Questions tagged [bias]
The difference between the expected value of a parameter estimator & the true value of the parameter. Do NOT use this tag to refer to the [bias-term] / [bias-node] (ie the [intercept]).
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Expectile loss to reduce dependent variables overestimation
Say I have a a bunch of covariates $X$, and a dependent variable $y$, where $y$ is collected from people. However, I know from psychology that people will tend to overestimate $y$ given $X$ in some ...
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Is this a correct explanation of the asymptotic bias of maximum likelihood?
I want to be sure I understand, so please critique the following:
In regular parametric statistical models, the non-linear maximum likelihood estimator is biased. Given some data, $y_i$, parameters, $...
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Data taken from survey where survey-takers self report a continous variable
I have a problem with some health data that I'm trying to analyze. The main issue originates from a census variable is derived from self reported times. The variable is sleep duration, which is ...
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Why is the asymptotic bias of the maximum likelihood estimate $b(\theta) = \frac{b_1(\theta)}{n}+\frac{b_2(\theta)}{n^2}+...$?
Firth (1993) states in his introduction that for a $p$-dimensional parameter $\theta$ the asymptotic bias of the maximum likelihood estimate $\hat{\theta}$ may be written as:
$b(\theta) = \frac{b_1(\...
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Statistical analysis to interpret beta effect size for two different elastic net model
I have two elastic net model and I want to compare their coefficient to say if they have any significant beta effect changes across these two models.
I thought of using Anova but realized since we don'...
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Best way to address selection bias when outcome cannot be randomized
I have an (low incidence) binary outcome compared between 2 groups. The intervention for group 1 is coming from a specific type of center (academic) while group 2 from a different center. It is not ...
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Test for Look-ahead bias in Time Series Forecasting
I have a general question regarding testing for look-ahead bias. Is there any technical test for look-ahead bias in training data? Especially in the context of time series forecasting e.g. predicting ...
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Notable changes when modeling unevenly univariate spaced time series as an evenly spaced multivariate time series?
When attempting to model univariate data (although, this could easily be extended to the multivariate case) that is unevenly spaced over time, a natural approach to be able to apply common time series ...
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Difference between consistent and unbiased estimator [duplicate]
I have a problem where I have to think of an example to explain a practical example of consistency and unbiased. The example I thought of is the sample mean.
Consistency is when the estimator (sample ...
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Proof of attenuation bias in multiple linear regression model
Consider the case of measurement error with a single explanatory variable measured with error
\begin{equation}
y=\beta_0 + \beta_1 x_1 + \beta_2 x_2 + ... + \beta_k x^{\ast}_k + \nu
\label{...
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Is it possible to use poststratification when some observations have missing values on the variables used as strata?
This is a theoretical question, so I don't have data to share.
Let's say I know the percentage of men and women in my population of interest, as well as the distribution of occupations and age ...
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Providing biased data to analyst -- how could they use information about the bias? [closed]
I'm working on a project that provides an anonymized dataset to a service. Clients of this service will often use our data to make inferences to the population it's drawn from.
Our data is known to be ...
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Regress y on residuals of x and z [closed]
I have the following set up:
$y_i = \beta_0 + \beta_1 x_i + \beta_2 z_i + e_i$, where $e_i$ is extracted from a Normal (0,1) distribution independently of $x$ and $z$. The true values are $\beta_0 = \...
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Determine direction of bias with measurement error
We want to estimate the following population model:
$$y_i=\beta x_i+\epsilon_i$$
with $E[y_i]=E[x_i]=$ and $E[x_i\epsilon_i]=0$. We cannot observe $x_i$ directly, but we observe two variables $x_i^a$ ...
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Bias in survival analysis: nice summary of all the different types and remedies
I am quite new to the field of survival analysis and am getting lost and confused with all the different types of bias that can occur, particularly in observational studies. For example, it appears ...
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Is there any bias introduced by evaluating a model and decisions based on this model on the same data set?
