Questions tagged [risk]

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7 views

Risk adjustments for outliers with extreme consequences

I have a vague memory of an adjustment to expected value calculations to account for highly improbable events with extreme outcomes. An example is the lottery. The odds of hitting it are ...
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18 views

How to calculate the reclassification calibration statistic (RC statistic)?

In risk prediction models there is a need to evaluate the added diagnostic value of a new variable (biomarker). Different measures have been suggested, among them there is the reclassification ...
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17 views

Admissible and Inadmissible actions

Consider the following loss matrix. $\begin{array}{|c|c|c|c|} \hline & \alpha_1 & \alpha_2 & \alpha_3 \\ \hline \theta_1 & 1000& -300& 4000\\ \hline \theta_2 & -1000&...
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9 views

Approaches for a “risk segmentation” applied to auto insurance

I wonder about approaches for a risk segmentation applied to auto insurance. i.e. Suppose I have all the states within United States, and I wanna say: "Ok, Alaska and Alabama belong to group 1; ...
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11 views

Providing Statistical evidence that credit portfolios have different risk behaviour

I work in the risk department of a credit company and I was asked to analyse and bring some statistical evidence that two portfolios have different risk behaviour. So, my goal is to find if, for ...
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30 views

Accidents as precursors of condition: how does that fit with Bayesian inference?

I'm currently trying to identify what approach should I use for my problem. I want to make a risk assessment for each subject having or not a specific condition C (5% of prevalence), sample size ...
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1answer
20 views

Predicting risk factors

i'm trying to find predictive risk factors i already found out that young age at diagnosis is a risk factor ( binary logistic regression) But now i want to know the exact age when the risk is highest....
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28 views

Characterization of risk factors for a very rare condition

I am looking at a cohort of patients including 13000 patients, out of which only 160 have condition A. Out of these patients, only 6 have condition B. I would like to be able to characterize those ...
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12 views

Independent and Identically distributed random variables with value at risk [duplicate]

Suppose that $W_1$ and $W_2$ are i.i.d. and $P(W_i>x)=x^{-1/2}$ and $x$ is greater than or equal to $1$ and $i=1,2.$ How do you show that $P(W_1+W_2>x)=(2\sqrt{x-1})/x$? I know it involves ...
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34 views

How should I interpret a weighted genetic risk score?

I created a weighted Genetic Risk Score (GRS) by summing the product of the SNP-dosages times their regression coefficients from the GWAS in which I found them. So: ...
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19k views

Is it wrong to rephrase “1 in 80 deaths is caused by a car accident” as “1 in 80 people die as a result of a car accident?”

Statement One (S1): "One in 80 deaths is caused by a car accident." Statement Two (S2): "One in 80 people dies as a result of a car accident." Now, I personally don't see very much difference at all ...
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1answer
26 views

Whats is the difference between using risk() and cvrisk() in the R package mboost

I am currently running an additive model using the function gamboost() in the package mboost. When using the ...
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59 views

Combining Risk Scores based on Different Models

Let's say for example there are two models for different medical conditions that fall under the general category of medical conditions. For condition one, we have m features, and we built a ...
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“proof” of subaddivity of Var for elliptical distributions makes incredibly unjustified assumption

Look at the slide below. It says it wants to "prove subaddivity" for elliptical distributions, but subaddivity requires the result to hold for ALL LOSSES $L_1$ and $L_2$, but the slide assumes that $...
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9 views

What's a simple explanation for risk and its formula in survival analysis, weibull regression

I have that if the model is $\ln(\mu_i) = \beta_0 + \beta_1 x_1$ where $x_1 \in \{0,1\}$ and represents tired (or anything suitable, sex, etc). The model also has a shape parameter, $\gamma$. ...
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26 views

Bounds for the expected value of the Kolmogorov-Smirnoff loss function

Let $$ \mathcal{F}=\{F:\mathbb{R}\longrightarrow\mathbb{R}: \text{$F$ is the CDF of some probability measure on $\mathbb{R}$}\}. $$ Consider the loss function, $L:\mathcal F\times\mathcal F\to\mathbb ...
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14 views

question about the logit model for credit risk

i have this question in one of the past exams . Discuss which model you would choose to calculate the probability of default of corporate firms and give a rationale for including OR excluding the RE/...
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55 views

