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

Filter by
Sorted by
Tagged with
0
votes
1answer
16 views

Measuring mutual dependencies between variables. The most fundamental relation

One has a simple dataset of 3 independent variables, e.g., x, y, z. Now: y and z are logically connected (this is known a priori) and indeed a nice & tight correlation (small scatter) between ...
0
votes
1answer
21 views

F-distribution likelihood interval, does it have to be symetric?

F-distribution : https://en.wikipedia.org/wiki/F-distribution I was told that the confidence interval for the ratio of variances (the $F$-function) is a symmetric interval for instance : $$ [ F_{1 -...
0
votes
1answer
28 views

Can I use chi square goodness of fit test to solve the following problem?

I got the following question for my statistics finals exam yesterday. As the average proportion of female in the three locations is 0.473 I made the following table. 1) How can I proceed from here? ...
0
votes
0answers
31 views

What is the basis for statistical inference?

I wrote in a document something similar to this: Based on the collected samples, we hope to infer ... I was asked to provide a citation for my claim. I guess I ...
3
votes
1answer
114 views

Does model $R^2$ affect the interpretation of its coefficients?

First question: is it possible for a multiple regression model to have "big" and significant coefficients but a low $R^2$ value? Let's say the value of $R^2$ is 0.0005 and my coefficient of interest ...
0
votes
1answer
20 views

Kernel density, why does my subset appear to have a larger spread than the original series?

I have a series that is 1500 observations long called alt_intercept. From it, I created a subset that contains values only if another series (called pvalue) is less ...
0
votes
1answer
33 views

why does y axis sometimes change from normal histogram to kernel density?

Consider the distributions I have plotted below. They are of the same variables, one in normal histogram form and another in kernel density (Epachanov). As far as I know, the auc of the kernel ...
0
votes
0answers
10 views

What is the suitable distance function for zero-inflated matrix?

I have a feature matrix, where the columns correspond to the features and the rows are the data points. My matrix is zero-inflated, meaning there are many false-negative zero entries in my matrix. I ...
0
votes
1answer
18 views

How to identify relationship between variables from scatterplots?

I want to understand the relationship between a region's health and wellness demographics (% obese, % smokers etc.) and their injury rates, for ex. how does change in a metric say '% obese people' ...
0
votes
0answers
18 views

References: CI interval for preimage of Poisson mean

Looking for references or where to look to be able to deal with the following. Suppose I have some count data $(X_i)_{i=1}^{z}$, such that each $X_i$ is independent and Poisson distributed with mean $...
0
votes
0answers
32 views

Best sampling method within the normal family

Suppose that we want to make the best Bayesian inference about some value $\mu$ we have some normal prior about it. I.e. $\mu\sim N(\mu_0, \sigma_0^2)$ with known parameters. To do so, we can choose ...
1
vote
1answer
30 views

Sufficient Statistic of Uniform $(-\theta,0)$

Let $X_1, ... , X_n$ be i.i.d random variables Uniform $(-\theta,0)$ , with $\theta > 0$ parameter \begin{align}f_{\theta}(x_1,x_2,\cdots,x_n)&=\prod_{i=1}^nf(x_i;\theta) \\&=\frac{1}{(\...
0
votes
1answer
22 views

Does random sampling from a dataset produce the same distribution as the original space?

Let's say we have a dataset $D$ with $N$ rows and $M$ columns. Each column is a feature. And for each feature $X_1, X_2,..., X_N $~ iid $F_p$ where $F_p$ is the distribution for feature p. Now let's ...
2
votes
0answers
29 views

Compute the parameters of a distribution from samples drawn from the tail of the distribution

I have a collection of N samples drawn from a population by the following process: Draw M samples from the population, where each sample is a non-negative real number Drop all but the N samples with ...
2
votes
1answer
59 views

Observed deterministic variables in MCMC

I need to model a measurement of an "exponential decay" i.e. I have a histogram of counts $Y$ over an array of (time-) intervalls. I want to use MCMC to infer parameters ($A_1,\lambda_1,A_2,\lambda_2,\...
1
vote
1answer
41 views

How to infer a missing observation in a state space model?

I read here that "structural time series models handle missing values naturally, following the rules of conditional probability. Posterior inference can be used to impute missing values, with ...
1
vote
1answer
38 views

Test vs control group - how to increase the accuracy of my estimate?

