On behalf of a Fortune 100 company, we created statistical models to determine the probabilities and likely severities of accidents for different employee and accident types. By focusing on the areas and types of accidents, we estimated that the company could save approximately $3 million annually in costs.

Our client, an online seller of software, wanted to maximize the profitability of its television advertising.

We developed a model to determine the profitability of television advertising by station, time of day, and day of week. This model is used to determine how to allocate television advertising dollars. For another client, we analyzed and suggested improvements to a similar model for mail advertising.

Substantial increases in the effectiveness of advertising were obtained in both cases.

A major service company wanted to classify its accounts by value of revenue generation in a certain business situation. Only a few pieces of information were available on each account.

Analysis & Inference was asked if statistical methods could be used to classify the accounts. We applied state-of-the-art methods from statistical and machine learning theory and data mining to the information available.

Assignments were made with substantial accuracy that was demonstrated to be unobtainable by chance, and were validated on data not used to construct the model. The technique resulted in considerable new revenue.

By law, royalties from the retransmission of distant television signals is regulated by a panel of arbitrators at the Library of Congress called the Cable Royalty Tribunal. These royalties are drawn from a pool of funds contributed by local television stations who receive distant signals. The several owners of the major categories of retransmitted programming, when unable to agree on a division of the pot, submit their claims before the arbitrators.

Analysis & Inference has worked on behalf of one of the owners, the Public Broadcasting Corporation. We critiqued surveys presented for the purpose of establishing shares of the different parties. In addition we specified and estimated statistical models that made possible a more objective determination of shares than had otherwise been provided through the expert testimony of economists and survey professionals. In one hearing the analysis showed, and the panel agreed, substantially revised upward the share of their client, and a second time, was believed to be convincing in maintaining their prior level.

How to lower test marketing costs for a direct market publisher. Client used client response modeling where each title was marketed. Of the more than 55 million pieces of direct mail offers over a two-year year period; 10 million were test marketing pieces. The company rolled out only those titles with higher response rates in the test marketing, so about half the potential titles were never published.

An initial testing revealed that the costs of using outside lists in the test marketing phase far exceeded the benefits, and recommended using outside lists only in the "rollout" phase of direct mailings. In the second phase, we combined data from different models in order to improve overall response rate.

The publisher had performed statistical modeling list by list, without correlating the different models. The models we proposed first chose which books to market, then chose the clients, and finally chose the proper advertising vehicle. These selections were done on an individual client basis based on client profiles and the results of logistic regression modeling.

By combining models, while still retaining the list-specific information, we helped the publisher improve the response rate while lowering test marketing costs.

On behalf of a large national grocery chain, developed statistical model to project claim payout rates from historical patterns. The model was based on a statistical procedure called the "Fisher-Lange" method.

In a litigation matter involving a global engineering and construction company and one of the world's largest energy companies, Analysis & Inference was asked to determine the probability of bolts failing along an undersea pipeline, causing leakage of oil or gas.

Using several years of data detailing inspections and breaks found for thousands of bolts along hundreds of joints along the pipeline, Analysis & Inference constructed sophisticated "maximum likelihood" models to determine the probability of failure over the lifetime of the field.

Analysis & Inference was asked to write an expert report setting forth its findings. Dr. William Fairley testified on these findings at the international arbitration proceeding related to the litigation, which is still pending.

For a major pharmaceutical company, we analyzed company and external data to determine the reliability and potential biases in using external data sources. We analyzed physician-specific data for a period of 36 months concerning product marketing to approximately 1 million prescription drug subscribers.

A federal agency stated that a state Blue Cross Blue Shield organization had benefited improperly from their dual role as administrator of federal Medicaid insurance and as a provider of private health insurance.

Retained by the state Blue Cross Blue Shield, Analysis & Inference designed exhaustive sampling and auditing of pertinent files in the insurer's very large databases of claims and insureds to determine the facts.

A senior statistician of Analysis & Inference assisted the insurer's counsel in explaining the sampling methodology at the negotiations. Using these facts, the provider established, to the satisfaction of the federal investigators, that breaches of their duties as administrator did not occur, or occurred in negligible degree and amount.

Developed custom application for global construction company for pricing insurance costs. Distributed application is used by sales staff nationwide and consolidates data for analysis, cost allocation, and premium tracking by corporate insurance group.

