###### Pretest probability financial definition of pretest probability

Definition of pretest

**probability**in the Financial Dictionary - by Free online English dictionary and encyclopedia. What is pretest**probability**? Meaning of pretest**probability**as a finance term. What does pretest**probability**mean in finance?###### Error probability in synchronous digital circuits due to power supply noise

This paper presents a probabilistic approach to model the problem of power supply voltage fluctuations. Error

**probability**calculations are shown for some 90-nm technology digital circuits. The analysis here considered gives the timing violation error**probability**as a new design quality factor in front of conventional techniques that assume the full perfection of the circuit. The evaluation of the error bound can be useful for new design paradigms where retry and self-recovering techniques are being applied to the design of high performance processors. The method here described allows to evaluate the performance of these techniques by means of calculating the expected error**probability**in terms of power supply distribution quality ...###### Conditional Probability and Rare Events - Data Science Chalk Talk

Conditional

**probability**refers to the**probability**of a generic event, given some extra information. More specifically, the conditional**probability**of one event A with respect to B: Expresses the**probability**of A given that B has occurred. If the two events are independent, the simple and conditional**probability**coincides (the occurrence of B has nothing…###### 5. Conditional Probability

If your friend tells you that an even number showed up, what is the

**probability**that you rolled a 5? It cant happen since 5 is an odd number.. So what is happening in these cases? Well, you are learning some additional information that leads us to change the**probability**of an event occurring. In effect, knowing additional information changes the sample size we use to compute the probabilities. Therefore, the**probability**of our event occurring must change.. The notation P(F│E) means the**probability**of F occurring given that (or knowing that) event E already occurred. For the above dice example, F = {roll a 5}, and E = {result is an odd number}, and we found that P(F│E) = 33.33%.. Conditional probabilities are useful when presented with data that comes in tables, where different categories of data (say, Male and Female), are broken down into additional sub-categories (say, marriage status).. To compute the probabilities of dependent data, we use the Conditional**Probability**Rule. In ...###### Conditional probability of survival in patients with newly diagnosed glioblastoma<...

TY - JOUR. T1 - Conditional

**probability**of survival in patients with newly diagnosed glioblastoma. AU - Polley, Mei Yin C.. AU - Lamborn, Kathleen R.. AU - Chang, Susan M.. AU - Butowski, Nicholas. AU - Clarke, Jennifer L.. AU - Prados, Michael. PY - 2011/11/1. Y1 - 2011/11/1. N2 - Purpose: The disease outcome for patients with cancer is typically described in terms of estimated survival from diagnosis. Conditional**probability**offers more relevant information regarding survival for patients once they have survived for some time. We report conditional survival probabilities on the basis of 498 patients with glioblastoma multiforme receiving radiation and chemotherapy. For 1-year survivors, we evaluated variables that may inform subsequent survival. Motivated by the trend in data, we also evaluated the assumption of constant hazard. Patients and Methods: Patients enrolled onto seven phase II protocols between 1975 and 2007 were included. Conditional survival probabilities and 95% CIs were ...###### Conditional Probability - Definition, Formula, Probability Of Events - World News Headlines

Conditional

**probability**is the**probability**of an event occurring given that another event has already occurred. The concept is one of the quintessential concepts in**probability**theoryTotal**Probability**RuleThe Total**Probability**Rule (also known as the law of total**probability**) is a fundamental rule in statistics relating to conditional and marginal. Note that conditional probability…###### Slides7 v1 - Sampling Distributions Utku Suleymanoglu UMich Utku Suleymanoglu(UMich Sampling Distributions 1 21 Introduction...

View Notes - Slides7_v1 from ECON 404 at University of Michigan. Sampling Distributions
Utku Suleymanoglu
UMich Utku Suleymanoglu (UMich) Sampling Distributions 1 / 21 Introduction Population

###### Pretest probability assessment derived from attribute matching | BMC Medical Informatics and Decision Making | Full Text

Pretest

**probability**(PTP) assessment plays a central role in diagnosis. This report compares a novel attribute-matching method to generate a PTP for acute coronary syndrome (ACS). We compare the new method with a validated logistic regression equation (LRE). Eight clinical variables (attributes) were chosen by classification and regression tree analysis of a prospectively collected reference database of 14,796 emergency department (ED) patients evaluated for possible ACS. For attribute matching, a computer program identifies patients within the database who have the exact profile defined by clinician input of the eight attributes. The novel method was compared with the LRE for ability to produce PTP estimation |2% in a validation set of 8,120 patients evaluated for possible ACS and did not have ST segment elevation on ECG. 1,061 patients were excluded prior to validation analysis because of ST-segment elevation (713), missing data (77) or being lost to follow-up (271). In the validation set, attribute###### Regular conditional probability - Wikipedia

that is a

**probability**measure defined on a Radon space endowed with the Borel sigma-algebra) and a real-valued random variable T. As discussed above, in this case there exists a regular conditional**probability**with respect to T. Moreover, we can alternatively define the regular conditional**probability**for an event A given a particular value t of the random variable T in the following manner:. ...###### CiteSeerX - An Application of Recurrent Nets to Phone Probability Estimation

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): This paper presents an application of recurrent networks for phone

**probability**estimation in large vocabulary speech recognition. The need for efficient exploitation of context information is discussed###### Patent US6912298 - Object detection using dynamic probability scans - Google Patents

Methods and apparatus, including computer program products, for detecting an object in an image. The techniques include scanning a sequence of pixels in the image, each pixel having one or more property values associated with properties of the pixel, and generating a dynamic

**probability**value for each of one or more pixels in the sequence. The dynamic**probability**value for a given pixel represents a**probability**that the given pixel has neighboring pixels in the sequence that correspond to one or more features of the object. The dynamic**probability**value is generated by identifying a dynamic**probability**value associated with a pixel that immediately precedes the given pixel in the sequence; updating the identified dynamic**probability**value based on the property values of the immediately preceding pixel; and associating the updated**probability**value with the given pixel.###### Bivariate categorical data analysis using normal linear conditional multinomial probability model. - Semantic Scholar

Bivariate multinomial data such as the left and right eyes retinopathy status data are analyzed either by using a joint bivariate

**probability**model or by exploiting certain odds ratio-based association models. However, the joint bivariate**probability**model yields marginal probabilities, which are complicated functions of marginal and association parameters for both variables, and the odds ratio-based association model treats the odds ratios involved in the joint probabilities as working parameters, which are consequently estimated through certain arbitrary working regression models. Also, this later odds ratio-based model does not provide any easy interpretations of the correlations between two categorical variables. On the basis of pre-specified marginal probabilities, in this paper, we develop a bivariate normal type linear conditional multinomial**probability**model to understand the correlations between two categorical variables. The parameters involved in the model are consistently estimated###### 4.2.2 - Sampling Distribution of the Sample Proportion | STAT 500

