Probabilistic analyses

It is essential to have a random data source for any meaningful statistical analysis. Unfortunately, in reverse engineering this fundamental requirement is more difficult to satisfy than in most other fields. The level of randomness is often a concern in many reverse engineering projects. Both economic and technical restrictions have imposed some limits on data randomness in reverse engineering. Practically speaking, most reverse engineering projects only have a limited number of parts to work with, partially due to fiscal consideration and partially due to part availability. 

Many reverse engineering projects start with a few or even only one OEM part. It might already be a monumental task to get just that one patented ball bearing from the OEM that owns the proprietary data of the bearing and refuses to sell any new part to the company trying to reverse engineer it. To obtain multiple new OEM parts from a sole-source supplier to satisfy the statistical randomness requirement can be very difficult at times. A statistical requirement of multiple OEM parts might impose a prohibitively expensive 

After the establishment of performance standards for comparison, statistical analysis in the probabilistic method can be another task. Chapter 6 presented an introductory discussion on the statistics about how many test sample parts are required to demonstrate compliance with the statistical performance requirement and within an acceptable confidence level. More details on this subject can be found in statistics reference books. 

---

The formulations for the failure governing stress for most stress systems can be found in Young (1989). Using the variance equation and the parameters for the dimensional variation estimates and applied load, a statistical failure theory can be formulated for a probabilistic analysis of stress rupture. 

K. Lindenberg, K. E. Shuler, V. Seshadri, and B. J. West, Langevin equations with multiplicative noise theory and applications to physical processes, in Probabilistic Analysis and Related Topics, Vol. 3, A. T. Bharucha-Reid (ed.), Academic Press, San Diego, 1983, pp. 81-125. 

The multimedia model present in the 2 FUN tool was developed based on an extensive comparison and evaluation of some of the previously discussed multimedia models, such as CalTOX, Simplebox, XtraFOOD, etc. The multimedia model comprises several environmental modules, i.e. air, fresh water, soil/ground water, several crops and animal (cow and milk). It is used to simulate chemical distribution in the environmental modules, taking into account the manifold links between them. The PBPK models were developed to simulate the body burden of toxic chemicals throughout the entire human lifespan, integrating the evolution of the physiology and anatomy from childhood to advanced age. That model is based on a detailed description of the body anatomy and includes a substantial number of tissue compartments to enable detailed analysis of toxicokinetics for diverse chemicals that induce multiple effects in different target tissues. The key input parameters used in both models were given in the form of probability density function (PDF) to allow for the exhaustive probabilistic analysis and sensitivity analysis in terms of simulation outcomes [71]. 

The key input parameters used in the 2 FUN model were given in the form of probability density function (PDF) to allow the exhaustive probabilistic analysis and sensitivity analysis in terms of simulation outcomes. 

Despite these problems EST databases are a valuable source of large-scale analysis of human variation. They will become even more valuable as the data continue to grow at the present rate. An algorithm for computer-aided SNP mining should contain filters to eliminate the potential sequence errors. Such filters can be based on the probabilistic analysis of sequence features. It can also take into account that multiple occurrences of a variant are more trustworthy, and it may furthermore focus on improving the quality of base-calling if the fluorescent traces are available for closer srcutiny. 

USEPA] US Environmental Protection Agency. 1997. Policy for use of probabilistic analysis in risk assessment guiding principles for Monte Carlo analysis. Washington (DC) ORD, USEPA. 

The major benefit of 2nd-order Monte Carlo analysis is that it allows analysts to propagate their uncertainty about distribution parameters in a probabilistic analysis. An analyst need not specify a precise estimate for an uncertain parameter value simply because one is needed to conduct the simulation. The relative importance of our inability to precisely specify values for constants or distributions for random variables can be determined by examining the spread of distributions in the output. If the spread is too wide to promote effective decision making, then additional research is required. 

To complete the two-photon transition, the two photons must arrive at the absorber within the virtual state lifetime r. For classical uncorrelated photons the probability of accidental overlap increases with photon flux density. Therefore excitation by short, tightly focused laser pulses is needed for the TPA. Probabilistic analysis gives the two-photon transition rate ... 

As HRC is a composite of key flammability parameters, it should be (and is) a good predictor of flame and fire test results [27], For this reason, HRC was selected as the sole explanatory variable for a probabilistic analysis of flammability. 

