Episode #125 of the Stack Overflow podcast is here. We talk Tilde Club and mechanical keyboards. Listen now

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
57 views

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 ...
4
votes
3answers
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 ...
0
votes
1answer
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). ...
1
vote
0answers
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 ...
0
votes
0answers
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 ...
2
votes
1answer
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 ...
2
votes
2answers
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 ...
0
votes
1answer
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 ...
0
votes
0answers
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 ...
4
votes
1answer
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 ...
0
votes
0answers
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 ...
2
votes
1answer
216 views

Understanding how the determinant of the multidimensional normal likelihood can overrule the prior probability

I am doing Bayesian inference. I have a normal prior probability distribution of some theoretical parameter $\theta$ and I am trying to update my knowledge of $\theta$ using some data $D$ and a model $...
1
vote
1answer
24 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 ...
0
votes
1answer
29 views

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 <...
1
vote
1answer
52 views

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) \\...
0
votes
0answers
36 views

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?
1
vote
1answer
44 views

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: ...
1
vote
1answer
67 views

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 ...
1
vote
1answer
45 views

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 ...
0
votes
2answers
58 views

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 ...
3
votes
1answer
58 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 ...
0
votes
1answer
37 views

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, \...
2
votes
0answers
28 views

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 ...
2
votes
0answers
33 views

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 ...
4
votes
1answer
46 views

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 ...
0
votes
0answers
30 views

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 ...
0
votes
0answers
11 views

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 ...
1
vote
0answers
18 views

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. ...
0
votes
4answers
109 views

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 ...
1
vote
3answers
72 views

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 ...
1
vote
0answers
34 views

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 ...
0
votes
1answer
18 views

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 ...
2
votes
2answers
109 views

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 ...
3
votes
1answer
105 views

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 ...
0
votes
0answers
26 views

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, ...
0
votes
1answer
19 views

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: ...
0
votes
1answer
51 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. ...
0
votes
0answers
17 views

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, ...
1
vote
2answers
46 views

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 ...
1
vote
1answer
30 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 ...
1
vote
0answers
18 views

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-...
3
votes
1answer
94 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: $...
3
votes
0answers
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 ...
0
votes
1answer
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 ...
3
votes
1answer
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: ...
1
vote
0answers
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 $f(x-\theta)=uniform(\theta-.5,\theta+.5)$.
2
votes
1answer
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 ...
0
votes
0answers
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 $R^2$? ...
1
vote
2answers
37 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 ...
1
vote
1answer
50 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 $E[X^2]= Var[X] + E[X]^2$