For this problem, we know $p=0.43$ and $n=50$. First, we should check our conditions for the sampling distribution of the sample proportion.. \(np=50(0.43)=21.5\) and \(n(1-p)=50(1-0.43)=28.5\) - both are greater than 5.. Since the conditions are satisfied, $\hat{p}$ will have a sampling distribution that is approximately normal with mean \(\mu=0.43\) and standard deviation [standard error] \(\sqrt{\dfrac{0.43(1-0.43)}{50}}\approx 0.07\).. \begin{align} P(0.45,\hat{p},0.5) &=P\left(\frac{0.45-0.43}{0.07}, \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}},\frac{0.5-0.43}{0.07}\right)\\ &\approx P\left(0.286,Z,1\right)\\ &=P(Z,1)-P(Z,0.286)\\ &=0.8413-0.6126\\ &=0.2287\end{align}. Therefore, if the true proportion of American who own an iPhone is 43%, then there would be a 22.87% chance that we would see a sample proportion between 45% and 50% when the sample size is 50.. ...

###### pr.probability - Inequality on probability distributions - MathOverflow

I would like to know if the following inequality is satisfied by all

**probability**distributions (or at least some class of**probability**distributions) for all integer $n \geq 2$. $\int_0^{\infty} F(z)^{n-1}(1-\frac{F(z)}{n})\left[zF(z)^{n-2} - \int_0^z F(t)^{n-2}dt\right]f(z)dz$ $\leq \int_0^{\infty} F(z)^{n-1}\left[zF(z)^{n-1} - \int_0^z F(t)^{n-1}dt\right]f(z)dz $. Some comments follow:. 1) F(z) is the cumulative distribution function of any**probability**distribution over positive real numbers. The outer integral runs over the entire support of the distribution, thus, in general, from zero to infinity. f(z) is the**probability**density function. 2) I will be happy even if this is proved for bounded support distributions, in which case, the outer integral runs from 0 to some upper limit H.. 3) Note that both the LHS and the RHS are always non-negative. This is because of the special form of what is inside the square brackets. For both the LHS and the RHS, the second term in the square bracket (i.e. ...###### Joint and Marginal Probability Density Functions of Independent

Let X, Y be independent, standard normal random variables, and let U = X + Y and V = X - Y. (a) Find the joint

**probability**density function of (U, V) and specify its domain. (b) Find the marginal**probability**density function of U.###### Probability estimates for fading and wiretap channels from ideal class zeta functions

In this paper, new

**probability**estimates are derived for ideal lattice codes from totally real number fields using ideal class Dedekind zeta functions. In contrast to previous work on the subject, it is not assumed that the ideal in question is principal. In particular, it is shown that the corresponding inverse norm sum depends not only on the regulator and discriminant of the number field, but also on the values of the ideal class Dedekind zeta functions. Along the way, we derive an estimate of the number of elements in a given ideal with a certain algebraic norm within a finite hypercube. We provide several examples which measure the accuracy and predictive ability of our theorems.###### Visualizing chance: Tackling conditional probability misconceptions

Probabilistic reasoning is essential for operating sensibly and optimally in the 21st century. However, research suggests that students have many difficulties in understanding conditional probabilities and that Bayesian-type problems are replete with misconceptions such as the base rate fallacy and confusion of the inverse. Using a dynamic pachinkogram, a visual representation of the traditional

**probability**tree, we explore six undergraduate**probability**students reasoning processes as they interact with this tool. Initial findings suggest that in simulating a screening situation, the ability to vary the branch widths of the pachinkogram may have the potential to convey the impact of the base rate. Furthermore, we conjecture that the representation afforded by the pachinkogram may help to clarify the distinction between probabilities with inverted conditions ...###### Velocity probability distribution scaling in wall-bounded flows at high Reynolds numbers<...

TY - JOUR. T1 - Velocity

**probability**distribution scaling in wall-bounded flows at high Reynolds numbers. AU - Ge, M. W.. AU - Yang, Xiang I.A.. AU - Marusic, Ivan. PY - 2019/3. Y1 - 2019/3. N2 -**Probability**density functions (PDFs) give well-rounded statistical descriptions of stochastic quantities and therefore are fundamental to turbulence. Wall-bounded turbulent flows are of particular interest given their prevalence in a vast array of applications, but for these flows the scaling of velocity**probability**distribution is still far from being well founded. By exploiting the self-similarity in wall-bounded turbulent flows and modeling velocity fluctuations as results of self-repeating processes, we present a theoretical argument, supported by empirical evidence, for a universal velocity PDF scaling in high-Reynolds-number wall turbulence.. AB -**Probability**density functions (PDFs) give well-rounded statistical descriptions of stochastic quantities and therefore are fundamental to turbulence. ...###### Probability Analysis in Active Trader Pro - Fidelity

The

**Probability**Calculator in Fidelitys Active Trader Pro can help you to determine the**probability**of an underlying equity or index trading above, below, or between certain price targets on a specified date.###### Double and single-bisection methods for subjective probability assessment in a location-scale family - Open Research Online

A common problem is to determine by an elicitation process the parameters of a subjective distribution in a location-scale family. One method is to elicit assessments of the median and one other quartile, equate the assessed median to the location parameter, and estimate the scale from the difference. In a second method, all three quartiles are elicited and then the scale is estimated from the interquartile range. With either method, the location and scale estimates are not made independently. These methods are here studied by introducing

**probability**models for the elicitation process itself. It is shown that the second (full-quartiles) method has important advantages not held by the first.. ...###### st: R: Re: conditional probability

Dear Nico, I would go logistic in that instance (however, take a look at what others do in your research field for managing the same issues). Kindest Regards, Carlo -----Messaggio originale----- Da: [email protected] [mailto:[email protected]] Per conto di [email protected] Inviato: giovedì 21 luglio 2011 23.20 A: Carlo Lazzaro; [email protected] Oggetto: st: Re: conditional

**probability**, Thanks Carlo, but if I want to consider also some personal , characteristics (age, gender, ect). How I can estimate these**probability**? , is it enough a simple probit or logit? , thanks again , Nico , , 2011/7/19 Carlo Lazzaro ,[email protected],: ,, Nico wrote: ,, and prob(B,H) is the jointly**probability**to hiring a black worker ,, conditional on being a H worker ,, ,, ,, High skilled Low skilled Total ,, ---------------------------------------------- ,, Black 20 40 60 ,, ,, Others 30 50 80 ,, ---------------------------------------------- ,, Total 50 90 ...###### z score - When a one-tailed test passes but a two-tailed test does not - Cross Validated