As an example, let's say we have some financial time series such as closing prices of some stock and we would like to evaluate the ability of different models to forecast future closing prices as well ...
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Variable selection with a theoretical DAG vs algorithmically discovered DAG
I'm analysing data from an electronic health record and determining what variables to include in a model to close back doors and omit bias.
I've read that it is important to have a subject specific ...
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What type of bias is this?
I have a longitudinal cohort study, with individuals that diagnosed with Disease A at "start", and they all developed Complication B at "end" in my study period (my study period ...
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How to compare two multivariate distribution (of distances) to zero in terms of mean and variance in R?
We have N 3D coordinates estimated with two methods and want to compare them with a reference set of N 3D coordinates which is the ground truth, so in notations:
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mlogit + logitr packages fail to recover true estimates of mixed logit random coefficient model
I am running Monte-Carlo simulations on a simple DGP of a mixed logit random coefficient model to check if the mlogit and logitr ...
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Tossing Until First Heads Outcome, and Repeating, as a Method for Estimating Probability of Heads
Consider the problem of estimating the heads probability $p$ of a coin
by tossing it until the first heads outcome is observed. Say we get $k_1$
tosses, then $U_1 = \frac{1}{k_1}$ is an estimate for $...
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Censoring and then re-entering subjects
I am following a group of woman during the study period and performing the analysis using Cox model, comparing non-users against users of the investigated medicine. However, to remove the impact of ...
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Analysis of the bias resulting from PCA [closed]
Suppose that we generate some dataset from $y = X \beta + \epsilon,$ where $\epsilon$ is some independent error, and the rows of $X$ come from some distribution (unspecified for now). Suppose you run ...
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Bias and Variance of a Honest Random Forest
I am trying to read the paper Estimation and Inference of Heterogeneous Treatment
Effects using Random Forests. In the section 3.1(Theoretical Background), page 13 paragraph 2, The authors have ...
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Are missing variables an important factor when considering instrumental variable analysis?
I'm currently reading some papers that deal with the effects of education on health (smoking and obesity). Mostly they use an IV approach (college availability).
However in several analysis, only a ...
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Proof of the bias-variance decomposition in Bishop's book
I am trying to rewrite the demonstration given in Bishop's book: Pattern Recognition and
Machine Learning (2009)
I reproduce the figure (page 149) in which I am unclear about the step leading from (3....
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How to improve sample representativeness for longitudinal data collected via an online platform?
I am working with a longitudinal dataset exploring cognitive ageing (e.g., memory performance over time). Participants complete the study annually. Inclusion criteria for this study are 1) UK resident,...
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Question about Analogy to Statistics
If anyone could help me verify if my analogy is correct, thanks so much!
Here is an analogy:
A population is like a pot of soup.
We stir the pot of soup with the ladle because naturally the contents ...
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Can I use Shapley values with metadata (i.e. information about observations that I didn't train my model on)?
I'm training a set of models (random forest/XGBoost) for an ordinal regression task. I'm (tentatively) planning to use Shapley values to infer feature performance.
I also have some metadata that my ...
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How to determine whether a sample from a known population is significantly biased?
I have a large dataset (the population) and a large subset of it (the sample) containing the same, continuous variables. The sample represents more than 90% of the population but is not random -- we ...
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Conceptually, what is the bias of the standard error of an estimator?
I'm reading Muthén and Muthén (2002) to learn how to use Monte Carlo simulation to estimate statistical power in regards to the coefficients of a model that is linear in its coefficients.
I understand ...
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How normalizing data cause not problem in prediction?
In algorithms that perform better with data normalization or deep learning problems such as classification, how normalizing data does not bias our algorithm? I mean, in training or even testing, we ...
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How to avoid bias/avoid overfitting when choosing a machine learning model? [closed]
My typical workflow in the past, when creating machine learning models, has been to do the following:
Decide on some candidate model families for the task at hand.