I would like to find out if there is a way to reduce the statistical noise from my estimate of incremental value added from a certain customer treatment. Assume we have a group of clients for which we ...
1
vote
0answers
20 views

Synthetic Control method: how to select V matrix?

I am learning Synthetic Control method and reading paper."Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program" We need to minimize ...
1
vote
1answer
21 views

Extracting useful metrics from price info

First, an admission: my stats knowledge is minimal - purely practical applications in a fairly narrow range. I'm mostly a mechanic with a good bit of experience building and wrenching on ML/DS systems ...
2
votes
2answers
50 views

Is it a valid to use one sample to estimate the population parameter and to decide whether another observation is in the population?

I have two groups of samples. Sample A is obtained from population A and sample B is a mixture of unknown origin i.e. some observations of sample B may come from population A and some may not. How can ...
0
votes
0answers
27 views

What exactly is the 'population' in samples of one time occurrences?

for example, let's say there is a policy that randomly allocated immigrants to every municipality of a country, and I am interested in the effect of increased immigrant population on voting outcomes. ...
0
votes
2answers
42 views

Which statistical test to use for binned data?

I researched for hours but cannot find the direction for the right test to use. I have a frequency distribution which shows bins on the x-axis that contain amount spent: 0-5\$ 6\$-10\$ greater than ...
0
votes
1answer
32 views

What exactly is a prior in MAP and how do we get it?

I've recently been studying MAP (Maximum a posteriori estimation). From what I've learned, the prior P(Θ) is an expected distribution of Θ, where Θ is a likelihood <...
0
votes
0answers
30 views

Why Mann-Whitney stat value is different in R and Python?

I'm calculating Mann-Whitney for a two-sided hypothesis and I'm getting different values for the statistic value: in R ...
0
votes
2answers
54 views

Central Limit Theorem - Significance of Sample Count

According to a Khan Academy's lecture, the Central Limit Theorem is defined as follows: Central limit theorem states that as the sample size increases, the sampling distribution of the sample mean ...
0
votes
1answer
43 views

How to bootstrap samples from data that has more than dependent variable?

I understand bootstrap sampling with replacement. But what i still not sure about is that how to apply this approach to sample from data that has more than one dependent variables. For example, ...
0
votes
0answers
15 views

A measure of confidence given data with known variation coefficient

I need to create a classification model to diagnose a certain illness, for that i have been given a dataset of 7 analytes (medical features) with known variation coefficients due to biological ...
0
votes
1answer
29 views

error estimate or confidence interval on a probability

Imagine I have $N$ 6-sided die, all identical but not fair, so that the probability of getting 1 is $P(1)$, the probability of getting 2 is $P(2)$ etc. I would like to run an experiment (rather than ...
0
votes
1answer
34 views

How can I normalize Bayesian Network query result?

While taking a Bayesian network tutorial on YouTube, I was watching a video explaining the Bayesian Network probability inference. Somehow, at the end of the tutorial, the lecturer did not explain how ...
0
votes
2answers
38 views

Why is degrees of freedom not considered while calculating standard deviations of samples in independent samples t-test?

In paired samples t-test, while calculating the standard deviation of differences, we take into consideration the degrees of freedom in the formula of calculating t by using n-1 instead of n for ...
1
vote
1answer
53 views

Inference using robust statistics

I'm simulating the overall usage of a cluster using historic deployment data. Due to the nature of the simulation, there are some heavy points (i.e. very low overall usage). As a result, the variance ...
0
votes
0answers
30 views

Debiased regularised regression (elastic net)

I have ~55,000 binary observations and 12 explanatory variables (EVs). I am looking to perform variable selection, followed by inference on the effect of the retained EVs on the binary outcome. Since ...
0
votes
1answer
565 views

If the VIF is 2 then what is the value of correlation coefficient $R^2$

If variance inflation factor is 2 what is the value of correlation coefficient $R^2$? $$VIF = \frac{1}{1-R^2}$$ Given $VIF =2$, then is this calculation correct? $$\begin{align} 2 &= \frac{1}{1-...
7
votes
2answers
539 views

Does the posterior necessarily follow the same conditional dependence structure as the prior?