As @Aksakal says, there is nothing weird about this: it is easy to see that the significance level (for a continuous random variable) is equal to the

**probability**of a type I error. So your one-sided and two sided test have the same type I error**probability**. What differs is the power of the two tests. If you know that the alternative is an increase, then for the same type I error**probability**, the type II error**probability**is lower with the one sided test (or the power is higher). In fact, it can be shown that, for a given type I error**probability**(and in the univariate case), the one sided test is the most powerfull you can find, whatever the alternative is. This is thus the UMPT, the Uniformly Most Powerful Test. It all depends on what you want to test. Assume you want to buy lamps from your supplier and the supplier says that the life time of a lamp is 1000 hours (on average). If you want to test these lamps then you will probably not care if these lamps live longer so you will test $H_0: ...###### Algebra 1 Chapter 12 - Data Analysis and Probability - Concept Byte - Conditional Probability - Page 771 2 | GradeSaver

Algebra 1 answers to Chapter 12 - Data Analysis and

**Probability**- Concept Byte - Conditional**Probability**- Page 771 2 including work step by step written by community members like you. Textbook Authors: Hall, Prentice, ISBN-10: 0133500403, ISBN-13: 978-0-13350-040-0, Publisher: Prentice Hall###### Conditional Probability Formula | Basic Probability | Engineering Intro

Definition: If the

**probability**of any event depends on the occurrence of some other event then, it is called conditional**probability**. Formula of conditional....###### How Warren Buffett Used Probability Analysis for Investment Success

Warren Buffett considers one basic principle, elementary

**probability**, the core of his investing philosophy, helping him to identify tremendous stock opportunities.###### Different types of target probability have different prefrontal consequences | [email protected]

One of the factors known to affect target detection is target

**probability**. It is clear, though, that target**probability**can be manipulated in different ways. Here, in order to more accurately characterize the effects of target**probability**on frontal engagement, we examined the effects of two commonly-used but different target**probability**manipulations on neural activity. We found that manipulations that affected global stimulus class**probability**had a pronounced effect on ventrolateral prefrontal cortex and the insula, an effect which was absent with manipulations that only affected the likelihood of specific target stimuli occurring. This latter manipulation only modulated activity in dorsolateral prefrontal cortex and the precentral sulcus. Our data suggest two key points. First, different types of target**probability**have different neural consequences, and may therefore be very different in nature. Second, the data indicate that ventral and dorsal portions of prefrontal cortex respond to ...###### Conditional probability tree diagram example (video) | Khan Academy

Using a tree diagram to work out a conditional

**probability**question. If someone fails a drug test, what is the**probability**that they actually are taking drugs?###### What is prior probability? definition and meaning - BusinessDictionary.com

Definition of prior probability:

**Probability**that a certain event or outcome will occur. For example, economists may believe there is an 80%**probability**that the economy will grow by more than 2% in the coming year. Prior**probability**...###### Probability Distributions - CenterSpace

NMath Stats from CenterSpace Software is a .NET class library that provides functions for statistical computation and biostatistics, including descriptive statistics,

**probability**distributions, combinatorial functions, multiple linear regression, hypothesis testing, analysis of variance, and multivariate statistics.. NMath Stats provides classes for computing the**probability**density function (PDF), the cumulative distribution function (CDF), the inverse cumulative distribution function, and random variable moments for a variety of**probability**distributions, including beta, binomial, chi-square, exponential, F, gamma, geometric, logistic, log-normal, negative binomial, normal (Gaussian), Poisson, Students t, triangular, and Weibull distributions. The distribution classes share a common interface, so once you learn how to use one distribution class, its easy to use any of the others. This functionality can be used from any .NET language including VB.NET and F#.. The NMath Stats library is part ...###### D2D Communication for Enabling Internet-of-Things: Outage Probability Analysis - IEEE Journals & Magazine

IEEE Xplore, delivering full text access to the worlds highest quality technical literature in engineering and technology. | IEEE Xplore

###### Simulink USS block - probability analysis | Physics Forums - The Fusion of Science and Community

I was under the impression that the uncertain state block within the robust control toolbox was the direction to go, but so far I havent been able to decipher the help information to learn how to use and apply it. (And as far as I can understand, it would be ideal b/c I can also run the model varying all the uncertain variables a certain number of times from the command line ...

###### Download free e-book on error probability in AWGN

Download free e-book on error

**probability**in AWGN for BPSK, QPSK, 4-PAM, 16QAM, 16PSK and more. Matlab/Octave simulation models provided.###### Download free e-book on error probability in AWGN

Download free e-book on error

**probability**in AWGN for BPSK, QPSK, 4-PAM, 16QAM, 16PSK and more. Matlab/Octave simulation models provided.###### circular error probability

the extent to which ordnance will miss the target A Gulf War usage, from the illustration by concentric rings on a chart: There was something called circular error

**probability**, which simply meant the area where a bomb or missile was…###### Error probabilities in random-phase binary optical signalling (Corresp.) - IEEE Journals & Magazine

Expressions for the error probabilities in the detection of binary coherent orthogonal equienergy optical signals of random phase in thermal background noi

###### Prior probability distribution | World Library - eBooks | Read eBooks online

Prior

**probability**distribution: lt;div class=hatnote|>Not to be confused with |a priori probability|.| |||||||||This article in... World Heritage Encyclopedia, the aggregation of the largest online encyclopedias available, and the most definitive collection ever assembled.###### CiteSeerX - Citation Query Base-calling of automated sequencer traces using phred. II. error probabilities

CiteSeerX - Scientific documents that cite the following paper: Base-calling of automated sequencer traces using phred. II. error probabilities

###### Sankhya: The Indian Journal of Statistics

Sankhya: The Indian Journal of Statistics. 2001, Volume 63, Series B, Pt. 3, pp. 251--269. UNIFIED BAYESIAN AND CONDITIONAL FREQUENTIST TESTING FOR DISCRETE DISTRIBUTIONS. By. SARAT C. DASS, Michigan State University. SUMMARY. Testing of hypotheses for discrete distributions is considered in this paper. The goal is to develop conditional frequentist tests that allow the reporting of data-dependent error probabilities such that the error probabilities have a strict frequentist interpretation and also reflect the actual amount of evidence in the observed data. The resulting randomized tests are also seen to be Bayesian tests, in the strong sense that the reported error probabilities are also the posterior probabilities of the hypotheses. The new procedure is illustrated for a variety of testing situations, both simple and composite, involving discrete distributions. Testing linkage heterogeneity with the new procedure is given as an illustrative example.. AMS (1991) subject classification. ...