Equity Risk Model using an autoencoder

I am trying to create a statistical equity risk model using an autoencoder in a similar fashion to how one would use PCA to derive the systematic and specific risk components of a stock's returns. I ...
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49 views

RiskMetrics VAR calculations and conditional distribution of sum of log returns

According to Tsay's book in Chapter 7, for the Risk Metrics model: A nice property of such a special random-walk IGARCH model is that the conditional distribution of a multiperiod return is ...
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30 views

Using Keras NN to predict risk

Question What is the best activation to use for a keras NN predicting risk of a single binary outcome? Is it sigmoid? And are there some approaches I can use to ...
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1answer
293 views

How is True risk equal to the expected value of the empirical risk?

We know that the empirical risk is : $L_s = \frac{1}{n} \sum_{i=1}^{n} l(f(x_i),z_i)$ where, $n$ = number of samples,$l(f(x),z)$ is a loss function, $S = (z_1,...,z_n)$ are the provided samples to ...
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159 views

How to calculate expected risk from fitted Cox PH model in R?

I'd like to calculate expected risk (cumulative incidences), which are derived from fitted Cox PH model using R packages. I have the fitted Cox PH model like as follows: [Variables] Dataset: 10,...
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16 views

Existence of Minimum Risk equivariant estimator

$X\sim f(x-\theta)$ . Let $y_i=x_i-x_n$ for $i =1,\cdots,n-1$. Let loss $L(\theta,t)=\rho(t-\theta)$ . Let there exist an equivariant estimator $T_0$ with finite risk. If $\rho$ is convex and ...
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Model fitting vs minimizing expected risk

I'm confused about the mechanics of model fitting vs minimizing risk in decision theory. There's numerous resources online, but I can't seem to find a straight answer regarding what I'm confused about....
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159 views

Why is the risk function defined to be the expectation of loss function?

In decision theory, we define the risk associated with a particular predictor function as the expected value of the loss function. Since the input and output are considered random variables therefore ...
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28 views

Why would results from cmprsk differ from those from riskRegression in competing risk analysis?

I have a dataframe with a number of covariates or different types (binary, numeric, factors) and 2 competing outcomes. The presence of one outcome would preclude the occurrence of the other outcome. ...
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1answer
21 views

Person months to annual risk

if a study reports a risk of 4 cases per 1000 person months can that be converted into an annual risk per 100,000 people? if so, how? Thanks
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1answer
30 views

What is the optimal strategy to invest a limited resource in N uncertain options?

Suppose I have a £100 to invest in 2 options. Each option has a expected value, but the value is unknown. Option A has the highest average expected value, but a bigger uncertainty range. If we just ...
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180 views

True risk vs emprical risk

I tried to understand the difference between true and empirical risk by the post in wiki. There it states that the true risk cannot be computed because the distribution P(x,y) is unknown. My first ...
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1answer
108 views

Is risk modeling a hypothesis-driven, scientific endeavor?

One could hypothesize that factors x1, x2, x3 predict y. ...
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62 views

comparison of two estimators

Assume we have a data set $\mathbf{x}_{n} = (x_{1}, \dots, x_{n})$. Let $\delta_{1}(\mathbf{x}_{n})$ and $\delta_{2}(\mathbf{x}_{n})$ be two consistent estimators of some parameter $\theta \in R^{k}$. ...
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1answer
70 views

Convert classifier output for disease to probability using Bayes

Method 1 I am given a classifier for some disease that takes as input patient characteristics and has some sensitivity and specificity. Hence the classifier is a function c(patient characteristics) ...
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116 views

Simulation of a random variable given the moment generating function after exponential tilt

The random variable $S$ follows a distribution with moment generating function $$M_S(v)=\frac{\beta\mu v}{1+(1+\beta)\mu v-M_X(v)}$$ I have been looking in some books about this m.g.f and I found ...
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65 views

How to calculate the VaR of an equally weighted portfolio of 2 assets using the copula approach?

