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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7 views

Interpreting predictive models in the presence of omitted variables

Suppose the best predictive model from a set of possible models is a univariable model, due to lots of moderate correlations with other variables for example. However, if I use this model for ...
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I was doing this course ' Bayesian Methods for machine learning' on coursera and I got stuck on few conditional statements expansion and manipulation

I have doubt in three conditional expansions : How is P(w,y|x) = P(y|w,x).P(w) ? How is P(w|y,x) = P(y,w|x)/P(y|x) ? How is <...
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How to perform joint inference on multivariate normal variables?

Suppose I have the following model: $$\begin{aligned} \text C &\sim \mathcal N \left(\mu, \delta^2\right) \\ \forall i: \text L_i | \text C = c &\sim \mathcal N \left(c, \lambda_i^2 \right) \\...
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Expectation of exponential family distributions

Is there a closed form of the following marginal (one dimensional data) $\pi(\theta|y) = \mathbb{E}_{x \sim \pi_R(x|y)} \pi(\theta|x)$, where both $\pi, \pi_R$ are exponential family distributions?
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Statistics help! Reporting ANOVA results!

I am new to statistics and I need some help in understanding how to report the data of some tests I am running on R, I hope this is the right place! I have a dataset: ...
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Treating missing data in making Bayesian inference

Suppose we have two biased coins $X_1,X_2$ that are possibly correlated to each other. In each round, when both the coins are tossed, there can be four possible outcomes: $(HH,HT,TH,TT).$ Let's ...
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A problem on finding UMP test [on hold]

The problem is from the book "Testing of Statistical Hypotheses", by Lehmann (3.10.3) Let $X_i(i=1,2,3,....,n)$ be a random sample from a distribution with exponential density $f_{\theta}(x)=ae^{-a(...
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Time series explaining the trend

I'm very new to time series analysis and I've been tasked with trying to make sense of some data and was hoping you smart folks out there could provide some guidance. I have some data relating to ...
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Relationship between mean and variance of samples

I am thinking about the relationship between sample mean and variance in an example. If we want to look at the average goals per month for a soccer team. And we have mean and variance of goals for ...
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1answer
53 views

Bayesian inference about means, observing only the sum of two random variables

I have: $X \sim \mathcal{N}(\mu_x, \sigma_x^2)$ and $Y \sim \mathcal{N}(\mu_y, \sigma_y^2)$. $X$ and $Y$ are independent. $\mu_x$ and $\mu_y$ are not known and I want to learn about them (Bayesian ...
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If a distribution’s scale parameter cannot equal 1, is it part of a scale family?

In general if $f$ is a scale family we have that if $X\sim f(x\mid\lambda)$ then $\frac{X}{\lambda}\sim f(x\mid 1)$. However what if $f$ has the constraint that its scale parameter $\lambda \in (1, \...
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Help with Old exam questions on Bayesian Inference Problem [closed]

I've been trying to teach myself bayesian inference and I found a question sheet online ---> https://math.mit.edu/~dav/05.dir/ps6.pdf. I was attempting to solve question 4 but I'm not sure the method ...
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Is bootstrapping appropriate for this scenario?

There are 2 binary classification models (Denoted modelA and modelB) that we built with different approaches, both of which are expected to output the probability of possitive outcome. There's a ...
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Motivations for experiment design in statistical learning?

My interests in statistics centre around statistical learning, including Bayesian inference, inference in combinatorial spaces, Monte Carlo methods, Markov decision processes, modeling stochastic ...
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fit a model to data

I want to fit a model to a data set, however each point is actually a distribution (i.e. I have the samples for each distribution). In an ideal world, I would assume that the distributions are ...
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inferential approach for estimating error rate on classified population

I am looking mainly for ideas and approaches which I could not find by just Googling. I created a classification model to predict about 175 unique classes from text features. I trained the model on ...
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Any research on learning Bayesian network structure with a limit on the parent set size?

