Sample Size Calculation for Finding Unseen Species

Estimation of the number of species extant in a geographic region has been discussed in the statistical literature for more than sixty years. The focus of this work is on the use of pilot data to design future studies in this context. A Dirichlet-multinomial probability model for species frequency data is used to obtain a posterior distribution on the number of species and to learn about the distribution of species frequencies. A geometric distribution is proposed as the prior distribution for the number of species. Simulations demonstrate that this prior distribution can handle a wide range of species frequency distributions including the problematic case with many rare species and a few exceptionally abundant species. Monte Carlo methods are used along with the Dirichlet-multinomial model to perform sample size calculations from pilot data, e.g., to determine the number of additional samples required to collect a certain proportion of all the species with a pre-specified coverage probability. Simulations and real data applications are discussed

Towards a Likelihood Ratio Approach for Bloodstain Pattern Analysis

In this work, we explore the application of likelihood ratio as a forensic evidence assessment tool to evaluate the causal mechanism of a bloodstain pattern. It is assumed that there are two competing hypotheses regarding the cause of a bloodstain pattern. The bloodstain patterns are represented as a collection of ellipses with each ellipses characterized by its location, size and orientation. Quantitative measures and features are derived to summarize key aspects of the patterns. A bivariate Gaussian model is chosen to estimate the distribution of features under a given hypothesis and thus approximate the likelihood of a pattern. Published data with 59 impact patterns and 55 gunshot patterns is used to train and evaluate the model. Results demonstrate the feasibility of the likelihood ratio approach for bloodstain pattern analysis. The results also hint at some of the challenges that need to be addressed for future use of the likelihood ratio approach for bloodstain pattern analysis

Quantifying the association between discrete event time series with applications to digital forensics

We consider the problem of quantifying the degree of association between pairs of discrete event time series, with potential applications in forensic and cybersecurity settings. We focus in particular on the case where two associated event series exhibit temporal clustering such that the occurrence of one type of event at a particular time increases the likelihood that an event of the other type will also occur nearby in time. We pursue a non‐parametric approach to the problem and investigate various score functions to quantify association, including characteristics of marked point processes and summary statistics of interevent times. Two techniques are proposed for assessing the significance of the measured degree of association: a population‐based approach to calculating score‐based likelihood ratios when a sample from a relevant population is available, and a resampling approach to computing coincidental match probabilities when only a single pair of event series is available. The methods are applied to simulated data and to two real world data sets consisting of logs of computer activity and achieve accurate results across all data sets

An Evaluation of Soil Test Information in Agricultural Decision Making

The value of soil-test information in planning fertilizer application levels is determined by using agricultural field-plot data to estimate the posterior distribution of mean soil-nitrate concentrations at a given location. Optimal decisions concerning fertilizer application levels are made with respect to this posterior distribution. Average reductions in fertilizer application rates range from 15 to 41 percent, depending on the form of prior information that is available

Perceived strength of forensic scientists’ reporting statements about source conclusions

Three studies investigated lay people’s perceptions of the relative strength of various conclusions that a forensic scientist might present about whether two items (fingerprints, biological samples) have a common source. Lay participants made a series of judgments about which of two conclusions seemed stronger for proving the items had a common source. The data were fitted to Thurstone–Mosteller paired comparison models to obtain rank-ordered lists of the various statements and an indication of the perceived differences among them. The results reveal the perceived strength of several types of statements, relative to one another, including verbal statements regarding strength of support (e.g. ‘extremely strong support for same source’), source probability statements (e.g. ‘highly probable same source’), random match probabilities (e.g. RMP = 1 in 100 000), likelihood ratios, and categorical statements (e.g. ‘identification’). These comparisons in turn provide insight into whether particular statements about the strength of forensic evidence convey the intended meaning and will be interpreted in a manner that is justifiable and appropriate