# Questions tagged [inverse-prediction]

Predicting an explanatory variable from an observation of the dependent variable, also called inverse regression or calibration.

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### Predicting simulated data for a known curve

I have hit a roadblock with a research problem and could really use your expertise. I have a pre-existing curve created by extrapolating known fitted experimental data. As shown below, the x-axis is, ...
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### Seeking Guidance on Constrained Input Modeling for Soil Moisture Correction Using Rainfall Observations

I find myself immersed in the intricacies of working with 2D modeled fields (images) representing soil moisture in regions where direct observations are unfortunately absent. However, there is a ...
183 views

### Calculating uncertainty of predictions - standard error or error calculus?

I'm looking to create a calibration function for a lab instrument I have: $y = A + Bx$ Where $y$ is the "true" output and $x$ is the initial reading. I have a dataset of ~100 readings that I ...
1 vote
42 views

### is it possible to use an existing non-linear relationship (GAM) to estimate back one of the independent variable?

Hi I have used a set of data to estimate the relationship between v0 (response variable) and v1-v6 (independent variables) through a non-linear model using GAM. The model is fitted with data between ...
• 261
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### How can I make predictions for new samples in the same subject, conditional on one observation?

I have fitted a Bayesian multilevel model. Example: $$Y \sim Normal(\mu, \sigma)\\ \mu = \alpha + \beta * time + z_{subject}\\ z_{subject} \sim Normal(\bar{z}, \sigma_z)$$ I have fitted this to some ...
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### How to deal with treatment variable when using inverse probability weighting (IPW)?

I have a dataset which contains around 10,000 observations. I want to estimate the treatment effect (suppose the treatment variable is T, which is a dummy and outcome variable is Y, and X represents ...
320 views

### Inverse Predictive Posterior

Suppose I have a parametric nonlinear model, say $$y_i |\theta \sim N(f_{\theta}(x_i), \sigma^2)$$ with known form of $f_\theta$. We get data $d=(y_i,x_i)_{i=1,\ldots,n}$ and obtain posterior ...
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### Is it inappropriate to predict an independent variable using a linear model? [duplicate]

In an A-Level maths textbook that I am reading about least-squares regression, it states that a regression line should only be used to predict the dependent variable and not the independent variable. ...
• 111
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### R's lm(), get x when y is known [duplicate]

Here is some data and a logarithmic model: df <- data.frame( x = 1:8, y = c(7.5,6,5.2,4.3,3.9,3.4,3.1,2.9) ) model <- lm(y ~ log(x), data = df) I am ...
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### Should I use the prediction interval or inverse prediction interval to calculate the uncertainty of $x$ when using reverse regression?

I'm calibrating a piece of lab instrumentation. I create solutions of known concentration ($x$) and measure my instrument response ($y$). On unknown samples, I measure the response and use the ...
49 views

### Model fit after inverse regression and forward stagewise on residuals

I work with prediction of height based on genetic information. The data is several hundred thousand data points from every organism, but a simplified version could be: ...
50 views

### Which is the error of a value corresponding to the maximum of a function?

This is my problem: I use data observed with MUSE (which is an astronomical instrument provides cubes, i.e. an image for each wavelength with a certain range, link ) to extract a measure of redshift. ...
4k views

### Inverse Regression vs Reverse Regression

I'm aware there's a great number of questions which deal with the mathematical difference between the two, but I'm still confused as to best practice. Basically I'm looking at a situation where we ...
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### Neural Network Inversion and its consequences

I am currently looking at Federated Learning. Here is a good example from google. The idea is that training happens on multiple devices. This means on one hand that training data never leaves a user (...
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### Regression and calibration/inverse regression - the same?

In principle, I've a simple task: There are some physical quantities (temperature, pressure and molecule number) measured by a sensor and I want to use them to regress the concenctration of a gas. I ...
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### inverse.predict chemcal package

I have noticed that the inverse.predict function (chemCal package) does not take into account all the degrees of freedom of the ...
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### If X can predict Y in regression, why isn't Y guaranteed to predict X?