###### Normal rvs bb - THE NORMAL DISTRIBUTION OTHER CONTINUOUS DISTRIBUTIONS AND SAMPLING DISTRIBUTION 1 In its standardized form the...

View Notes - Normal rvs_bb from BUS 45730 at Carnegie Mellon. THE NORMAL DISTRIBUTION, OTHER CONTINUOUS DISTRIBUTIONS, AND SAMPLING DISTRIBUTION
1. In its standardized form, the normal distribution

###### Statistics - (Probability|Sampling) Distribution [Gerardnico]

Mode: for a discrete random variable, the value with highest

**probability**(the location at which the**probability**mass function has its peak); for a continuous random variable, the location at which the**probability**density function has its peak ...###### Extracting Risk-Neutral Probability Distributions from Option Prices Using Trading Volume as a Filter

Downloadable! This paper introduces a new technique to infer the risk-neutral

**probability**distribution of an asset from the prices of options on this asset. The technique is based on using the trading volume of each option as a proxy of the informativeness of the option. Not requiring the implied**probability**distribution to recover exactly the market prices of the options allows us to weight each option by a function of its trading volume. As a result, we obtain implied**probability**distributions that are both smoother and should be more reflective of fundamentals.###### OSA | Image mensuration by maximum a posteriori probability estimation*

We present an algorithm for pulse width estimation from blurred and nonlinear observations in the presence of signal dependent noise. The main application is the accurate measurement of image sizes on film. The problem is approached by modeling the signal as a discrete position finite state Markov process, and then determining the transition location that maximizes the a posteriori

**probability**. It turns out that the blurred signal can be represented by a trellis, and the maximum a posteriori**probability**(MAP) estimation is obtained by finding the minimum cost path through the trellis. The latter is done by the Viterbi algorithm. Several examples are presented. These include the measurement of the width of a road in an aerial photo taken at an altitude of 5000 ft. The resulting width estimate is accurate to within a few inches.. © 1978 Optical Society of America. Full Article , PDF Article ...###### PPT - Module 2: Probability, Random Variables & Probability Distributions Module 2b PowerPoint Presentation - ID:1590320

Module 2:

**Probability**, Random Variables &**Probability**Distributions Module 2b . Random Variable. What is a random variable? When experiments lead to categorical results, we assign numbers to the random variable: e.g., defective = 0, functional = 1 Why do we assign numbers?...###### probability distribution law是什么意思 海词词典

海词词典，最权威的学习词典，专业出版probability distribution law是什么意思，probability distribution law的用法，probability distribution law翻译和读音等详细讲解。海词词典：学习变容易，记忆很深刻。

###### Classroom Activities: Demonstrating Probability, Simulations, and Probability Distributions - Texas Instruments - content

This activity demonstrates the

**probability**of an event happening with the simulation of a coin toss. Students will learn how probabilities can be computed. They will simulate distributions to check the reasonableness of the results. They also explore various**probability**distributions.###### pr.probability - Can you explain the description of the Lovasz Local Lemma by Moser+Tardos? - MathOverflow

The Lovász Local Lemma (or LLL) concerns itself with the

**probability**of avoiding a collection of bad events A, given that the set of events is nearly independent (each bad event A ∈ A has**probability**which is bounded above in terms of the number of other events A, A, etc. from which it is not independent), there is a non-zero**probability**of avoiding all of the bad events simultaneously. The original presentation seems to be the Lemma on page 8 of this pdf (the link to which can be found on Wikipedias page on the LLL); several other papers present it in a similar fashion.. In the article [arXiv:0903.0544], restricting to the setting where the bad events of the LLL are defined in terms of a**probability**space of independently distributed bits, Moser and Tardos present a probabilistic algorithm for sampling from the event space until an event is found which avoids all bad events, which requires at most polynomially many samples with high**probability**. However, their characterization of ...###### Relative Probabilities - Week 2 | Coursera

Video created by Duke University for the course Behavioral Finance. Welcome to the second week. In this session, we will discover how our minds are inclined to distort probabilities, and either underestimate or overestimate the likelihood of ...

###### Chi-Square Distribution Probability Density Function (PDF) Calculator - Analytics Calculators

Compute the

**probability**density function (PDF) for the chi-square distribution, given the degrees of freedom and the point at which to evaluate the function x. The chi-square distribution PDF identifies the relative likelihood that an associated random variable will have a particular value, and is very useful for analytics studies that consider chi-square distribution probabilities.###### Human error probability assessment during maintenance activities of marine systems - Open Access Repository

Objective: The objective of this study is to develop Human Error

**Probability**model considering various internal and external factors affecting the seafarers performance.Background: Maintenance operations on-board ships are highly demanding. Maintenanceoperations are intensive activities requiring high man-machine interactions in challenging and evolving conditions. The evolving conditions are weather conditions, workplace temperature, ship motion, noise and vibration and workload and stress. For example, extreme weather condition affects the seafarers performance hence increasing the chances of error and consequently, can cause injuries or fatalities to personnel. An effective human error**probability**model is required to better manage maintenance on board ships. The developed model would assist in developing and maintaining effective risk management protocols.Method: The human error**probability**model is developed using**probability**theory applied to Bayesian Network. The model is tested using ...###### Bayes Theorem - The Anti-Aging Medical Clinic

Bayes theorem is a

**probability**principle set forth by the English mathematician Thomas Bayes (1702-1761). Bayes theorem is of value in medical decision-making and some of the biomedical sciences. Bayes theorem is employed in clinical epidemiology to determine the**probability**of a particular disease in a group of people with a specific characteristic on the basis of the overall rate of that disease and of the likelihood of that specific characteristic in healthy and diseased individuals, respectively. A common application of Bayes theorem is in clinical decision making where it is used to estimate the**probability**of a particular diagnosis given the appearance of specific signs, symptoms, or test outcomes. For example, the accuracy of the exercise cardiac stress test in predicting significant coronary artery disease (CAD) depends in part on the pre-test likelihood of CAD: the prior**probability**in Bayes theorem. In technical terms, in Bayes theorem the impact of new data on the merit of ...###### Calibrated probability assessment - Wikipedia

Calibrated

**probability**assessments are subjective probabilities assigned by individuals who have been trained to assess probabilities in a way that historically represents their uncertainty. In other words, when a calibrated person says they are 80% confident in each of 100 predictions they made, they will get about 80% of them correct. Likewise, they will be right 90% of the time they say they are 90% certain, and so on. Calibration training improves subjective probabilities because most people are either overconfident or under-confident (usually the former). By practicing with a series of trivia questions, it is possible for subjects to fine-tune their ability to assess probabilities. For example, a subject may be asked: True or False: A hockey puck fits in a golf hole Confidence: Choose the**probability**that best represents your chance of getting this question right... 50% 60% 70% 80% 90% 100% If a person has no idea whatsoever, they will say they are only 50% confident. If they are ...###### How Quantifying Probability Assessments Influences Analysis and Decision Making: Experimental Evidence from National Security...

