# Questions tagged [identifiability]

A model is identifiable if a single set of parameters can be found that will yield the best fit.

210 questions
Filter by
Sorted by
Tagged with
1 vote
14 views

### Understanding why volatility in diffusion process $(X_t)_{t \in[0,T]}$ is identifiable/known for continuous observations, but the drift is not?

Why is it that when dealing with continuous time observations of a diffusion process $(X_t)_{t \in[0,T]}$, we say that the volatility $\sigma^2$ is "perfectly identifiable" and just usually ...
• 147
24 views

### Identification of the transition probability of a time homogeneous MDP with subsampling

I am dealing with a MDP (or a temporal causal SEM) problem with missing observations. I want to know under what assumptions the transition probability can be identified from the observation. ...
6 views

### Identification of Richer Conditional Expectation from Less Rich Ones

Let $X_1,X_2$ be uniformly distributed and suppose that we know the quantities $E[Y | c_1 X_1 + c_2 X_2 = v]$ for all values of $c_1,c_2,v$ (i.e. we know all of the expectation of $Y$ conditional on ...
• 1,461
30 views

### An estimation method/algorithm for estimating the value of a specific parameter in a convex function

I am looking for an estimation/iteration process to estimate the value of a specific unobserved parameter of a convex function that fits the observed data of the other variables closely. Specifically, ...
• 21
1 vote
15 views

I'm using Differential Evolution to locate the global minimum in a search space with the objective function being the Root Mean Squared Error. I'm using a mathematical model with number of parameters $... • 111 0 votes 1 answer 32 views ### Beta distributed transition probability in CEA I am reading a paper on cost-effective analysis and trying to replicate their results. (paper: https://ascopubs.org/doi/full/10.1200/GO.20.00288) The probabilistic model in the paper assumes that the ... 2 votes 0 answers 55 views ### Identification techniques when$E(u_i|\text{do}(X_i))\not=0$In this article Chen & Pearl make the following 2 statements: "Identification techniques are available for models in which X is far from satisfying$E(u_i|X_i)=0$" in response to Stock &... • 3,262 0 votes 0 answers 15 views ### Joint inference vs composition of estimators I’m currently playing around with a toy problem at work. Assume I have a bivariate distribution with four parameters which I want to estimate, two marginal parameters and two which steer dependence. I ... 0 votes 0 answers 9 views ### How do I handle underidentification in Bifactor ESEMs? I hope you can help me to find some answers to my questions. Following Morin, Arens, & Marsh (2016; references below), I’m trying to conduct a bifactor exploratory structural equation model (... 0 votes 0 answers 22 views ### Near-perfect "multicollinearity" between categorical variables in linear regression analysis I have a panel dataset which consists of 100,000 observations and 30 variables. Two of the variables, one binary ($x_1$) and one categorical ($x_2$with ~4000 categories), are nearly "collinear&... 0 votes 0 answers 26 views ### Are Non-Parametric Models more "Identifiable" compared to Parametric Models? Are Non-Parametric Models more "Identifiable" compared to Parametric Models? I have read about the notion of "Identifiability" in statistics - Identifiability (or "Label ... • 5,754 1 vote 1 answer 139 views ### Fix second-order factor loadings to equal in all second-order factors with two first-order factor indicators? CFA / SEM I am conducting a CFA followed up by a SEM analysis. In my original model I had 13 latent variables. As some of these were highly correlated, I created second-order factors, of which 3 are indicated ... 0 votes 0 answers 27 views ### Expected value of log-likelihood and KL divergence Background: Let$x_t = Ax_{t-1} + w_t$be a discrete linear time invariant system where:$x_t \in \mathbb{R}^d$for all time samples$t$corresponds to the state vector$A\in \mathbb{R}^{d\times d}$... • 61 2 votes 1 answer 110 views ### What's the purpose of do-calculus? I understand backdoor adjustment blocks backdoor paths and front door adjustment combines the causal effect of different nodes. The purpose of both is to eventually identify the causal effect of a ... 5 votes 3 answers 394 views ### Why do we need identification in causal inference? I am reading Pearl's causality book and it states, Identifiability ensures that the added assumptions conveyed by$M$... will supply the missing information without explicating$M$in detail. ... 1 vote 1 answer 29 views ### Identification of structural parameters in a linear model (treatment effect context) Suppose that we have$N$observations indexed by$i=1,...,N$. The observations are partitioned in three groups indexed by$g=1, 2,3$. Here, we consider potential outcomes$Y_{ig}^0,Y_{ig}^1,Y_{ig}^2$. ... • 501 3 votes 1 answer 33 views ### Identifiability of multivariate instrumental variable model I'm interested in estimating the effects of$X_1$and$X_2$on$Y$in the directed acyclic graph below.$U_1$and$U_2$are unobserved confounders. Based on Definition 7.4.1 on p. 248 of Causality ... • 31 0 votes 0 answers 13 views ### Model identifiability based on loadings matrix For$\textbf{y}=\mathbf{\mu}+\mathbf{\Lambda f}+\mathbf{\epsilon}$, let$\Phi=\textbf{cov}(\textbf{f})$to be a$m\times m$symmetric matrix containing$\frac{m(m+1)}{2}$unique factor variances and ... • 111 3 votes 2 answers 137 views ### Using a DAG to understand omitted variable bias in OLS vs Binary Dependent Variable Regression Suppose I have three variables.$A$and$U$are continuous variables but$U$is unobserved.$Y$is the binary outcome.$A$and$U$are independent. Let the true model be from the typical probit or ... • 31 2 votes 2 answers 175 views ### A realistic example of a non identifiable model? Given the definition of statistical model identifiability : identifiable iff$P_\theta = P_{\theta'} \implies \theta = \theta' ~~ \forall \theta, \theta' \in \Theta$we can see that, for example,$X \...
• 191
10 views

I have a question on the identifiability when I do maximum likelihood estimation with logit model. I use discrete factor random effect model for the unobserved heterogeneity. B is a binary outcome of ...
• 11
1 vote
28 views

### Re-parameterization to resolve non-identifiability in this squiggly model (linear combination of logistic functions)?

So my desire here is to be able to capture a variety of temporal dynamics governing the change in value of some feature of interest. I want the model to be able to represent, for example, bounded: ...
419 views

### Maximum Likelihood For the Normal Distribution

I get using Maximum Likelihood Estimation to find unknown parameters of a function. But in the normal distribution, we know probability density function is f(x)=1/σ√2π(e^−(x−μ)2/(2σ^2)) where μ is ...
• 21
1 vote
48 views

### Identifiability of discrete HMM with categorical observations

My setup is simple. I have two categorical distributions with probabilities $p$ and $\tilde{p}$ that generate an observation depending on whether the hidden state is 1 or 0, respectively. In other ...
1 vote
97 views

• 886
1 vote
112 views

### Why does estimability imply identifiability?

Let $P_{\theta}$ be the distribution (known up to a parameter $\theta$ in parameter space $\Theta$) of a random variable. A parameter (function) $\gamma=g\left(\theta\right)$ is called identifiable if ...
• 1,125
So suppose we have a model $f(x|\theta)$ that is theoretically identifiable, so that $\theta_1 \neq \theta_2$ implies $f(x|\theta_1) \neq f(x|\theta_2)$. However, suppose that data collection is very ...