One of the assumptions in a model is the conditional dependence between random variables in the joint prior distribution. Consider the following model, $$p(a,b|X) \propto p(X|a,b)p(a,b)$$ Now suppose ...
0
votes
0answers
13 views

Data distributions extrapolation

Is there a way to extrapolate (according to variance or other statistics) distributions from data? In other words, I have a gene expression matrix in which rows are genes while columns are samples (i....
1
vote
0answers
31 views

On estimators that do not converge to a constant

Say one had constructed an estimator $\hat{\mu}_n$ for a parameter $\mu$ and that such estimator had the property that $$ \hat{\mu}_n \xrightarrow {d} X $$ where $X$ is a random variable with an ...
1
vote
3answers
45 views

Does Normality Imply Randomness?

I have data indicating the number of counts per minute (so 60 rows in total - one for each minute - and # of events in that minute). I have ran the Shapiro - Wilk test which implies the data does not ...
0
votes
0answers
16 views

Bayesian estimation of weighted proportion

Having bayesian estimates of a proportion is relatively easy. You model that proportion as a binomial variable, you choose a beta-binomial prior and by using the likelihood you obtain a beta-binomial ...
2
votes
2answers
95 views

What is the meaning of × in statistics?

What is the meaning of the symbol × in an ANOVA context? More specifically what is the meaning of × in the following table? ...
0
votes
0answers
14 views

In the fully supervised case, provided we have contingency matrices, is Bayesian inference the optimal method?

BACKGROUND Imagine that we have contingency matrices, i.e., counts or frequencies, linking the features (say, columns) and targets (rows). One could then compute the posterior probabilities, i.e., ...
0
votes
0answers
14 views

Machine learning: is the effect of one predictor adjusted for the others?

In machine learning - notably ensemble methods such as random forest, gradient boosting, extreme gradient boosting etc - can we say that the effect obtained for one predictor is ADJUSTED for all other ...
0
votes
0answers
61 views

How can I get the 95% simultaneous confidence interval for four proportions?

300 male high school students are surveyed on their smoking frequencies, the results are following: Frequency (1)never smoke (2) 1-4/day (3) 5-10/day (4)more than 10/day Number of people ...
1
vote
1answer
45 views

Inferring random variables from their sum

Suppose I have a large set of receipts that list the items I bought, but only list the total cost. One day I might have bought Milk, Butter, and Eggs. A different day I might have bought Bread, Milk,...
3
votes
0answers
24 views

How to Use Chi-Squared Test for Inference about Three-way independence

If I recall correctly, three random variables X, Y, and Z are three-way independent iff these two statements are met: P(X∩Y∩Z) = P(X)P(Y)P(Z) X, Y, and Z are all pairwise independent of each other. ...
1
vote
1answer
25 views

Calculate risk between classes

I am doing some exercises about logistic regression with SAS and I need to calculate and interpret odds. For calculating the individual probabilities I use those formulas: While later, the Professor,...
0
votes
1answer
41 views

How time series structure can affect the independence of residuals condition for MLR?

I am going through all four conditions for Multiple Linear Regression and stick with this question: what happens with the independence if we have time series data structure?
1
vote
0answers
11 views

How to compare two statistical distributions with unavailability measurements?

I have two different measuring instruments to evaulate if an electronic device is working or not. These instruments provide a working/not-working reading each day and at the end of the month I compute ...
1
vote
1answer
37 views

Generalizing Bayesian methods by assuming a “distribution of distributions” instead of a prior

Bayesian methods assume a prior distribution with several hyperparameters. Unfortunately, this is asymptotically incorrect, because distributions in the real world are never exact. For example, the ...
0
votes
0answers
16 views

Testing equality of difference in coefficients from four regressions

This question is a follow-up/extension to this post. Suppose I have four regressions. $y_i=x_i\beta_i+\epsilon_i,\quad i=1,2,3,4$ I want to test whether $(\beta_1-\beta_2)-(\beta_3-\beta_4)>0$....
11
votes
2answers
174 views

Why aren't “error in X” models more widely used?

When we calculate the standard error of a regression coefficient, we do not account for the randomness in the design matrix $X$. In OLS for instance, we calculate $\text{var}(\hat{\beta})$ as $\text{...