National security is one of many fields where public officials offer imprecise

**probability**assessments when evaluating high-stakes decisions. This practice is often justified with arguments about how quantifying subjective judgments would bias analysts and decision makers toward overconfident action. We translate these arguments into testable hypotheses, and evaluate their validity through survey experiments involving national security professionals.###### Cost-Sensitive Multi-class Classification from Probability Estimates - VideoLectures.NET

For two-class classification, it is common to classify by setting a threshold on class

**probability**estimates, where the threshold is determined by {ROC} curve analysis. An analog for multi-class classification is learning a new class partitioning of the multiclass**probability**simplex to minimize empirical misclassification costs. We analyze the interplay between systematic errors in the class**probability**estimates and cost matrices for multi-class classification. We explore the effect on the class partitioning of five different transformations of the cost matrix. Experiments on benchmark datasets with naive Bayes and quadratic discriminant analysis show the effectiveness of learning a new partition matrix compared to previously proposed methods.###### Probability distribution - Wikipedia

In

**probability**theory and statistics, a**probability**distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment. In more technical terms, the**probability**distribution is a description of a random phenomenon in terms of the probabilities of events. For instance, if the random variable X is used to denote the outcome of a coin toss (the experiment), then the**probability**distribution of X would take the value 0.5 for X = heads, and 0.5 for X = tails (assuming the coin is fair). Examples of random phenomena can include the results of an experiment or survey. A**probability**distribution is specified in terms of an underlying sample space, which is the set of all possible outcomes of the random phenomenon being observed. The sample space may be the set of real numbers or a set of vectors, or it may be a list of non-numerical values; for example, the sample space of a coin flip would be {heads, tails} .**Probability**distributions ...###### Probability and statistics EBook - Socr

This section will establish the groundwork for Bayesian Statistics.

**Probability**, Random Variables, Means, Variances, and the Bayes Theorem will all be discussed. Bayes Theorem Bayes theorem is associated with**probability**statements that relate conditional and marginal properties of two random events. These statements are often written in the form the**probability**of A, given B and denoted P(A,B) = P(B,A)*P(A)/P(B) where P(B) not equal to 0. P(A) is often known as the Prior**Probability**(or as the Marginal**Probability**) P(A,B) is known as the Posterior**Probability**(Conditional**Probability**) P(B,A) is the conditional**probability**of B given A (also known as the likelihood function) P(B) is the prior on B and acts as the normalizing constant. In the Bayesian framework, the posterior**probability**is equal to the prior belief on A times the likelihood function given by P(B,A). Media:Mario.jpg ...###### Probability and statistics EBook - Socr

This section will establish the groundwork for Bayesian Statistics.

**Probability**, Random Variables, Means, Variances, and the Bayes Theorem will all be discussed. Bayes Theorem Bayes theorem is associated with**probability**statements that relate conditional and marginal properties of two random events. These statements are often written in the form the**probability**of A, given B and denoted P(A,B) = P(B,A)*P(A)/P(B) where P(B) not equal to 0. P(A) is often known as the Prior**Probability**(or as the Marginal**Probability**) P(A,B) is known as the Posterior**Probability**(Conditional**Probability**) P(B,A) is the conditional**probability**of B given A (also known as the likelihood function) P(B) is the prior on B and acts as the normalizing constant. In the Bayesian framework, the posterior**probability**is equal to the prior belief on A times the likelihood function given by P(B,A). ...###### IEICE Trans - On Bit Error Probabilities of SSMA Communication Systems Using Spreading Sequences of Markov Chains

We study asynchronous SSMA communication systems using binary spreading sequences of Markov chains and prove the CLT (central limit theorem) for the empirical distribution of the normalized MAI (multiple-access interference). We also prove that the distribution of the normalized MAI for asynchronous systems can never be Gaussian if chains are irreducible and aperiodic. Based on these results, we propose novel theoretical evaluations of bit error probabilities in such systems based on the CLT and compare these and conventional theoretical estimations based on the SGA (standard Gaussian approximation) with experimental results. Consequently we confirm that the proposed theoretical evaluations based on the CLT agree with the experimental results better than the theoretical evaluations based on the SGA. Accordingly, using the theoretical evaluations based on the CLT, we give the optimum spreading sequences of Markov chains in terms of bit error probabilities. ...

###### Interpreting Probability Models | SAGE Publications Inc

The author provides a stepwise approach for evaluating the results of fitting

**probability**models to data as the focus for the book . . . . All this is packaged very systematically . . . . the booklet is highly successful in showing how**probability**models can be interpreted.. --Technometrics. Tim Futing Liaos Interpreting**Probability**Models. . . is an advanced text . . . . Liaos text is more theoretical, but is well exemplified using case studies . . . . this is a text for the more advanced statistician or the political scientist with strong leanings in this direction!. --John G. Taylor in Technology and Political Science What is the**probability**that something will occur, and how is that**probability**altered by a change in some independent variable? Aimed at answering these questions, Liao introduces a systematic way for interpreting a variety of**probability**models commonly used by social scientists. Since much of what social scientists study are measured in noncontinuous ways and thus cannot ...###### Proving This! - Hoffmann on Bayes Theorem - Vridar

How can it be useful in determining whether events actually transpired in the past, that is, when the sample field itself consists of what has already occurred (or not occurred) and when B is the

**probability**of it having happened?. Statements like this (and its ilk; there are at least 3 of them in Hoffmans quotes) demonstrate a complete lack of understanding of both**probability**and Bayes theorem. Heres a real-world, routine application of Bayes theorem in medicine (it was in my**probability**textbook in college, although the disease wasnt specified): Lets say 1% of the population is HIV+. Furthermore, HIV antibody tests have a 1% false positive rate (which used to be true, but now its much lower) and a 0.1% false negative rate (this number is not so important). If you take an HIV test and the result is positive, what is the**probability**that you actually have the disease? Using Bayes theorem, one gets around 50%. Note that were not talking about future possibilities here - you either ...###### Kipling - Incorporation of Transition Probabilities

