For questions about how to parameterize some statistical model, or comparisons between different ways to parameterize.

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Orthogonality of Canonical Parameter with Sufficient Statistic [closed]

For a regular exponential family expressed as, $$ f(x \mid θ_1,θ_2 )= \exp \{θ_1 t_1 (x)+θ_2 t_2 (x)+c(θ_1,θ_2 )+d(x) \} , $$ show $θ_1$ is orthogonal to $\text{E}[t_2 (X)]$ and $θ_2$ is orthogonal ...
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1answer
43 views

How should I parametrize a nonlinear increasing function?

I want to learn a nonlinear monotone increasing function $f$ parametrized using a set of weights $w$. Given an input $x$, I can calculate the gradient of the loss with respect to $f(x)$ ...
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26 views

Spherical Parameterization of Variance-Covariance Matrix in Mixed-Effects Regression

I wonder if someone can please help me with a passage on the article by José Pinheiro and Douglas Bates on unconstrained matrix parametrization. I have been slowly working through it, and getting ...
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0answers
16 views

how to find the aleatory uncertainty in parameter using Bayes?

Generally, the uncertainty can be categorized into aleatory and epistemic according to whether it can be reduced or not. In Bayesian statistics, one "true fixed parameter" is presumed as discussions ...
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23 views

How to constrain higher-order interaction terms in hierarchical bayesian regression models with multiple categorical and metric predictors

Greetings Statistics Wizards! I am building a hierarchical bayesian regression model in which the predicted (y) variable is metric (numerical, continuous) and the predictor variables are both ...
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1answer
42 views

Objective interpretation of a parameter

In the following model equation (purely statistical / descriptive model, no mechanistic information involved): $$ Y = a \times X^b $$ considering that $Y$ and $X$ are two measurements, say, $Y$ is ...
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17 views

Multivariate normal: from canonical parameterization to mean parameterization (or vice versa)

In their book (https://www.eecs.berkeley.edu/~wainwrig/Papers/WaiJor08_FTML.pdf) Wainwright and Jordan consider two types of parameterizations in the exponential family, the canonical parameterization ...
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22 views

Parameterization of the ANOVA model and interpretation of the overall F-test

I've recently encountered the following concept regarding linear regression: the inclusion of an intercept will change the interpretation of both the overall F-test and the individual parameter ...
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1answer
25 views

Log likelihood for inverse gamma

For a gamma distribution, the answer to this question shows that you can just use the log of the gamma distribution density function. Is the same true for inverse gamma? It is the same as the log of ...
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1answer
35 views

Questions regarding interpretation of item parameters: inconsistent results between classical item analysis and item response analysis

I was not trained as a psychometrician, so my questions may be concept-related. If you know different resources, books, or articles that can clear my confusions, please let me know. Thank you very ...
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0answers
16 views

p-test for parameter

Statisticians, number magicians, I was wondering what the best way is to check for the equality of two parameters including possibly a confidence interval and p-value. $$H_0:\beta_1=\beta_2\vert\ ...
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1answer
119 views

Questions Regarding Item Response Models – the 3PL model vs. the mixture of 2PL and 3PL model

I currently work on an item analysis for an assessment. The assessment consists of 25 multiple-choice questions. Each question has 4 choices with one correct answer. I used different IRT models to ...
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1answer
33 views

OLS parameter estimation of an expression?

During my research for a class, I came across a paper that said they estimated an equation using OLS. But the parameter they were estimating appeared to be an expression that looked like this (not the ...
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0answers
20 views

Under what assumptions can parameter estimate uncertainty be estimated from the Hessian?

