Bayesian adaptive estimation of arbitrary points on a psychometric function

Bayesian adaptive methods have been extensively used in psychophysics to estimate the point at which performance on a task attains arbitrary percentage levels, although the statistical properties of these estimators have never been assessed. We used simulation techniques to determine the small-sample properties of Bayesian estimators of arbitrary performance points, specifically addressing the issues of bias and precision as a function of the target percentage level. The study covered three major types of psychophysical task (yes-no detection, 2AFC discrimination and 2AFC detection) and explored the entire range of target performance levels allowed for by each task. Other factors included in the study were the form and parameters of the actual psychometric function Psi, the form and parameters of the model function M assumed in the Bayesian method, and the location of Psi within the parameter space. Our results indicate that Bayesian adaptive methods render unbiased estimators of any arbitrary point on psi only when M=Psi, and otherwise they yield bias whose magnitude can be considerable as the target level moves away from the midpoint of the range of Psi. The standard error of the estimator also increases as the target level approaches extreme values whether or not M=Psi. Contrary to widespread belief, neither the performance level at which bias is null nor that at which standard error is minimal can be predicted by the sweat factor. A closed-form expression nevertheless gives a reasonable fit to data describing the dependence of standard error on number of trials and target level, which allows determination of the number of trials that must be administered to obtain estimates with prescribed precision.

Stopping rules in Bayesian adaptive threshold estimation

Threshold estimation with sequential procedures is justifiable on the surmise that the index used in the so-called dynamic stopping rule has diagnostic value for identifying when an accurate estimate has been obtained. The performance of five types of Bayesian sequential procedure was compared here to that of an analogous fixed-length procedure. Indices for use in sequential procedures were: (1) the width of the Bayesian probability interval, (2) the posterior standard deviation, (3) the absolute change, (4) the average change, and (5) the number of sign fluctuations. A simulation study was carried out to evaluate which index renders estimates with less bias and smaller standard error at lower cost (i.e. lower average number of trials to completion), in both yes–no and two-alternative forced-choice (2AFC) tasks. We also considered the effect of the form and parameters of the psychometric function and its similarity with themodel function assumed in the procedure. Our results show that sequential procedures do not outperform fixed-length procedures in yes–no tasks. However, in 2AFC tasks, sequential procedures not based on sign fluctuations all yield minimally better estimates than fixed-length procedures, although most of the improvement occurs with short runs that render undependable estimates and the differences vanish when the procedures run for a number of trials (around 70) that ensures dependability. Thus, none of the indices considered here (some of which are widespread) has the diagnostic value that would justify its use. In addition, difficulties of implementation make sequential procedures unfit as alternatives to fixed-length procedures.

Prevalence of SOS-mediated control of integron integrase expression as an adaptive trait of chromosomal and mobile integrons

BACKGROUND Integrons are found in hundreds of environmental bacterial species, but are mainly known as the agents responsible for the capture and spread of antibiotic-resistance determinants between Gram-negative pathogens. The SOS response is a regulatory network under control of the repressor protein LexA targeted at addressing DNA damage, thus promoting genetic variation in times of stress. We recently reported a direct link between the SOS response and the expression of integron integrases in Vibrio cholerae and a plasmid-borne class 1 mobile integron. SOS regulation enhances cassette swapping and capture in stressful conditions, while freezing the integron in steady environments. We conducted a systematic study of available integron integrase promoter sequences to analyze the extent of this relationship across the Bacteria domain. RESULTS Our results showed that LexA controls the expression of a large fraction of integron integrases by binding to Escherichia coli-like LexA binding sites. In addition, the results provide experimental validation of LexA control of the integrase gene for another Vibrio chromosomal integron and for a multiresistance plasmid harboring two integrons. There was a significant correlation between lack of LexA control and predicted inactivation of integrase genes, even though experimental evidence also indicates that LexA regulation may be lost to enhance expression of integron cassettes. CONCLUSIONS Ancestral-state reconstruction on an integron integrase phylogeny led us to conclude that the ancestral integron was already regulated by LexA. The data also indicated that SOS regulation has been actively preserved in mobile integrons and large chromosomal integrons, suggesting that unregulated integrase activity is selected against. Nonetheless, additional adaptations have probably arisen to cope with unregulated integrase activity. Identifying them may be fundamental in deciphering the uneven distribution of integrons in the Bacteria domain.