Learning a maximum-scored Bayesian network structure with bounded treewidth is rather popular in recent years, as stated in the paper A survey on Bayesian network structure learning from data in 2019. ...
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Bayesian Hypothesis Tests with continuous priors

I am new to the Bayesian world, and I'm trying to understand how hypotheses tests are performed here (as opposed to the frequentist framework). I am aware that likelihoods, priors and posteriors can ...
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3answers
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Bayesian Inference: Feeding Posterior back in as Prior

I've just started reading about Bayesian Inference, and one thing I've wondered about is if it's possible to feed the posterior in as a new prior for a new model, using the same data. Or would that ...
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Why is a frequentist confidence interval equivalent to a credible interval with flat priors?

It's a commonly quoted result that frequentist confidence intervals are equivalent to a bayesian credible interval assuming a flat prior. Ignoring for now questions about invariance under ...
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1answer
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Statistical test to check whether an item meets the specification

I have a data on emission of an automobile which a company manufactures. The emission test was conducted on roads near towns and villages and the data is as follows. According to a new rule passed ...
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Possible methods for parameter estimation of a compound Poisson

Let $X_i$ be iid and each $X_i$ takes one value among $(0,1,-1)$ with probs $(p_1,p_2,1-p_1-p_2)$ respectively. Let $N$ be a Poisson RV with mean $\lambda$, and $$Z=\sum_{i=0}^N X_i$$ be a compound ...
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Should I use a machine learning model to calculate propensity score?

In my study, running a simple linear model to calculate de propensity score for each example seemed to not be able to model my treatment choosing process correctly. My question is, does it make sense ...
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How can I model this?

I have a question about whether I can model in a way that solves this problem: Suppose a swimming coach has 100 athletes and only cares about the distance they can each swim in 5 minutes. From this, ...
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1answer
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Comparing 3 means from 1 sample

I'm trying to compare mean interest levels of 3 products. The same sample was asked about each of the three products. How can I test for equal means among the three products? Other information: ...
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1answer
40 views

Bayesian inference for a conditional probability

I'm simplifying my research question and want to know whether the question can be properly modeled or not. Suppose we have two coins $X_1,X_2$ and assume that the outcomes are possibly correlated. ...
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Robust Expectation-Maximization?

The Expectation-Maximization (EM) algorithm is useful for applying the Maximum Likelihood Estimation (MLE) when there exist latent (hidden) variables in the model. However, when dealing with outliers, ...
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addressing the effect of the independent variable on the dependent variable for 2 different types of individuals

I am estimating the effect of a continous treatment X (that goes from 0 to 1) on a dependent variable y (data is taken through an experiment). I have around 250 Individuals in my dataset that can be ...
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1answer
28 views

After term not significant difference-in-differences

I ran a difference-in-differences model and I have an interpretation issue. My difference between treated and control is not significant before and after. In the same time, my interaction term is ...
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How to detect calendar effects for stock prices (day-of-week, month, etc.)

This is a python/pandas question just as much as it is a statistical one. How would I go about determining the typical delta for day-of-week and month effects of a given time series? Taking the day-...
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1answer
85 views

Bayesian online changepoint detection (modeling assumptions in recursive derivation)

I am reading Bayesian Online Changepoint Detection (https://arxiv.org/pdf/0710.3742.pdf), and I do not understand one step in the derivation of Equation $3$. For completeness, this is my derivation: $...
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35 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 ...
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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 ...
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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: ...
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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 $f(x-\theta)=uniform(\theta-.5,\theta+.5)$.
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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 ...
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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 $R^2$? ...
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2answers
35 views

Estimating population mean $\mu$ based on a sampling distribution

I've learned that under certain codnitions I can assume the mean of the distribution of sample means to be approx. equal to the real mean of the underlying population. Additionaly, the standard ...
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1answer
44 views

Distribution Bounded

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 $E[X^2]= Var[X] + E[X]^2$
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Causal Inference in Mortality Rates

I was wondering how does one study the average treatment affect in scenarios suchs as mortality rates. For example: suppose we want to study the effect that a certain medicine has on the mortality ...
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How to generate more samples from a dataset

My question is simple: I have a dataset with multiple numerical features (let's say 1500 data points with 7 features). The question is the following: ...
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Inference on Error Covariance Matrix in SUR/GLS?

Suppose I have panel data $\{y_{it},X_{it}\}_{i=1...N,t=1...T}$ and the following linear (seemingly unrelated regression) model: $y_{it} = \beta_i X_{it} + u_{it}$ where the errors are correlated ...
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1answer
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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 ...
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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 -...
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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? ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...