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Questions tagged [inference]

Drawing conclusions about population parameters from sample data. See https://en.wikipedia.org/wiki/Inference and https://en.wikipedia.org/wiki/Statistical_inference

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Verifying whether $X$ is a complete statistic

The pmf of $X$ is as follows: $X = -1 \rightarrow p(x)= \theta$ $X = 0 \rightarrow p(x)= \theta^2$ $X = 1 \rightarrow p(x)= 1-\theta-\theta^2$ I know that to show whether $X$ is complete it is ...
311 views

Does order of events matter in Bayesian update?

I'm wondering whether the order of events can lead to different Bayesian update. For example, consider a coin-tossing problem with unknown $p$, the probability of Head. Initially, $p$ is known to ...
30 views

How to exclude events with low data (eg. threshold, outliers)

I have this data set and I want to filter only "Event" with a good conversion rate. We can say that good are those that have a higher than average conversion (but maybe you have better ideas). ...
17 views

How do I find the expected values and covariance matrix of the order statistics of iid random variables sampled from the standard normal distribution?

Recently I was trying to learn more about Normality tests and came to know about Shapiro-Wilk test for Normality. I understood most part of it but one thing I didn't understand is that how do I find ...
14 views

How to convert cohen's h to a percent difference in groups in R?

I'm trying to calculate the minimum detectable effect in an experiment after n samples. I'm able to use the pwr package like this to compute the minimum ...
39 views

Rate of convergence of gradient descent inference in likelihood maximization

I am reading this classic paper on convergence properties of EM for Gaussian Mixture Models. In section 5, the authors compare EM with a gradient based inference approach. The gradient approach ...
84 views

Bayesian update for Beta distribution

I'm wondering how to find a posterior of a beta distribution when the "new information" is not an outcome of a binomial trial. Let $p$ be the probability of Head of a (biased) coin toss. As usual in ...
20 views

Hypothesis test for the difference of two means, should I consider annualized or monthly returns?

I have 10 years monthly returns. I calculated annualized return multiplying the mean return over the period for 12. Then I calculated the excess returns as difference between the annualized mean ...
17 views

Using hold-out method for validation set: How to choose a DL model with model selection?

After >170 deep learning experiments were I did a (almost) full factorial design with >15 factors. I cannot measure performance with cross validation because that would require to much training of ...
34 views

Conducting “inference” on Titanic data set (and other non-random/“population-encompassing” data sets alike)

Presume I'm given a data set like Titanic, where the data on all the passengers is available (hence "population-encompassing" in the title). Then, by inertia, I proceed to conduct statistical ...
30 views

Recommended textbooks for student majoring in applied statistics [duplicate]

I am currently a second year science student double majoring in biochemistry and applied statistics. The stats course im doing this semester (Statistical Theory) is focused on joint probability ...
216 views

37 views

Who invented train/validation/Test method and when?

I can't seem to find here or in other places the earliest source for this method. it seems the holdout method was separately proposed by Highleyman in 1962, and cross validation was separately ...
17 views

Which group of dieters in this study had the lowest all-cause mortality rate? can this be determined without a t-test?

I'm having trouble determining whether between the vegan and pescatarian group which had the lowest all-cause mortality rate given the results from the study and whether this inference can be made ...
27 views

Ways to extract patterns yielding high scores

Suppose I have a table, containing several features and a score denoting the performance (higher is better) of the corresponding features. Like this: ...
28 views

Incorrect bounds in solution to question on pitman estimator in Casella and Berger problem 7.35 [closed]

For Casella and Berger problem 7.35, the solution is shown. For part (c), are the bounds in the integral incorrect, or am I missing something? Here $f(x-\theta)=uniform(\theta-.5,\theta+.5)$.
44 views

Validating uncertainty quantification

Regression performance is often evaluated by means of cross-validation. However, classical cross-validation only regards the mean of the identified parameters. How can one quantify the quality of the ...
30 views

Interpretation of adjusted $R^2$ in causal inference [duplicate]

If one is only interested in the causal effect of a feature on the outcome $Y \sim F + C$ (here $F$ is the treatment and $C$ the control variables), what is the interpretation of adjusted $R^2$? ...
Estimating population mean $\mu$ based on a sampling distribution
Suppose Random variable $X$ ~ Bernoulli $( p )$ . How can we prove that $E[(X-p)^4]$ $\leq$ $p^4 + ( 1- p)^4$. ? I know that $E[(X-p)^2]$ = $Var[X]$ and $E[X^2]= Var[X] + E[X]^2$