The computed transition

**probability**matrix reflects the characteristics of the particular sequence of observed facies employed in the computation. These particular characteristics may diverge somewhat from the expected sequence characteristics for a region. For example, a transition from facies A to facies B may never occur in the selected core, although it is known to occur elsewhere in the study area. To overcome this shortcoming, Kipling allows the user to modify the computed TPM to better match geological expectations. This is accomplished simply by editing the entries in the matrix. Because the modified facies membership probabilities are linked by formulas to the transition**probability**matrix, any changes to this matrix will automatically be reflected in the modified probabilities and facies predictions, and also in any existing plots of those values. This allows you to easily investigate the influence of the transition**probability**values on the sequence of predicted facies. Previous ...###### Bayes Theorem (Work) - Charlotte Mecklenburg Library

This program covers the important topic Bayes Theorem in

**Probability**and Statistics. We begin by discussing what Bayes Theorem is and why it is important. Next, we solve several problems that involve the essential ideas of Bayes Theorem to give students practice with the material. The entire lesson is taught by working example problems beginning with the easier ones and gradually progressing to the harder problems. Emphasis is placed on giving students confidence in their skills by gradual repetition so that the skills learned in this section are committed to long-term memory. (TMW Media Group, USA)###### Bayes Theorem, A Quick Introduction | Maverick Christian

In the situation where hypothesis H explains evidence E, Pr(E,H) basically becomes a measure of the hypothesiss explanatory power. Pr(H,E) is called the posterior

**probability**of H. Pr(H) is the prior**probability**of H, and Pr(E) is the prior**probability**of the evidence (very roughly, a measure of how surprising it is that wed find the evidence). Prior probabilities are probabilities relative to background knowledge, e.g. Pr(E) is the likelihood that wed find evidence E relative to our background knowledge. Background knowledge is actually used throughout Bayes theorem however, so we could view the theorem this way where B is our background knowledge ...###### Elementary Statistics: Picturing the World Plus MyLab Statistics with Pearson eText -- Access Card Package, 5th Edition

Part One. Descriptive Statistics. 1. Introduction to Statistics. 1.1. An Overview of Statistics. 1.2. Data Classification. 1.3. Data Collection and Experimental Design. 2. Descriptive Statistics. 2.1. Frequency Distributions and Their Graphs. 2.2. More Graphs and Displays. 2.3. Measures of Central Tendency. 2.4. Measures of Variation. 2.5. Measures of Position. Part Two.

**Probability**&**Probability**Distributions. 3.**Probability**. 3.1. Basic Concepts of**Probability**and Counting. 3.2. Conditional**Probability**and the Multiplication Rule. 3.3. The Addition Rule. 3.4. Additional Topics in**Probability**and Counting. 4. Discrete**Probability**Distributions. 4.1.**Probability**Distributions. 4.2. Binomial Distributions. 4.3. More Discrete**Probability**Distributions. 5. Normal**Probability**Distributions. 5.1. Introduction to Normal Distributions and the Standard Normal Distribution. 5.2. Normal Distributions: Finding Probabilities. 5.3. Normal Distributions: Finding Values. 5.4. Sampling Distributions and the ...###### Assessing Risk Factors with Bayes Theorem

A really good clinician not only embraces Bayes Theorem, they live and die by Bayes Theorem. Any veteran PA or NP makes decisions based on Bayes Theorem.

###### A practical approach for incorporating dependence among fields in probabilistic record linkage | BMC Medical Informatics and...

Methods for linking real-world healthcare data often use a latent class model, where the latent, or unknown, class is the true match status of candidate record-pairs. This commonly used model assumes that agreement patterns among multiple fields within a latent class are independent. When this assumption is violated, various approaches, including the most commonly proposed loglinear models, have been suggested to account for conditional dependence. We present a step-by-step guide to identify important dependencies between fields through a correlation residual plot and demonstrate how they can be incorporated into loglinear models for record linkage. This method is applied to healthcare data from the patient registry for a large county health department. Our method could be readily implemented using standard software (with code supplied) to produce an overall better model fit as measured by BIC and deviance. Finding the most parsimonious model is known to reduce bias in parameter estimates. This novel

###### Evaluation of the usefulness of a D dimer test in combination with clinical pretest probability score in the prediction and...

TY - JOUR. T1 - Evaluation of the usefulness of a D dimer test in combination with clinical pretest

**probability**score in the prediction and exclusion of Venous Thromboembolism by medical residents. AU - Owaidah, Tarek. AU - AlGhasham, Nahlah. AU - AlGhamdi, Saad. AU - AlKhafaji, Dania. AU - ALAmro, Bandar. AU - Zeitouni, Mohamed. AU - Skaff, Fawaz. AU - AlZahrani, Hazzaa. AU - AlSayed, Adher. AU - Elkum, Naser. AU - Moawad, Mahmoud. AU - Nasmi, Ahmed. AU - Hawari, Mohannad. AU - Maghrabi, Khalid. PY - 2014. Y1 - 2014. N2 - Introduction: Venous thromboembolism (VTE) requires urgent diagnosis and treatment to avoid related complications. Clinical presentations of VTE are nonspecific and require definitive confirmation by imaging techniques. A clinical pretest**probability**(PTP) score system helps predict VTE and reduces the need for costly imaging studies. D-dimer (DD) assay has been used to screen patients for VTE and has shown to be specific for VTE. The combined use of PTP and DD assay may ...###### Essay:Bayes theorem and jurisprudence - RationalWiki

It may not look like much, but Bayes theorem is ridiculously powerful. It is used in medical diagnostics, self-driving cars, identifying email spam, decoding DNA, language translation, facial recognition, finding planes lost at the bottom of the sea, machine learning, risk analysis, image enhancement, analyzing Who wrote the Federalist Papers, Nate Silvers FiveThirtyEight.com, astrophysics, archaeology and psychometrics (among other things).[5][6][7] If you are into science, this equation should give you some serious tumescence. There are some great videos on the web about how to do conditional

**probability**so check them out if you are wishing to know more about it. External links are provided on the bottom of this page. Let us now use breast cancer screening as a example of how Bayes theorem is used in real life. Please keep in mind that this is just an illustration. If you have concerns about your health, then you should consult with an oncologist. Let us say that a person is a 40-year-old ...###### Concepts

Bayes Theorem stated is, the conditional

**probability**of A given B is the conditional**probability**of B given A scaled by the relative**probability**of A compared to B. I find it easier to understand through a practical explanation. Lets say you are having a medical test performed at the recommendation of your doctor, who recommends … Continue reading A Brief Introduction to Bayes Theorem. ...###### nmaynes1 - Page 2 - Nathans Blog

