Probability Flashcards
(34 cards)
What is the forensic science process?
1.Crime scene - evidence collection/submission
2. laboratory analysis - analysis carried out, results of analysis
3. evidence interpretation - interpretation of results/reporting interpretation
4. court - presentation of findings
Detection of marks/traces at crime scene ————> Evidence presentation in court
What impacts does the actions/decision taken at the crime scene have?
- impact on the questions asked of the evidence
- the type of analysis undertaken on ehibits in the laboratory
- the approach taken to make inferences about the results of the analysis
- how those conclusions are presented as intelligence and/or evidence
What is the role of a forensic scientist?
- Crime scne - acquire/collect evidence
- Laboratory analysis - Develop/select appropriate analytical strategies and models and conduct examinations
- Evidence interpretation and court - Meaningful interpretation of results and communication findings in courts
What uncertainty is there in the forensic science process?
Every stage has unknowns and involves human decision making. Unknowns at every stage of forensic science process elad to uncertainty.
Uncertainty is described as:
- Not simply ‘imperfect knoledge’ (Taroni & Biedermann, 2014; Taroni et al., 2010
- Absence of complete determinism (Sense about science, 2013, Walker et al., 2003)
What is the reasoning under uncertainty?
*Probability theory and specifically Bayes, the ‘only coherent and logical foundation’ for reasoning under uncertainty (Berger et al., 2011, p.1)
* Probability is a measure of certainty / uncertainty of an event. It tells you how likely is an event
What is probability theory?
Probability theory is the mathematical study of random phenomena to minimize ambiguity in interpretation.
-> Random phenomenon / process / experiment
What is a random phenomenon?
A random phemonenon is a process or an experiment whose outcome cannot be predicted before the experiment is performed. We do, however, know in advance what outcomes are possible in the experiment.
What’s an example of a random phenomenon?
Consider rolling an unbiased dice:
- Can you guess with absolute certainty what number will appear when we roll this dice?
- No
- Yes - do we know the possible outcomes?
What is outcome?
Outcome - specific result of a random experiment
Dice - could be 5
What is sample space?
Set of all possible outcomes of a random phenomenon, process, experiment.
Dice - 1,2,3,4,5,6
What is event?
A set of possible outcomes (can include >1) of a random experiment. It’s a subset of the sample space of an experiment.
Dice - 2,4,6 (event A- EVEN)
What is probability?
Pobability quantifies possibility.
Many events can’t be predicted with total / absolute certainty ,we can only say how likely are the events to occur using probability theory.
Absolutely certain - 1
Maybe (equal chance) - 0.5
Not possible - 0
Data types
Categorical - qualitative data:
- nominal
- ordinal
Numerical - quantitative data:
- discrete - finite distinct values that can be counted
- continuous - infinite possible values that can be measured but not counted
What is discrete data?
Objective -> frequency
If all outcomes are equally probable:
probability of an event happening = number of ways it can happen / total number of outcomes of the random experiment
Probability example - random phenomenon of the roll of an unbiased dice
A - represents even outcome when an unbiased dice is rolled
P(A) = 3/6
P = 0.5 - equal chance
Probability example - single outcome
A - represents outcome of value >5/=6 when an unbiased dice is rolled
P(A) = 1/6
= 0.17
Nearer to 0 so nearer to not possible
Casework example - A body has been found in a flat - gunshot wound to head. A suspect has been arrested
- foreign fibres recovered from victim’s t-shirt similar to suspects jumper
- sample space = event A (orange) and event B (grey)
For understanding - only physical characteristics (i.e. colour) has been used to characterise the fibres recovered.
Random phenomenon of interest - selection of fibres from recovered victim’s t-shirt
> outcome = a fibre (particular colour)
> possible events
1. fibres from victims t-shirt - orange
2. foreign fibres - not orange (Event A)
How is a Venn diagram used to visualise probability?
Visual representation of logical relationship
(commonalities and differences) between events and their outcomes that aid in calculation of probabilities.
* Typically uses intersecting and non-
intersecting circles/ovals (although other closed figures like squares may be use) to denote relationship
*A large rectangle is used to represent the
sample space and events are represented within this rectangle
For scenarios that involve multiple sequential
or simultaneous repetition of random experiments, each outcome is considered as a set of possible combinations of outcomes of the experiments/phenomena.
Pros - particularly useful in visualisation and probability calculations of sequential events.
Example:
Sample space - A and B
A - recovered fibres foreign to victim’s t-shirt
B -recovered fibres that belong to victim’s t-shirt
How is a Tree diagram used to visualise probability?
Visual representation of probabilities and
outcomes that aid in calculation of probabilities
* 2 main parts - nodes and branches
Nodes: parent and sibling. Parent - event, probability of 1. Sibling - other possible events or outcomes
Branches: probability of occurence of event
at branch end
To calculate probability of a series of events, multiply along branches. Total probability of events = add probabilities along the column.
Pros - particularly useful in visualization and probability calculation of sequential events.
Example :
Origin
- 5/12 A = Grey (outcome - node)
- 7/12 B = Orange (event - node)
How to estimate probability?
Particularly for complex event combinations
* important to visualize event relationships
* a tree diagram or a venn diagram should be used for visualization
What are event types?
Based on event of interest in sample space.
- Target event
- Complement event
Sample space:
1. All other outcomes that don’t agree with event of interest (complement event) P(Ac) or P(A)
2. Outcomes of interest that agree with event of interest (Target event) P(A)
What is the probability solution for the casework - fibres on the victims’s t-shirt?
Mutually exclusive events
Example of this