The National Science Foundation awarded Analysis & Inference two consecutive grants to find new statistical methods for classifying risks taken on by insurers. Statisticians at the firm conducted research on state-of-the-art statistical analysis, focusing on (Bayesian) "shrinkage" estimation, to determine better ways to form classes of risks and to estimate the probabilities and amounts of claims arising from the classes. The work was recognized in publications of articles in top statistics journals.

General Dynamics owns a shipyard nearly three-quarters of which is located in Quincy, Massachusetts. In 1976 Quincy's Board of Assessors increased the property's assessment by approximately two-thirds. General Dynamics took exception to the board's method of valuation. The resulting litigation came before the Commonwealth's Superior Court. General Dynamics' central position was that the position was that the proper procedure would be to base valuation upon the discounted value of expected net income from the yard, not upon replacement cost less depreciation as the Board of Assessors had done.

In expert testimony, A&I estimated the appropriate rate for discounting the shipyard's future net income. A major factor incorporated in deriving this estimate was the risk of the yard, determined according to accepted principles of contemporary finance theory.

General Dynamics won a $12.4 million abatement on the court's finding that the valuation method proposed by General Dynamics was much more accurate than the one used by Quincy's Board of Assessors. Judge Zobel relied heavily upon Analysis & Inference, as General Dynamic's statistical expert. On appeal, the Commonwealth's Supreme Judicial Court affirmed Judge Zobel's decision.

A European manufacturer of implanted medical devices learned of premature failures of one of its products after implantation.

After consulting with the FDA on the problem, at the manufacturer's request Analysis & Inference undertook an analysis of the then rates of failure, and projected probabilities of failure, of the devices — using models of the data drawn from standard tools of product reliability in industry, and survival analysis in medicine.

The manufacturer was able to answer questions from its distributors and to more accurately assess its legal position.

A nationally recognized engineering firm asked Analysis & Inference to document the underpinnings in the theory of probability that supported an important line of service concerned with brittle fracture of metals, that they provided to large industrial customers. The statisticians at Analysis & Inference who did the work published the research, with permission, in the volume Risk Analysis in the Private Sector

To assess the role of private insurance for nuclear power plants, the Nuclear Regulatory Commission contracted with Analysis & Inference — given its expertise in insurance risk classification and risk analysis — to study an unusual source of risk information along with related aspects of insuring power plants.

Analysis & Inference obtained the rates that insurers charged nuclear power plant operators to insure their operations against catastrophic accidents beyond the limits of the Price-Anderson Act federal insurance provided as a federal subsidy for nuclear power. These rates reflect the private insurance market's assessment of the risk of a nuclear power plant catastrophe. Since to the insurer expected loss is to a first approximation the product of the dollar loss times the probability of that loss, having the premium charged to nuclear power plants and the potential dollar loss enables one to solve this equation for the probability of loss.

Thus a then-novel market-based probability of loss — based on reliability analysis — was obtained. The Report of the study, authored by staff members of Analysis & Inference, was published by the Commission as Design, Costs, and Acceptability of an Electric Utility Self-Insurance Pool for Assuring the Adequacy of Funds for Nuclear Power Plant Decommissioning Expense, NUREG/CR-2370.

The National Highway Traffic Safety Administration (NHTSA) is authorized to require an automobile recall to protect the public against an "unreasonable risk of accident". NHTSA made an initial determination that there was a safety-related defect in the rear axles of some Saturn manufactured by General Motors. GM challenged that finding on the ground first, that the evidence was inconsistent with the finding of a defect; second, there was no "unreasonable" risk existed; and finally, that a recall would subject it to disproportionately large costs given the anticipated benefits.

Analysis & Inference contributed to assessing the statistical evidence of risk.

A shareholder's suit against a major service firm went to mediation. A key factual issue dealt with interpreting the statistical "time series" of the firm's stock prices, and regression analyses undertaken on behalf of the firm that found a break in the series was not traceable to failure to make proper disclosures.

Analysis & Inference identified a critical flaw in the application of statistical methods by the prominent economist who presented his findings at the mediation. The senior statistician at Analysis & Inference who did the work spoke at the mediation regarding the flaw.

Counsel for plaintiffs credited the statistician as an important contributor to the settlement that was reached.

The methodology of "event history analysis" treated in financial economics is often used for the purpose of testing the existence and estimating the amount of a change (a possible "changepoint") in the price of a security. For example, plaintiff shareholders bring a suit against a company whose stock appears to have suddenly dropped, and for which an explanation in terms of management actions is believed causal.

Analysis & Inference has supported the economist applying this kind of methodology in such a case.

In this case our role is to provide expert statistical support to other experts.