Bayes Theorem stated is, the conditional

**probability**of A given B is the conditional**probability**of B given A scaled by the relative**probability**of A compared to B. I find it easier to understand through a practical explanation. Lets say you are having a medical test performed at the recommendation of your doctor, who recommends … Continue reading A Brief Introduction to Bayes Theorem. ...###### Carrier, Bayes Theorem, and Jesus Existence - The Bart Ehrman Blog

As it so happens, I am finishing a PhD in the theory of

**probability**. I may not be recognized as a world-class expert on the subject, but I may be able to contribute some useful thoughts here.. Anyway, I agree with you that the Bayesian approach cannot produce precise numerical values for the**probability**of historical events. So were not going to get a definite**probability**of Jesus existence that way. I do think, however, that the Bayesian framework can still be useful in a more qualitative way.. The basic Bayesian idea is that we have some set of mutually exclusive hypotheses H1, H2, and so on. We assign some initial (prior)**probability**to each of those hypotheses. We then make some observation O. There will be some conditional**probability**P(O,H1), which is the**probability**of observing O given that H1 is true. Likewise for all the other hypotheses. These conditional probabilities are called the likelihoods. Bayes theorem then allows us to move to a final**probability**P(H1,O), which is the ...###### Comparing linear probability model coefficients across groups - Professorer og lektorer

This article offers a formal identification analysis of the problem in comparing coefficients from linear

**probability**models between groups. We show that differences in coefficients from these models can result not only from genuine differences in effects, but also from differences in one or more of the following three components: outcome truncation, scale parameters and distributional shape of the predictor variable. These results point to limitations in using linear**probability**model coefficients for group comparisons. We also provide Monte Carlo simulations and real examples to illustrate these limitations, and we suggest a restricted approach to using linear**probability**model coefficients in group comparisons ...###### Discrete Probability Models and Methods - Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding ...

The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoffs bound, Hoeffdings inequality,

###### Veritasium: Bayes Theorem explained - paulvanderlaken.com

Veritasium makes educational videos, mostly about science, and recently they recorded one offering an intuitive explanation of Bayes Theorem. They guide the viewer through Bayes thought process coming up with the theory, explain its workings, but also acknowledge some of the issues when applying Bayesian statistics in society. The thing we forget in Bayes Theorem is…

###### A Conditional Probability Mass Function - Wolfram Demonstrations Project

The

**probability**mass function of a pair of discrete random variables is the function The conditional mass function of given is the function Thus the mass function lefthand plot computes probabilities of intersections while the conditional mass function righthand plot computes conditional probabilities For each value the slice through the conditional mass function at that value gives the distribu###### Approaching 1/2 Probability - Analysis and Calculus - Science Forums

I ran into a coin flip problem where flipping 4 coins has a 6/16 or 3/8

**probability**of landing 2 heads and 2 tails. I expected this value to be 1/2, because you have a 50% chance of getting heads or tails. Then that is only 6 of the possible 16 outcomes, instead of 8. Then I realized that the num...###### Using Bayes Theorem for Command Input: Principle, Models, and Applications - Google Research

Entering commands on touchscreens can be noisy, but existing interfaces commonly adopt deterministic principles for deciding targets and often result in errors. Building on prior research of using Bayes theorem to handle uncertainty in input, this paper formalized Bayes theorem as a generic guiding principle for deciding targets in command input (referred to as BayesianCommand), developed three models for estimating prior and likelihood probabilities, and carried out experiments to demonstrate the effectiveness of this formalization. More specifically, we applied BayesianCommand to improve the input accuracy of (1) point-and-click and (2) word-gesture command input. Our evaluation showed that applying BayesianCommand reduced errors compared to using deterministic principles (by over 26.9% for point-and-click and by 39.9% for word-gesture command input) or applying the principle partially (by over 28.0% and 24.5%).. ...

###### Conditional probability, Independence of events. video lecture by Prof Prabha Sharma of IIT Kanpur

Conditional

**probability**, Independence of events. tutorial of**Probability**Theory and Applications course by Prof Prabha Sharma of IIT Kanpur. You can download the course for FREE !###### September 2018 Fed Rate Hike Probability & Analysis

Federal Reserve rate hikes can send shockwaves through stock markets and put many people to sleep. But just because the nitty-gritty of the countrys fiscal policy isnt exciting to most does not mean were unaffected.. For one thing, the Feds seven rate hikes since Dec. 2015 have cost credit card users an extra $9.65 billion in interest to date. That figure will swell by at least $1.6 billion this year if the Fed raises its target rate on September 26, as expected. One more rate hike is expected from the Fed in the final quarter of 2018, too.. The rising cost of debt puts a lot of pressure on consumers. For example, it will take the average person in Magnolia, TX nearly 13 years to pay off his or her balance. With that in mind, WalletHub also conducted a nationally representative survey to gauge public sentiment. And while most people still have some homework to do, weve got no shortage of opinions.. Below, you can find everything you need to know about Federal Reserve interest rate ...

###### Concurrent outbreak of influenza A and dengue infection: a probability analysis for dengue and influenza A coinfection Yasri S,...

The Egyptian Journal of Chest Diseases and Tuberculosis, The Official Journal of Egyptian Society of Chest Diseases and Tuberculosis AND Arab Thoracic Association

###### Urinary tract infection (peds) - WikEM

Patient A: Female patient in ED, ,1 year old, fever with no definitive source on examination, pretest

**probability**of UTI is 7%. Patient B: Male patient in ED, ,1 year old, circumcised, fever with no definitive source on examination, pretest**probability**of UTI is 0.5%. Patient C: Male patient in ED, ,1 year old, uncircumcised, fever with no definitive source on examination, pretest**probability**of UTI is 8%. Patient D: Female patient in ED, 2-6 years old, no fever but GU symptoms, pretest**probability**of UTI is 6.5%. Patient E: Female patient in ED, adolescent age range, no fever but urinary symptoms, pretest**probability**of UTI is 9% ...###### Conditional Probability: Game Show with Monty Interactive for 9th - 12th Grade | Lesson Planet

This Conditional Probability: Game Show with Monty Interactive is suitable for 9th - 12th Grade. The car is behind door one - no wait, it is behind door three. An interactive allows learners to visualize the Monty Hall problem.