Given a model with some parameters, some data it's attempting to reproduce, and a distance function to quantify how well the predictions correspond to the data, I can fit parameters via a general ...
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1answer
44 views

Beta binomial mean different from actual mean

I have data that I am fitting a beta binomial distribution to. The VGAM package for R is being used to do this. However, the the mean of the fitting beta binomial distribution is vastly different from ...
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21 views

Implementing evolutionary algorithms

We're trying to to minimize the following functions using Multi Objective Evolutionary Algorithms : $\mathrm{minimize}~\lambda_q(1-a)E(N)E(X)+\lambda_xE(N)E(\max(X/a-R,0))$ ...
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1answer
37 views

Parameters in a non-parametric model

I have not understood this Wikipedia statement: The difference between parametric model and non-parametric model is that the former has a fixed number of parameters, while the latter grows the ...
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2answers
57 views

Estimation of probability mass function using finite samples [closed]

Suppose $X_1, X_2, \dots, X_N$ are $N$ random samples of a discrete probability distribution such that $X_i \in \{1, 2, \dots, K\}$. The probability distribution $p$ used for sampling is ...
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1answer
89 views

Beta distribution vs beta binomial distribution: alpha and beta

I have been attempting to estimate alpha and beta from a beta binomial distribution given my data. There are R packages like VGAM to do this. I am wondering if there is a difference between estimating ...
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1answer
23 views

Prior for gamma distribution in “mean form”

I need to specify priors for the parameters of a gamma distribution. Normally the gamma distribution is parametrized in either the "rate-form'': ...
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0answers
10 views

Redundant parameters in multilevel models

I am a bit confused about the use of redundant parameters in multilevel models in order to speed the convergence of the Gibbs sampler. I don't understand how the model should be reparametrized. ...
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1answer
15 views

Is there a family of processes centred on the Poisson process?

I am looking for a model, characterized continuously by a single parameter, to describe the arrival times of buses with unit expected interarrival time. At one extreme of the parameter (say ...
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0answers
50 views

What have I done wrong implementing this Bayesian method for fitting a circle to noisy data?

I have noisy measurements of movement along a circle. I want to fit a circle to these measurements. I tried two methods, a straight forward moment fit, and then an ODR fit (described here. However ...
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1answer
117 views

CV for model parameter tuning AND then model evaluation

I have a basic question on using cross-validation for model parameter tuning (model training) and model evaluation (testing) similar to this Model Tuning and Model Evaluation in Machine Learning I ...
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2answers
194 views

Fisher information matrix determinant for an overparameterized model

Consider a Bernoulli random variable $X\in\{0,1\}$ with parameter $\theta$ (probability of success). The likelihood function and Fisher information (a $1 \times 1$ matrix) are: $$ \begin{align} ...
3
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1answer
398 views

Find the mode of a probability distribution function

I am trying the find mode of a probability distribution function given by \begin{equation} g(x/\alpha,\beta,\sigma)=\frac{1}{\Gamma \left( \alpha ...
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0answers
40 views

Parameter estimation using lmom package

As a part of my risk management job, I need to try to fit various distributions to loss data. I have been using the lmom package in R for estimating parameters for ...
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31 views

Optimize parameters?

I've been back-testing a trading strategy that has two parameters (both are # of days to look back), and I've tested the system for robustness by comparing my 10-year Sharpe ratio based on approx ...
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0answers
27 views

Verification of an optimal parameter from an empirical CDF

Suppose we have the following model for the variable $V_5$: $$V_5 = \prod_{k=1}^5(e^{\mu + 0.2X_k}+0.05e^{0.05Y_i - 0.00125}), X_i,Y_i\sim N(0,1)$$ What I wish to do is to solve the problem ...
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37 views

forcing certain parameters to be skipped during optim in R

I have a code which tests each possible order of ARIMA and selects the best model by choosing the one with the absolute minimum sum of lags from the PACF graph. The code then proceeds to add weight to ...
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1answer
361 views

Likelihood ratio test for comparing two exponential distributions

I am trying to use a likelihood ratio test to compare the parameters of two exponential distributions. by this thread Likelihood Ratio for two-sample Exponential distribution I found that I can use ...
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1answer
116 views

Point estimation MLE and MME

Consider the family of probability mass functions given by f(x;k) = 3(4^(k-x)) x = k + 1, k + 2,.... and indexed by parameter k E Z. For a random sample of size n, derive with justification: a) ...
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1answer
44 views

How do models, parameters, specifications, restrictions and assumptions relate?