The R-code procedure in the GARCH-EVT-Copula model estimation I have been able to do the following steps in R: Fit GARCH models to each series. Extract standardized returns. Transform standardized ...
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1answer
26 views

A simulation risk formulation where Bayesianism and frequentism is combined

For my mathematics bachelor-thesis at the Statistics Netherlands, i became acquainted with frequentist and Bayesian statistics. I had set up a simulation-study, and I am not sure if the risk I ...
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1answer
645 views

Different definitions of Bayes risk

I'm having trouble understanding the proper definition of Bayes risk. Let the data/variate $x \sim P(X|\theta)$, $\theta\in \Theta$, $\pi$ be a distribution on $\Theta$ (prior), $\hat \theta(x)$ be ...
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23 views

Include predictions as feature in regression. covariate or offset?

I have a regression setting in which I would like to explore the influence of a given variable on a certain patient condition, given a level of risk for the same outcome, predicted with a more complex ...
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17 views

Probability - Plant Production

I work for an agricultural company. We grow plant varieties that yield fruit. Some varieties do well, others do not. All plants need the key drivers of success: good soil, water, sun, etc. So here ...
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328 views

Interpretation of VAR for non normal distribution!

I want to compute the VAR and expected shortfall for log returns of monthly wholesale gas and electricity prices. The data is not normally distributed and I only have 72 observation for each. I ...
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1answer
62 views

help specifying a multilevel risk model

Hi and any help greatly appreciated specifying this model! I have a binary outcome, measured at the person level (coronary event). There are 9 'risk event' predictors (also binary coded as occurred/...
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126 views

I'm looking for a risk analysis book with citations from academic backgrounds that focuses on shocks and the unknown. Looking for a Taleb alternative [closed]

I'm less than ... enthusiastic about some of Taleb's claims regarding, say, the paleo diet. I make no comment on his political content, but I want someone more factual and hard, and less prone to ...
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1answer
14 views

Relative risk calculation for effect modification testing

I was trying to replicate an example from Knol et al (Knol 2012, Int J Epidemiol, Recommendations for presenting analyses of effect modification and interaction) but I dont get the same results as the ...
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1answer
347 views

Compound Poisson Process with Weibull jumps

I need to simulate a compound Poisson Process in R, however I am not clear with the algorithm to generate it. I have conceptual gaps. I know by definition that: A compound Poisson process is the ...
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1answer
114 views

Comparing estimators of equal risk

I'm attending a course in mathematical statistics and it seems the lecturer tacitly assumes that given estimators $T_1,T_2 : \Omega \to \Lambda$ of a parameter $g : \Theta \to \Lambda$, a loss ...
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1answer
172 views

Upper bound using Bayes risk

Bayes' risk is $L^*=0$ for a classification problem. $g_n(x)$ is a classification rule (plug-in) such that $g_n=0$ is $\eta_n(x)\leq 1/2$ and $g_n=1$ otherwise. The function $\eta$ is given by $\eta(x)...
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97 views

Monte Carlo approach in a distribution of a loss process

I am trying to estimate the next quantity using Monte Carlo method. I have the next well-known quantity called the Crámer-Lundberg risk process, given by the expression $$Y_t=x+ct-Z_t$$ where $Z_t=\...
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How to bet on a binary event based on the markov transition matrix, state probabilities and the odds

There is a coupon full of football matches for a given day from a bookkeeper. I have scrapped another website and i have aquired continuous history of a particular match between ...
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154 views

Is AUC (area under curve) a type of “empirical Bayes estimator”?

Questions: Is the AUC (area under the ROC curve) a type of "empirical Bayes estimator"? If we take the parameter space to be $\Theta = [0,1]$ and the prior $\Lambda$ to be Lebesgue measure, then the ...
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1answer
413 views

Difference between uGarchRoll Value at Risk and manual calculations

I am forecasting an equity return density using the uGarchRoll commandin R studio, specifying the standardized t-distribution as error distribution. The uGarchRoll command already forecasts the Value ...
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Value-at-Risk Interpretation

Regarding the VaR formula: VaR = -U-ZX Where U is the average return, X is the standard deviation and Z is the negative number of standard deviations that specifies the probability level associated ...