###### Statistics and Probability

1. Random events,

**probability**,**probability**space.. 2. Conditional**probability**, Bayes theorem, independent events.. 3. Random variable - definition, distribution function.. 4. Characteristics of random variables.. 5. Discrete random variable - examples and usage.. 6. Continuous random variable - examples and usage.. 7. Independence of random variables, sum of independent random variables.. 8. Transformation of random variables.. 9. Random vector, covariance and correlation.. 10. Central limit theorem.. 11. Random sampling and basic statistics.. 12. Point estimation, method of maximum likelihood and method of moments, confidence intervals.. 13. Confidence intervals.. 14. Hypotheses testing.. ...###### probability - Bayesian Network: Calculate probabillity of child node given all probabillity tables - Cross Validated

As you have described it, there is not enough information to know how to conditional

**probability**of the child from the parents. You have described that you have the marginal probabilities of each node; this tells you nothing about the relationship between nodes. For example, if you observed that 50% of people in a study take a drug (and the others take placebo), and then you later note that 20% of the people in the study had an adverse outcome, you do not have enough information to know how the**probability**of the child (adverse outcome) depends on the**probability**of the parent (taking the drug). You need to know the joint distribution of the parents and child to learn the conditional distribution. The joint distribution requires that you know the**probability**of the combination of all possible values for the parents and the children. From the joint distribution, you can use the definition of conditional**probability**to find the conditional distribution of the child on the parents.. ...###### Bayes theorem - Lesswrongwiki

A law of

**probability**that describes the proper way to incorporate new evidence into prior probabilities to form an updated**probability**estimate. Bayesian rationality takes its name from this theorem, as it is regarded as the foundation of consistent rational reasoning under uncertainty. A.k.a. Bayess Theorem or Bayess Rule. The theorem commonly takes the form: ...###### Similar papers for Mutagenic probability estimation of chemical compounds by a novel molecular electrophilicity vector and...

MOTIVATION
Mutagenicity is among the toxicological end points that pose the highest concern. The accelerated pace of drug discovery has heightened the need for efficient prediction methods. Currently, most available tools fall short of the desired degree of accuracy, and can only provide a binary classification. It is of significance to develop a discriminative and informative model for the mutagenicity prediction.
RESULTS
Here we developed a mutagenic

**probability**prediction model addressing the problem, based on datasets covering a large chemical space. A novel molecular electrophilicity vector (MEV) is first devised to represent the structure profile of chemical compounds. An extended support vector machine (SVM) method is then used to derive the posterior probabilistic estimation of mutagenicity from the MEVs of the training set. The results show that our model gives a better performance than TOPKAT (http://www.accelrys.com) and other previously published methods. In addition, a confidence level###### Probability density function - Simple English Wikipedia, the free encyclopedia

but this is not a continuous function, as only the numbers 1 to 6 are possible. In contrast, two people will not have the same height, or the same weight. Using a

**probability**density function, it is possible to determine the**probability**for people between 180 centimetres (71 in) and 181 centimetres (71 in), or between 80 kilograms (176.4 lb) and 81 kilograms (178.6 lb), even though there are infinitely many values between these two bounds. ...###### Review of Basic Probability - Background Material | Coursera

Were now going to review some of the basic concepts from

**probability**. Well discuss expectations and variances, well discuss Bayes theorem, and well also review some of the commonly used distributions from**probability**theory. These include the binomial and Poisson distributions as well as the normal and log normal distributions. First of all, I just want to remind all of us whats a cumulative distribution function is. A CDF, a cumulative distribution function is f of x, were going to use f of x to denote the CDF and we define f of x to be equal to a**probability**that a random variable x is less than or equal to little x. Okay. We also, for discrete random variables, have whats called a**probability**mass function. Okay. And a**probability**mass function, which well denote with little p, it satisfies the following properties. P is greater than or equal to 0, and for all events, A, we have that the**probability**that x is in A, okay, is equal to the sum of p of x over all those outcomes x that ...###### Determination of the Confidence Intervals for Multimodal Probability Density Functions | AVESİS

The shortest interval approach can be solved as an optimization problem, while the equally tailed approach is determined by using the distribution function. The equal density approach is proposed instead of the optimization problem for determining the shortest confidence interval. It is applied to multimodal

**probability**density functions to determine the shortest confidence interval. Furthermore, the equal density and optimization approach for the shortest confidence interval and the equally tailed approach were applied to numerical examples and their results were compared. Nevertheless, the main subject of this study is the calculation of the shortest confidence intervals for any multimodal distribution. ...###### Course introduction - Probability and Bayes Theorem | Coursera

Video created by Universidade da Califórnia, Santa Cruz for the course Bayesian Statistics: From Concept to Data Analysis. In this module, we review the basics of

**probability**and Bayes theorem. In Lesson 1, we introduce the different paradigms ...###### Testing the stability of implied probability density functions

Downloadable! Implied

**probability**density functions (PDFs) estimated from cross-sections of observed option prices are gaining increasing attention amongst academics and practitioners. To date, however, little attention has been paid to the robustness of these estimates or to the confidence that users can place in the summary statistics (for example the skewness or the 99th percentile) derived from fitted PDFs. This paper begins to address these questions by examining the absolute and relative robustness of two of the most common methods for estimating implied PDFs - the double-lognormal approximating function and the smoothed implied volatility smile methods. The changes resulting from randomly perturbing quoted prices by no more than a half tick provide a lower bound on the confidence intervals of the summary statistics derived from the estimated PDFs. Tests are conducted using options contracts tied to short sterling futures and the FTSE 100 index - both trading on the London International Financial###### Quantifying probabilities of volcanic events: The example of volcanic hazard at Mount Vesuvius

We describe an event tree scheme to quantitatively estimate both long- and short-term volcanic hazard. The procedure is based on a Bayesian approach that produces a

**probability**estimation of any possible event in which we are interested and can make use of all available information including theoretical models, historical and geological data, and monitoring observations. The main steps in the procedure are (1) to estimate an a priori**probability**distribution based upon theoretical knowledge, (2) to modify that using past data, and (3) to modify it further using current monitoring data. The scheme allows epistemic and aleatoric uncertainties to be dealt with in a formal way, through estimation of**probability**distributions at each node of the event tree. We then describe an application of the method to the case of Mount Vesuvius. Although the primary intent of the example is to illustrate the methodology, one result of this application merits...###### Probability distribution

probability density function (pdf) over the entire area of the dartboard (and, perhaps, the wall surrounding it) must be equal to 1, since each dart must land somewhere.. The concept of the

**probability**distribution and the random variables which they describe underlies the mathematical discipline of**probability**theory, and the science of statistics. There is spread or variability in almost any value that can be measured in a population (e.g. height of people, durability of a metal, etc.); almost all measurements are made with some ...