Intuitively, if X can predict Y in a multiple linear regression model, $y$ = $\beta_0$ + $\beta_1$$X + \beta_2$$Z$ + $e$ X and Y are associated. Since there's an association between them, why is ...
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### Regression vs Calibration [duplicate]

When reading on the wikipedia page of Calibration they said : " A reverse process to regression, where instead of a future dependent variable being predicted from known explanatory variables, a ...
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547 views

### Is a confidence interval symmetric when constructed on an inverse prediction of a logistic regression?

I have a dataset with a continuous variable paired with a binomial response. We want a one-sided confidence bound to determine at what value of the continuous variable would we get a desired ...
• 305
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### How to calculate the confidence interval of the x-intercept in a linear regression?

Since standard error of a linear regression is usually given for the response variable, I'm wondering how to obtain confidence intervals in the other direction - e.g. for an x-intercept. I'm able to ...
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### Error bars, linear regression and "standard deviation" for point

I have a set of experimental data points. I performed the measurements in triplicate, for each of the point of the data set. Therefore, I can draw each data point with the standard deviation of each ...
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1 vote
1k views

### Inverse prediction of SVM because AUC is lower than 0.5

I am training SVM by a dataset with 8 features using 10-fold CV. The AUC for testing data is under 0.5. I remember that somewhere it had been written that in cases with ...
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992 views

### Confidence interval for vertex of quadratic model, transforming parameters estimated by MLE

If I have a model $y=ax^2+bx+c+\epsilon$, and I use maximum likelihood estimation (in R, with nlm function) to estimate $(a,b,c)$ with a Hessian matrix $H$ as a ...
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761 views

### Finding ideal hypothetical data according to a regression model

Analogy We have 10 athletes. Each athlete is represented as a binary feature vector. We make these athletes compete in a 100 metre race. We get real value numbers corresponding to the time they took ...
1 vote
759 views

### Regression involving multiple measurements on known values (calibration)

Suppose I have two continuous variables Y and X and I want to predict a Y value given a specific X value. However, the dataset I have is composed of 15 particular Y values (that are known values) ...
70 views

### Prediction of features given predictor

I am working on a problem where my objective is to predict y given some features x1,x2,x3,...x8,x9 I solved this problem using some statistical and machine learning techniques like regression, trees, ...
84 views

### Confidence interval from two methods

I have some data in the form of (x,y) tuples, 50 tuples. I am trying to fit a quadratic so y = ax^2+bx+c My goal is to find the max of the quadratic, so max = -...
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### Why inverse of 'predict' function in R can not be used for dependent variable prediction in linear model?

When a regression is calculated with a simple linear model that returns intercept and slope for an equation like this $y=a + bx$ one can predict $y$, the response variable, based on that equation. ...
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1 vote
264 views

### Inverse prediction of percentile

Suppose we consider a linear normal regression $y\sim$Normal($\mu,\sigma$) and $\mu=a+bx$. I have seen documentations for methods for obtaining a confidence interval for $x$ for a specific mean value ...
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620 views

### linear model, given y, calculate the confidence interval for x

I fit the model y = a + b * x. And 95% CI for estimates of a and b are (a1, a2), (b1, b2), respectively. If we have a new observation ...
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### How to do 4-parametric regression for ELISA data in R

I am a biology student. We do many Enzyme Linked Immunosorbent Assay (ELISA) experiments and Bradford detection. A 4-parametric logistic regression (reference) is often used for regression these data ...
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578 views

### inverse logistic regression with binary covariates

I am currently using a hierarchical Bayesian framework to investigate a problem with both a single binary response variable and binary covariates, $P(Y=1 | X_i=1), i=1,\ldots,n$. Using R/JAGS I can ...
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1 vote
966 views

### Inverse prediction from binomial glm - how to obtain confidence intervals?

I am trying to use a glm with a binomial distribution (logit link) to analyse data from a dose response curve for the lethal effects of different bacterial strains. I now want to obtain estimates of ...
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