[a_i, b_i]$, what is the distribution of $\sum_iZ_i$?
If for example the $a_i$ and $b_i$ were fixed, then you would have independent identically distributed random variables with a finite variance, so the central limit theorem would apply. Whether this is a mixture distribution or not does not affect this result. What I am saying is that you can extend this to cases where the random variables are independent but not identically distributed, provided that the means and variances stay reasonable.
Apr
18
comment Regresssion of Accurate Data
Is there a non-linearity issue here? If your measurements are accurate but the device produces non-linear effects then linear regression will certainly make inaccurate predictions.