So this has been something I've been struggling with for a long time: The specification of a particular model is subjective. However, there seems to be objective ('true') values of the parameters we ...
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1answer
95 views

Confusing Holt-Winters parameters

I have got a model for forecasting using holt-winters. However the parameters confuse me... The parameters show that there is no trend or seasonality even though there is definite trend and ...
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0answers
32 views

Do assumptions for estimators affect population parameters?

TL;DR: Specifying a model (a collection of restrictions over a sample space) specifies the model parameters. Specifying an estimation procedure adds additional number of restrictions (assumptions?). ...
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1answer
78 views

Calibrating Generalized Hyperbolic distribution in R - which parameters are valid and allow for a numerical calculation of absolute moments

I am using the R-package ghyp in order to calibrate and model. In fact my coding is based on this paper. I know that I could do quite a robust fit using ...
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1answer
33 views

Stable Distribution Log-likelihood and AIC values

I have used the stableFit function from the fBasics package to come up with parameters (alpha, beta, gamma, and delta) for a stable distribution as you can see below: ...
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1answer
31 views

Definition of Parameters [duplicate]

I imagine this either extremely simple or extremely complex. I am trying to understand the interpretation of the term 'parameter'. A couple of quick online searches deliver an intuitive understanding ...
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1answer
136 views

Parameters for a Levy distribution in R

Can someone help me figure out how I can get parameter estimates for a levy distribution using R? Unlike the normal distribution and Student T distribution which has functions ...
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0answers
40 views

cross validation for parameter-tuning a metaheuristic

For a certain problem, I've come up with a novel metaheuristic. The question I'd like to answer is "Does my metaheuristic perform better than previous methods over most problem instances?". My ...
3
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1answer
92 views

Smoothing parameter for spline curve with duplicate points

I have body mass and age data for a population of individuals. I want to fit a cubic smoothing spline curve to the data. I'm using smooth.spline in R, which warns against using cross-validation to ...
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1answer
51 views

Choosing between two parameters in a model

I have a few parameters that are related (let's call them X1 and X2), and I want to use whichever one will provide the strongest model. The model has many other parameters. Would I simply be able to ...
2
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1answer
137 views

Best statistical notation for expected probability density

Assume that we have two multivariate normal distributions $\mathcal{N}_1 = \mathcal{N}(\mu_1, \Sigma_1)$ and $\mathcal{N}_2 = \mathcal{N}(\mu_2, \Sigma_2)$. We do these two steps: Pick a point, say ...
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1answer
29 views

Tuning paramaters SVM, DT, k-NN, NN

I'm trying to compare the predictive strenght of four different algorithms: support vector machines k-NN decision trees neural networks I've got a few questions concerning the parameter tuning: ...
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0answers
67 views

Assumptions implied by “pairwise marginal” parameterization of MRF

I'm trying to understand the assumptions of different parameterizations in a Markov network. In this case, I'm trying to understand the assumptions (and effects) that result from parameterizing ...
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0answers
42 views

Efficient scale & shape parameter estimation for generalized secant hyperbolic distribution needed

the (symmetric) generalized secant hyperbolic distribution GSHD is very flexible but I found not much at all on how to estimate its 3 parameters. Given the location, I need to obtain scale & shape ...
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2answers
170 views

How many parameters in this specific linear model with interaction?

I have a question where I am not sure about the answer: A linear model has the following characteristics: *A dependent variable ($y$) *One continuous variable ($x_l$), including a ...
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1answer
31 views

Reparametrisation of a model when an interaction is significant to facilitate the interpretation

It is admitted that it is complex to interpret main effects when they are involved in an interaction. Lets take a regular linear model, with two categorical 2 level variables A and B who are ...
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99 views

Is it reasonable to measure standard deviation from true value rather than mean?

I am evaluating the accuracy of GPS watches, taking many readings over a known distance. I've been calculating standard deviation using the mean reading, but because I know what the reading should be, ...
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26 views

Floor effects in Bayesian estimate, can I reparameterize?

I'm replicating an old study and I have two sets of existing estimates which measure a similar effect, namely the presence of a studied item in memory over time: ...