Table 16.3 contains the MCC results for a commercial transparent polyphenylsulfone polymer and three colors of the polyester carbonate polymer developed in this study based on the three-dimensional flammability criterion. The probabilistic analysis for these polymers using HRC as the sole explanatory variable (Equation 16.4) suggests that the PPSU (clear) has pNB = 0.18 0.14, i.e., an 18% 14% chance of passing the pHRR requirement of 14 CFR 25 while the clear, gray and white grades of the polyester carbonate have a 41%, 29%, and 22% ( 14%) chance of passing 14 CFR 25, respectively. The average... 

Analysis in which distributions are assigned to represent variability or uncertainty in quantities. The form of the output of a probabilistic analysis is likewise a distribution. 

In both cases, an extra compartment is introduced the absorption or the infusion balloon compartment for the extravascular and intravascular route, respectively. To model these disposition processes, we again apply probabilistic analysis for these compartments looking for the probability p(t + At) that a particle is present at time (t + At) in that compartment. Clearly, the necessary events are that the particle is present at time t, associated with the state probability p (t) AND that it remains in the compartment during the interval from t to (t + At), associated with the conditional probability [1 — h,At. Therefore, the probability of the desired joint event may be written as... 

In May 1997, the USEPA issued a policy on the nse of probabilistic techniqnes in characterizing nncertainty and variability. This policy recognizes that probabilistic analysis tools such as Monte Carlo analysis are acceptable, provided that risk assessors present adequate supporting data and credible assumptions (USEPA, 1998). 

Probabilistic analysis Calculations and expression of health risks using multiple-risk descriptors to provide the likelihood of various risk levels. Probabilistic risk results approximate a full range of possible ontcomes and the likelihood of each, which is often presented as a freqnency distribntion graph, thns allowing uncertainty or variability to be expressed quantitatively (USEPA, 1999). 

As implied by the name, distributional risk assessments use the entire data distribution to calculate exposure and risk. As described for the EPA Tier 1 assessment [5], a distributional analysis is not necessarily a probabilistic analysis. The EPA Tier 1 acute dietary assessment produces a dietary exposure distribution using the entire food consultation distribution and point estimates of residue concentration. There is no probability sampling in the Tier 1 assessment. 

It is frequently stated that probabilistic methods require more data than deterministic methods. This is not literally true it is possible to perform probabilistic calculations with input distributions based on small datasets or expert judgement. It is true that distributions derived from small datasets or expert judgement are likely to be very uncertain. However, if these uncertainties can be adequately represented within the probabilistic assessment, or dealt with by making conservative assumptions for the affected inputs, then probabilistic methods should still provide a useful refinement. Even in those cases where the uncertainties are too great to provide reliable estimates of exposure, probabilistic analysis may still be useful as a form of sensitivity analysis to identify priorities for data collection. 

Begimiing in the 1980s, Flamm et al. (1987) and Rulis (1989) documented FDA s exploration of the use of large databases of toxicity data to address very low exposures to components of food contact materials more efficiently. Flamm et al. (1987) performed a probabilistic analysis of carcinogenic potency data in an attempt to discern a dietary level below which no specific toxicity testing data should be considered prerequisite to judge the safety of a compound used in a food contact material. 

US Environmental Protection Agency (1997a) Policy for Use of Probabilistic Analysis in Risk Assessment at tbe US Environmental Protection Agency, May 15. USEPA Document No. EPA/630/R-97/001. Washington, DC USEPA. 

Concern over haphazard and unrecognized transfer of preponderance of evidence or more likely than not standards from the burden of persuasion to the burden of factual proof (burden of production) involves more than idle semantics. The adverse effects of failure to undertake a deliberate, two-step probabilistic analysis include (a) undue preference for particular probabilities of causation found in one epidemiologic study, especially when meta-analysis of multiple studies is not possible or available (b) unrecognized lowering of the burden of production with concomitant stiffening of the burden (standard) of persuasion (c) inappropriate fixation on simplistic quantitative rules such as the >50% likelihood rule and (d) poorly reasoned opinions because courts fail to explain exactly how they apply the >50%, more-likely than-not rule. 

There Is one general conclusion I do feel quite comfortable In drawing. Far too much risk assessment that Is done as slngle-value-best-estlmate analysis should In fact be done as probabilistic analysis. There are undoubtedly several reasons for this. Performing probabilistic analysis can get analytically messy. Obtaining subjective Judgmental estimates of uncertain coefficients can be awkward uid Is subject to a variety of pitfalls. And, idille most people appesu to be quite comfortable with such basic notions of uncertainty as "odds" unless care Is taken, the results of probabilistic analysis can become somewhat difficult to communicate to a semi-technical or non-technical audience. 

---