Divide dataset into train and test ...
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Addressing Patient Clustering in Tumor Gene Expression?
I have RNAseq data from various tumors, many of which were extracted from the same patients. These tumors are classified with categorical values, and my objective is to compare gene expression across ...
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Correction of labelling bias using the labeler identity as a feature
Suppose I have a dataset labeled by multiple analysts.
I assume that each analyst has some bias in his labeling.
Is there any literature on reducing the bias effect on the general model by using the ...
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How to set threshold for bias in machine learning?
I have a large dataset containing the fitting results which contains ~10k observations. The dataset includes ~10k predicted values and actual values for different datasets, and we define $bias_i = ...
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How to calculate the optimal weights and bias in SVM (by hand)
I've been trying to solve the following exercise:
-> Consider a dataset with two points in 1D: (x1 = 0, y1 = −1) and (x2 = √2, y2 = 1).
Consider also the mapping to 3D φ(x) = [1, √2x, x2].
a) Find ...
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Can selection bias lead to confounding bias?
I wonder if case-control matching will bring a new confounding bias into the matched design. In the following figure, $L$ is a confounder, $E$ is the exposure, D is the disease outcome. In the matched ...
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Accounting for spatial correlations in ROC analysis for image segmentation
Typically, we assume independent samples when performing ROC analysis.
But for image data, e.g. in a segmentation problem, pixels in a neighborhood come from the same image and are spatially ...
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Using threshold and bias at the same time in NN
I'm using NN with sigmoid binary activation. And for threshold I using 0,5. So if output < 0,5, it classified as 0. And if output >= 0,5 it classified as 1. But I'm using bias too at the same ...
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How to measure uncertainty and account for spatial bias when conducting ROC analysis on image data?
I have a task where I need to perform ROC analysis and measure the AUC of the ROC curve, but the data is image data.
I have pairs of images (which contain real-valued pixels) and masks (which contain ...
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Study design when exposure more likely to lead to test for outcome
I am doing an observational study looking at the association between a baseline exposure (binary) and the first instance of an abnormal blood test result (binary) among people with serial blood tests.
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Estimand dependent on the sample
Suppose we have a sample $S$ of IID data and two different real-valued functions of $S$, say $\theta(S)$ and $f(S)$, and the latter is intended to estimate the value of the former. For example, the ...
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Impact of variables available only for large geographic units in OLS and 2SLS
I ran a series of OLS and 2SLS regressions to study the impact of several geographic variables on the dependent variable which is a share of workers of a particular type. The issue is that my unit of ...
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Underestimation of residual variance in a hierarchical model
I'm trying to fit a simple hierarchical model using simulated data.
The model is
$$y_{ij} \sim N(\mu_i, \sigma^2)$$
$$\mu_i \sim N(\mu, \tau^2)$$
The log joint distribution of parameters and data is:
$...
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Manually adding edge-cases to a text classification model
Suppose I want to get training data for a model that deals with sentiment analysis for text that indicates an affirmative (yes) or negative (no) response, such as
...
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Cross-validation as strategy for training
Let's say I have a classification model to be trained and a relatively small dataset. The data is splited in k-folds (eg. k=5), in such a way that:
A, B and C are used for training, D for testing and ...
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Prediction biased by closest hyperpoints
I am building a boosted decision trees classification model, where the input variables vary smoothly with time.
The problem is that the predictions will always be biased by the most recent entries. I ...
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What is the sampling bias in sample Pearson correlation coefficient squared?
Suppose $r$ is the sample Pearson correlation coefficient estimator of two random variables $X$ and $Y$, while $rho$ is the population correlation coefficient. From various sources, e.g., Is the ...
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Poisson regression intercept downward bias when true intercepts are small
When fitting a Poisson regression on data with low expected values, the intercept term has a small bias even when the model is perfectly specified. Below, I simulated data just using $y \sim rPois(exp(...
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