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Questions tagged [risk]

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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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The function cvrisk() takes a lot of time to find the optimal mstop in the mboost R package [on hold]

I am working with the R package mboost and I am fitting a gam model to a large dataset (63,699 observations). I have split the original dataset into a training data ...
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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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risk-management using large deviations theory [on hold]

Crameers theorem says that $$P( \frac{1}{n} \sum X_i > x) \approx e^{-nL(x)}$$ where $L(x)$ is the legerende transform (see wikipeda page: https://en.wikipedia.org/wiki/Cram%C3%A9r%27s_theorem_(...
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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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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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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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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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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
40 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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1answer
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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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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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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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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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Can Failure Mode Effect Analysis (FMEA) method be used to find a cause of a failure?

In the research i am currently making, there is a problem in a company supply chain in it's supply chain (source) adaptability. I assumed that the main failure is "error in the company's system to ...
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Predicting probability distribution of value in time series of real numbers like Dow Jones?

While we are usually interested in predicting values of time series, it is often also valuable to predict probability distribution of the next value basing on its context - for example for risk ...
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1answer
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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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68 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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Method to adjust probability of an outcome for number at risk

Sorry if this is a silly question. I have a table of 2000 patients and the time at which a certain in-hospital outcome occurred. I have another table of these 2000 patients containing how long they ...
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1answer
87 views

Is risk modeling a hypothesis-driven, scientific endeavor?

One could hypothesize that factors x1, x2, x3 predict y. ...
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38 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
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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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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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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; 1. Fit GARCH models to each series. 2. Extract standardized returns. 3. Transform ...
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Identify risk/stress in financial markets from risk index

maybe someone could be helpful and give me some nice insights. I developed a financial stress index which should help me identify the risk situation on the financial markets. Now, I would like to ...
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1answer
23 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
419 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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Baseline rate `normalized' effect size measures for dichotomous outcomes?

I'm looking for a measure of effect size that represents how 'surprising' a finding is in a way that is comparable across independent experiments. For example, suppose we consider future rates of ...
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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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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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228 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
61 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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2answers
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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
257 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
108 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
147 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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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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57 views

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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1answer
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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
255 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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37 views

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 ...
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1answer
24 views

Quantification method for long term financial risk

I am working on a method to find a optimal allocation of money in various ways, like putting it on a savings account, investing it, paying off mortgage, etc. The scope of this method is to find a way ...
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1answer
209 views

The Kelly Criterion — Where Did I Go Wrong?

Suppose the following simple/basic investment scenario: I have $100$USD in my bank account as a starting point (will increase/decrease as I invest). There are $1,000$ different investments that I'm ...
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Efficient computation of the value-at-risk of a credit portfolio via summation of independent discrete random variables

With the application of computing a value-at-risk for a credit portfolio (tail percentile of a distribution) in mind, I am currently contemplating the possibility of estimating the distribution tail ...
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1answer
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Compounding Confidence Intervals as Risk?

Here's a hypothetical situation a colleague and I were discussing, and I'd be interested to hear your opinion(s) on this approach to utilizing confidence intervals: We are discussing a method of ...
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1answer
115 views

Mapping Frequentist Risk Notation to Regression

The frequentist risk in literature is defined as follows: $R(\theta, \delta) = E_{X|\theta} L(\theta,\delta(x)) = \int L(\theta,\delta(x)) p(x|\theta) dx$ This risk is focused on the quality of the ...